/

»*«T OF

V) Q NBS TECHNICAL NOTE 1101

^CAU O*

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Decision Analysis of

rategies for Reducing

Upholstered Furniture

Fire Losses

QC

100

05753

NO. 1101

1979

C.2
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The

Bureau's overall goal is to strengthen and advance the Nation's science and technology and

facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory,

and the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

Agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following, centers:

Absolute Physical Quantities2 — Radiation Research — Thermodynamics and

Molecular Science — Analytical Chemistry — Materials Science. THE NATIONAL ENGINEERING LABORATORY provides technology and technical

services to users in the public and private sectors to address national needs and to solve national problems in the public interest; conducts research in engineering and applied science

in support of objectives in these efforts; builds and maintains competence in the necessary

disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities; provides engineering measurement traceability services; develops test methods and proposes engineering standards and code changes; develops and

proposes new engineering practices; and develops and improves mechanisms to transfer

results of its research to the utlimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering2 — Mechanical ' Engineering and Process Technology2 — Building Technology — Fire Research —

Consumer Product Technology — Field Methods.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal Agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal Agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following divisions:

Systems and Software — Computer Systems Engineering — Information Technology.

'Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

! Some' divisions within the center are located at Boulder, Colorado, 80303.

The National Bureau of Standards was reorganized, effective April 9, 1978.
Mtart BOTM11 of Ste JUL 9 t97<3 Decision Analysis of Strategies for

Reducing Upholstered Furniture Fire Losses

i,„y-^«~ » ^v.--

>< M U

Susan Godby Helzer

Benjamin Buchbinder

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

Fred L. Offensend

Decision Analysis Group

SRI International

333 Ravenswood Avenue

Menlo Park, CA 94025

*^eau o* \U&lwtTU

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued June 1979
National Bureau of Standards Technical Note 1101

Nat. Bur. Stand. (U.S.), Tech. Note 1101, 155 pages (June 1979) CODEN: NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1979

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02078-8 Price $4.75

(Add 25 percent additional for other than U.S. mailing).
PREFACE

This report gives an evaluation of three representative alternatives

for reducing upholstered furniture fire losses. The project, the purpose

of which is to test the utility of decision analysis in evaluating fire

safety policy, has been sponsored by the Center for Fire Research,

National Bureau of Standards. The analysis was performed jointly by the

Program for Information and Hazard Analysis, Center for Fire Research

and the Decision Analysis Group, SRI International.

A preliminary project report was issued in November 1977 [1] . Since that time new data have become available which have been incorporated into the analysis. As this report goes to press more data are becoming available, which we will incorporate into any subsequent

refinements of this analysis. Toward that end, we solicit comments from,

the reader on new data sources as well as criticisms of the methods used.

Numbers in brackets refer to references listed at the end of this

report

.

iii
ABSTRACT

Decision analysis is used to evaluate alternative strategies for reducing residential upholstered

furniture fire losses. Three alternatives are evaluated: no-action, mandatory smoke detector installation, and the proposed upholstered furniture standard

under consideration by the Consumer Product Safety

Commission. Quantitative models are developed to assess fire losses and costs under each alternative.

The alternatives are evaluated on the basis of minimizing the total cost plus loss to society over time.

Subject to the assumptions set forth in the report,

the analysis shows that the detector alternative and

the proposed standard are essentially equivalent and

preferred to the no-action alternative. The proposed

standard is more effective in saving lives, whereas

the detector alternative is less costly to implement.

The sensitivity of the results to key assumptions and

input parameters is tested. The results are shown to

be particularly sensitive to the cost of the proposed

standard, the loss of life value assignment, and the

upholstered furniture replacement pattern.

Key words: Building fires; cost-benefit analysis;

costs; decision analysis; fire losses; furniture;

hazard analysis; probability; residential buildings;

sensitivity analysis; smoke detectors; standards;

upholstered furniture.

IV
SUMMARY

Fire is the second leading cause of accidental death in homes in

the United States. Thousands of Americans, are injured and killed and

billions of dollars of property are lost to fire each year. Reducing

these losses in a cost effective way requires the delicate balancing of

many physical, social and economic factors. This report sets forth a decision analysis approach for accomplishing this balance in establishing

fire safety policy.

The decision analysis method is demonstrated within the context of

the upholstered furniture fire safety problem. Upholstered furniture

fires account for more than 2 5 percent of all U.S. residential fire

fatalities. Three representative intervention strategies are considered.

The first is a policy of taking no formal action at all. The second is

the implementation of federal legislation requiring smoke detectors in

all U.S. residences. The third is the promulgation of the proposed

upholstered furniture standard currently under consideration by the

Consumer Product Safety Commission.

Quantitative models, constructed especially for the upholstered

furniture fire problem, are developed to assess the time varying costs

and losses that occur under each strategy. Historical statistics,

supplemented by expert judgment, are used to develop probability assignments for the fire loss model. Explicit value assignments are used to

convert casualty losses into economic terms. The most attractive strategy

from the standpoint of society is that which minimizes total expected

cost plus loss

.

The analysis shows a gradual reduction in loss under the no-action

alternative, due to the increased voluntary and locally required use of

smoke detectors and a naturally evolving more smolder-resistant furniture

population. The mandatory smoke detector alternative gives a rather

substantial reduction in loss , but at the measurable cost of the required

smoke detectors. The greatest loss reduction occurs under the proposed

standard, but at a greater cost and longer implementation period than

under the other two alternatives.

Table 1 gives a formal comparison of the alternatives. The alternatives are evaluated on a present value basis by discounting future

expected losses and costs for each year considered and then summing.

As shown in the table the present values of the cost plus loss under the

three alternatives are equivalent to within 10 percent. To the extent

that the alternatives are distinguishable, the proposed standard and

smoke detector alternatives are essentially equal and preferred to the

no- action alternative.
Table 1. Comparison of Three Alternatives

Present Value at 8% from 1977 to 2010

(Billions of Dollars)

Alternative Loss Cost Cost Plus Loss

No-Action $6.33

Detector Alternative 5.65

Proposed Standard 4.84

$0.00

0.30

1.12

$6.33

5.95

5.96

The sensitivity of the results to changes in the input parameters

is tested. Table 2 summarizes three key sensitivity studies. The

ranking of alternatives is sensitive to the cost of the proposed standard.

A significantly lower cost makes the proposed standard superior to the

other alternatives; a significantly higher cost makes it the least

attractive alternative. The comparison of alternatives is also somewhat

sensitive to furniture replacement patterns. Changing the time required

to replace existing furniture from 30 years to 15 years makes the proposed

standard about 10 percent more attractive than the next best option.

The effect of changing the value assignment on the amount that society

is willing to spend to save a single human life is also shown in table 2.

Our analysis shows that the proposed standard is preferred for value

assignments above our nominal value, whereas the detector alternative is

preferred for most assignments below the nominal value.

Additional sensitivity analysis shows that except for the studies

presented in table 2 it is difficult to produce a set of reasonable

assumptions under which one alternative is substantially superior to the

other two. Thus, on the basis of the information available for this

analysis, the most attractive of the three alternatives is either the

proposed standard or the smoke detector alternative. Further analysis

shows that a combination of the smoke detector and proposed standard

alternatives is slightly more attractive than either strategy alone,

yielding a cost plus loss about $100 million less than either alternative

separately.

Since some of the parameters upon which this analysis is based are difficult to estimate, the insights gained from this analysis must be

interpreted with the understanding that they are subject to change as new information becomes available on this difficult fire problem.

VI
Table 2. Selected Sensitivity Studies

Present Value of Cost Plus Loss

at 8% from 1977 to 2010

(Billions of Dollars)

Sensitivity

Study

No-Action

Alternative

Smoke Detector

Alternative

Proposed

Standard

First Year Cost of

Proposed Standard

to Manufacturers

$ 50 million

$137 million (nominal)

$300 million

$ 6.3

6.3

6.3

$ 6.0

6.0

6.0

$ 5.2

6.0

7.3

Estimated Time to

Replace Existing

Furniture

15 years

30 years (nominal)

6.3

6.3

5.9

6.0

5.6

6.0

Loss of Life Value

Assignment

$ 100 000 4.0

$ 300 000 (nominal) 6.3

$ 500 000 8.7

$1 000 000 14.5

3.9

6.0

8.0

13.1

4.2

6.0

7.7

12.2

vn
TABLE OF CONTENTS

Page

PREFACE iii

ABSTRACT iv

SUMMARY x V

LIST OF FIGURES xii

LIST OF TABLES xv

PART ONE. RESULTS OF THE DECISION ANALYSIS 1

1. INTRODUCTION . 3

2. METHOD OF APPROACH 5 2.1 Cost Plus Loss Criterion 5 2.2 Loss Assessment 5 2.3 Cost Assessment 7 2.4 Value Assignments 8

2.5 Dynamic Considerations 8

2.6 Sensitivity Analysis 8

3. PRINCIPAL RESULTS 9

3.1 Current Losses 9

3.1.1 Expected Loss Per Reported Fire 9

3.1.2 Value Assignments 9

3.1.3 Annual Number of Ignitions 11

3.1.4 Total Annual Losses Under Current Conditions . . 12

3.2 The No-Action Alternative 13

3.2.1 Losses Under the Fully Implemented No-Action

Alternative 13

3.2.2 Losses Under the No-Action Alternative Over Time 14

3.3 The Smoke Detector Alternative 16

3.3.1 Losses Under the Fully Implemented Smoke Detector

Alternative 16

3.3.2 Effectiveness of Smoke Detectors in Upholstered

Furniture Fires 17

3.3.3 Losses Under the Smoke Detector Alternative Over

Time 18

3.4 The Proposed Standard Alternative 18

3.4.1 Losses Under the Fully Implemented Proposed

Standard Alternative 19

3.4.2 Losses Under the Proposed Standard Alternative

Over Time 20

3.5 Cost of Implementing the Intervention Strategies .... 21

3.5.1 Cost of the No-Action Alternative 21

3.5.2 Cost of the Smoke Detector Alternative ..... 21

3.5.3 Cost of the Proposed Standard Alternative .... 23

3.5.3.1 First-Year Cost of the Proposed Standard . 23

3.5.3.2 Cost of the Proposed Standard Over Time . 23

viii
TABLE OF CONTENTS, continued

Page

3.6 Cost Plus Loss Evaluation of the Three Intervention

Strategies 25

3.6.1 Cost Plus Loss of No-Action Alternative 25

3.6.2 Cost Plus Loss of Smoke Detector Alternative . . 26

3.6.3 Cost Plus Loss of Proposed Standard Alternative . 27

3.6.4 Comparison of the Three Alternatives 27

3.6.5 Reduction in Loss of Life Under the Three

Alternatives 28

3.7 Selected Sensitivity Studies 30

3.7.1 Loss of Life Dollar Assignment 30

3.7.2 Proposed Standard Using the Backcoating Method . 31

3.7.3 Cost of the Proposed Standard Alternative .... 33

3.7.4 Cost of the Smoke Detector Alternative 33

3.7.5 Annual Number of Ignitions and Fatalities .... 35

3.8 Combination of Alternatives 36

PART TWO. DETAILED DERIVATION OF RESULTS 39

4. DEVELOPMENT OF CURRENT LOSSES FROM FIRE LOSS MODEL 41

4.1 Description of Fire Loss Model 41

4.1.1 Model Overview 41

4.1.2 Model Parameters 41

4.2 Probability Assignments for Current Conditions 43

4.2.1 Ignition Source Probabilities 44

4.2.2 Probabilities Leading to Discovery and Fire Type 44

4.2.2.1 Is Someone Home? 45

4.2.2.2 Is a Responsible Person Awake? 51

4.2.2.3 Is There a Functional Smoke Detector? . . 51

4.2.2.4 Is Fire Discovered Before Leaving Chair? . 51

4.2.2.5 Fire Type 5 3 4.2.2.6 Is Fire Reported? 55

4.2.2.7 Calculation of Conditional Probabilities

from Auxiliary Probability Trees 55

4.2.3 Extent of Flame Damage Probabilities 57

4.3 Loss Assignments 60

4.4 Value Assignments 64

4.5 Calculation of Losses Under Current Conditions 66

4.6 Number of All Upholstered Furniture Fires Under Current

Conditions 69

5. DERIVATION OF LOSS RESULTS UNDER THREE ALTERNATIVE

INTERVENTION STRATEGIES 72

5.1 Losses Under the No-Action Alternative 72

5.1.1 Steady-State Losses Under the No-Action

Alternative 72

IX
TABLE OF CONTENTS, continued

Page

5.1.1.1 Revised Functional Smoke Detector

Probability „ 73

5.1.1.2 Revised Ignition Source Probabilities . . 73

5.1.1.3 Revised Fire Type Probabilities 73

5.1.1.4 Revised Probabilities for Extent of Flame

Damage 75

5.1.1.5 Calculation of Steady-State Losses Under

No-Action Alternative 75

5.1.2 No-Action Alternative Losses Over Time 80

5.2 Losses Under the Smoke Detector Alternative 84

5.2.1 Revised Input Probabilities 84

5.2.2 Calculation of Steady-State Losses Under Smoke

Detector Alternative 84

5.2.3 Losses Under the Smoke Detector Alternative Over

Time 86

5.3 Losses Under the Proposed Upholstered Furniture Standard 87

5.3.1 The Barrier Method for Meeting the Proposed

Standard 88

5.3.1.1 Full Compliance 88

5.3.1.2 Partial Compliance 93

5.3.1.3 Losses Over Time 93

5.3.2 The Backcoating Method for Meeting the Proposed

Standard 95

5.3.2.1 Full Compliance 96

5.3.2.2 Partial Compliance 99

5.3.2.3 Losses Over Time 100

6. DERIVATION OF COST RESULTS 103

6.1 No-Action Alternative 103

6.2 Smoke Detector Alternative 103

6.3 Proposed Upholstered Furniture Standard 105

6.3.1 Cost of the Barrier Method 105

6.3.1.1 Initial Cost to Furniture Manufacturers . 105

6.3.1.2 Adjustment for Market Effects 108

6.3.1.3 Cost of the Barrier Method Over Time . . . 108

6.3.2 Backcoating Method for Meeting the Proposed

Standard 110

7. SENSITIVITY ANALYSIS 113

7.1 Sensitivity to Value Assignments and Time Preference . . 113

7.1.1 Value of Life 113

7.1.2 Cost of a Fire Injury 113

7.1.3 Discount Rate 115

7.1.4 Planning Interval 115

7.2 Furniture Population Parameters 115

7.2.1 Furniture Replacement Pattern 115

7.2.2 Smolder Resistance of Currently Produced

Furniture 120

x
TABLE OF CONTENTS, continued

Page

7.3 Parameters Governing the Smoke Detector Alternative . . 120

7.3.1 Smoke Detector Installation Level Under No-Action 120

7.3.2 Smoke Detector Installation Level Under Federal

Mandate 122

7.3.3 Fraction of Operational Smoke Detectors 123

7.3.4 Smoke Detector Purchase Cost 123

7.4 Parameters Affecting the Proposed Standard 125

7.4.1 Manufacturers' Cost of the Proposed Standard . . 125

7.4.2 Market Factor for Assessing Total Societal Cost

of Proposed Standard 127

7.4.3 Compliance Level 127

7.5 Summary of Sensitivity Results 129

ACKNOWLEDGEMENTS 130

REFERENCES 131

APPENDIX 134

xx
LIST OF FIGURES

Figure No. Page

1. Probability Tree 6

2

Annual Aggregate Loss Under Three Alternatives 15

3. Annual Societal Cost of Proposed Standard Using the

Barrier Method 25

4. Annual Cost Plus Loss Under Three Alternatives 26

5. Sensitivity of Results to Dollar Assignment on Loss of Life 31

6. Sensitivity of Results to Manufacturers' Cost of Proposed

Standard Using the Barrier Method 34

7. Sensitivity of Results to Percentage of Smoke Detector Costs

Assigned to Upholstered Furniture Fires 35

8. Sensitivity of Results to Changes in the Total Annual Number

of Residential Upholstered Furniture Fatalities and the

Annual Number of Upholstered Furniture Ignitions in

Residences 36

9. Probability Tree for Assessing Losses Per Upholstered

Furniture Fire 42

10. Schematic of Auxiliary Probability Tree 46

11A. Auxiliary Probability Tree for Cigarette Ignition Source

Under Current Conditions 47

11B. Auxiliary Probability Tree for Open Flame Ignition Source

Under Current Conditions 48

11C. Auxiliary Probability Tree for Electrical Ignition Source

Under Current Conditions 49

11D. Auxiliary Probability Tree for Other Ignition Source

Under Current Conditions - . . . . 50

12. Calculation of Discovery Probability Conditional on Home,

Awake, and Functional Parameters 52

13. Probability Assignments on Fire Type as Function of

Discovery and Ignition Class 54

14. Portion of Auxiliary Tree for Cigarette Ignition Source

Used in Sample Conditional Probability Calculation 56

15. Probability Distributions on Extent of Flame Damage

Conditional on Discovery and Fire Type 57

16. Cumulative Distribution on Aggregate Losses Under Current

Conditions 68

17. Calculation of Revised Fire Type Probabilities Under

No-Action Alternative 76

XII
LIST OF FIGURES, continued

Figure No. Page

18. Cumulative Distribution on Aggregate Losses Under No-Action

Alternative 79

19. Furniture Replacement Rate Curve 81

20. Annual Aggregate Loss Under No-Action Alternative 82

21. Cumulative Distribution on Aggregate Losses Under Smoke

Detector Alternative 85

22. Annual Aggregate Loss Under Smoke Detector Alternative ... 87

23. Cumulative Distribution on Aggregate Losses Under Proposed

Standard Using the Barrier Method 91

24. Annual Aggregate Loss Under Proposed Standard Alternative

Using the Barrier Method 95

25. Annual Aggregate Losses Under Proposed Standard Using the

Backcoating Method and Three Nominal Alternatives 102

26. Sensitivity of Results to Injury Value Assignment 114

27. Sensitivity of Results to Choice of Discount Rate 116

28. Sensitivity of Results to Planning Interval . 117

29. Comparison of Lane-Kocher and Nominal Furniture Replacement

Curves 118

30. Sensitivity of Results to Reduction in Cigarette Ignitions

Under No-Action 121

31. Sensitivity of Results to Smoke Detector Installation Level

Under No-Action 122

32. Sensitivity of Results to Smoke Detector Installation Level

Under Detector Alternative 12 3

33. Sensitivity of Results to Percentage of Properly Operating

Smoke Detectors 124

34. Sensitivity of Results to Manufacturers' Cost of Proposed

Standard Under Two Compliance Methods 126

35. Sensitivity of Results to Percentage of Compliant Furniture

Under Proposed Standard 128

36A. Fire Loss Model Probabilities for Cigarette Ignition Source

for Current Conditions Conditional on the Fire Being Reported

as Calculated from Figure 11A 135

36B. Fire Loss Model Probabilities for Open Flame Ignition Source

for Current Conditions Conditional on the Fire Being Reported

as Calculated from Figure 11B 136

xixi
LIST OF FIGURES, continued

Figure No. Page

36C. Fire Loss Model Probabilities for Electrical Ignition Source

for Current Conditions Conditional on the Fire Being Reported

as Calculated from Figure 11C 137

36D. Fire Loss Model Probabilities for Other Ignition Source

for Current Conditions Conditional on the Fire Being Reported

as Calculated from Figure 11D. . . 138

xiv
LIST OF TABLES

Table No. Page

1. Comparison of Three Alternatives vi

2

.

Selected Sensitivity Studies vii

3. Expected Losses Per Reported Fire Under Current Conditions . 10

4. Development of Annual Number of Upholstered Furniture Fire

Fatalities 11

5. Total Annual Reported Upholstered Furniture Fire Losses

Under Current Conditions 12

6. Total Annual Reported Upholstered Furniture Fire Losses

Under Fully Implemented No-Action Alternative 14

7. Total Annual Reported Upholstered Furniture Fire Losses

Under Fully Implemented Smoke Detector Alternative 17

8. Total Annual Reported Upholstered Furniture Fire Losses

Under Fully Implemented Proposed Standard Alternative With

80 Percent Compliance k 20

9. Cost of Smoke Detector Alternative 22

10. Summary of Manufacturers' Cost of the Proposed Standard . . 24

11. Comparison of Three Alternatives 28

12. Total Number of Fire Fatalities from 1977 thru 2010 Under

Three Alternatives 29

13. Calculation of Upper and Lower Bounds on Expenditure Per

Life Saved Under Two Alternatives to No-Action from 1977

to 2010 29

14. Comparison of Proposed Standard (Backcoating Method) with

Three Nominal Alternatives 33

15

.

Comparison of Combination Alternatives 37

16. Ignition Source Statistics from 2742 Upholstered Furniture

Fires 44

17. Probability Assignments on Ignition Class as Function of

Ignition Source 53

18. Statistics on Extent of Flame Damage for 2742 Upholstered

Furniture Fires 58

19. Loss Statistics for 2742 Upholstered Furniture Fires .... 61

20. Assumptions Used to Condition Expected Fatality Losses on Occupancy, Discovery, and Extent of Flame Damage 63

21. Assumptions Used to Condition Expected Injury Losses on Occupancy, Discovery, and Extent of Flame Damage 64

xv
LIST OF TABLES, continued

Table No. Page

22. Expected Loss Assignments as Function of Occupancy, Discovery

and Extent of Flame Damage 65

23. Dollar Loss Assignments as Function of Occupancy, Discovery

and Extent of Flame Damage 67

24. Probability Distributions on Aggregate Losses Under Current

Conditions 68

25. Reported Upholstered Furniture Fire Losses Under Current

Conditions 69

26. Ignition Source Distribution for All Fires Under Current

Conditions 71

27. Calculation of Revised Ignition Source Probabilities Under

No-Action Alternative 74

28. Calculation of Revised Extent of Flame Damage Probabilities

\ Under No-Action Alternative 77

29. Probability Distributions on Aggregate Losses Under No-Action

Alternative 78

30. Reported Upholstered Furniture Fire Losses Under Fully

Implemented No-Action Alternative 79

31. Total Annual Losses for Currently Installed Furniture

Population Assuming 60 Percent Installation Level of Smoke

Detectors 81

32. Calculation of Total Expected 1980 Losses .... 83

33. Probability Distributions on Aggregate Losses Under Smoke

Detector Alternative 85

34. Reported Upholstered Furniture Fire Losses Under Fully

Implemented Smoke Detector Alternative 86

35. Calculation of Revised Ignition Source Probabilities Under

Proposed Standard (Barrier Method) 89

36. Probability Distributions on Fire Type Under Fully

Implemented Proposed Standard (Barrier Method) with

100 Percent Compliance 90

37. Probability Distributions on Aggregate Losses Under Proposed

Standard Using the Barrier Method with 100 Percent Compliance 91

38. Reported Upholstered Furniture Fire Losses Under Fully

Implemented Proposed Standard (Barrier Method) with

100 Percent Compliance 92

39. Calculation of Total Annual Expected Losses, Number of

Ignitions, and Number of Reported Fires for Proposed Standard

(Barrier Method) with 80 Percent Compliance 94

xvi
LIST OF TABLES, continued

Table No. Page

40. Calculation of Revised Ignition Source Probabilities Under

Proposed Standard (Backcoating Method) 97

41. Probability Distributions on Fire Type Under Fully

Implemented Backcoating Method of Compliance with

Proposed Standard 98

42. Probability Distributions on Extent of Flame Damage for

Current Conditions, No Action, and Fully Implemented

Proposed Standard (Backcoating Method) 98

43. Probability Distributions on Aggregate Losses Under

Proposed Standard Using the Backcoating Method ' 99

44. Reported Upholstered Furniture Fire Losses Under Fully

Implemented Proposed Standard (Backcoating Method) with

100 Percent Compliance 100

45. Calculation of Total Annual Expected Losses, Number of

Ignitions, and Numbers of Reported Fires for Proposed

Standard (Backcoating Method) with 80 Percent Compliance . . 101

46. Annual Cost of Required Smoke Detectors 104

47. Manufacturers' First Year Cost of the Proposed Standard

Using the Barrier Method 106

48. Manufacturers' Annual Cost of Proposed Standard Using the

Barrier Method 109

49. Total Annual Societal Cost of Proposed Standard (Barrier

Method) 110

50. Manufacturers' Annual Cost of Proposed Standard Using the

Backcoating Method Ill

51. Annual Societal Cost of Proposed Standard 112

I 52. Comparison of Nominal Results with Results Obtained Using

Lane-Kocher Furniture Replacement Curve 119

53. Sensitivity of Results to Cost Per Installed Smoke Detector 125

54. Sensitivity of Results to Market Factors 127

xvii

Part One

RESULTS OF THE DECISION ANALYSIS

1 . INTRODUCTION

In 1975 over 300 000 Americans were seriously injured in fires.

Seventy-five hundred persons died. Direct property losses exceeded

$4 billion [2] . Considerable work is being directed toward reducing

these losses including basic research, community master planning,

public education, data collection, hazard analysis, and development and

improvement of product standards, building codes, and fire detection and

supression devices.

This report documents the development and testing of a methodology

for establishing rationally based fire safety policy. Motivation for

the project derives from the fire community's need to focus its limited

resources on loss reduction programs that provide the best balance

between loss reduction and program costs.

The methodology is developed using the discipline of decision

analysis. Decision analysis is used to evaluate complex decision

problems involving uncertainty. It provides a structured approach for

identifying decision alternatives, establishing outcome measures, and

developing the necessary models to evaluate the decision alternatives in

terms of the outcome measures selected. Probabilistic methods are used

to address uncertainty and explicit value judgments are introduced to

facilitate comparison of the alternatives. Decision analysis has been

used to evaluate a wide variety of strategic decision problems in the

public sector including nuclear safety [3] , transportation safety [4]

,

and research and development prioritization [5]

.

The methodology is applied to the upholstered furniture fire

safety problem. Smoldering cigarettes which have been inadvertently

dropped on furniture are a common cause of these fires. More than

one-fourth of all U.S. residential fire deaths result from upholstered

furniture fires [6] . Our analysis focuses on accidental fires in one- and two-family homes and apartments in which upholstered furniture is

the first item to ignite. We consider only fires that are reported to

fire authorities, since those are the fires which are responsible for

most of the loss and for which incidence statistics are available.

There are many possible intervention strategies for reducing

upholstered furniture fire losses, ranging from local public education

efforts to federal product standards. To demonstrate the methodology,

our analysis considers three representative intervention strategies.

The first strategy is a policy of taking no formal action at all. This

strategy provides the baseline against which the other decision alternatives are compared. The second alternative is a federal regulation

requiring the installation of at least one smoke detector in every home.

The third alternative is the proposed upholstered furniture standard

currently under consideration by the Consumer Product Safety Commission

(CPSC) [7] . The proposed standard sets forth criteria for eliminating

combinations of fabric and furniture construction that are vulnerable to

smoldering cigarette ignitions.
In demonstrating the methodology, we use a combination of fire loss

data and expert judgment to estimate the input parameters. Although we

use the best data available to the project team, there are significant

uncertainties and omissions in those data. Since our analysis is directed

toward distinguishing the clearly attractive alternatives from the less

desirable ones, we direct little effort toward refining our estimates of

parameters which do not significantly affect the comparison of the

alternatives . Our assumptions and our estimates of the input parameters

should be so interpreted.

The report is divided into two parts with a total of seven sections.

The first part, Results of the Decision Analysis, is directed at the

reader who is interested in the general methodology and principal

analytical results. Section 1 describes the purpose of the project and

introduces the upholstered furniture fire problem. Section 2 outlines

the basic method of approach. Section 3 summarizes the principal results

of the analysis giving a minimum of detail on their derivation.

The second part of the report, Detailed Derivation of Results,

provides the additional detail necessary to completely document the

input data and the model details, and provides additional results as well. Sections 4 through 6 and the appendix give the detailed derivation

of the losses and costs under the different intervention strategies.

Section 7 presents several sensitivity studies designed to test the

validity of our results to changes in the input assumptions.
2. METHOD OF APPROACH

This section describes the basic approach and analytical tools used

in evaluating the various intervention strategies. Although the models

are elaborated upon in the following sections, this is the only section

that presents an overview of our analytical approach.

2.1 Cost Plus Loss Criterion

The intervention strategies are evaluated from the standpoint of

minimizing total societal cost plus loss. That is, each alternative is

analyzed to determine its total fire-related losses and costs. The most

attractive strategy from the standpoint of society is the one that

minimizes the total cost plus loss.

It is important to note that the cost plus loss criterion does not

account for distributional effects. That is, the measure does not

address the question of who bears the costs and who enjoys the benefits

of a particular intervention strategy. These distributional effects

should ultimately be addressed, however, because the costs of the

alternatives are not always borne in proportion to the benefits received.

Nevertheless, this initial screening of the alternatives is limited to

examining the alternatives from the standpoint of society as a whole.

Use of the cost plus loss criterion necessitates that assessments

be made of the costs and the losses occurring under each alternative.

We first describe our approach for assessing the losses and costs. We

then describe our approach for converting non-monetary losses into

monetary terms and for modeling the performance of the alternatives over

time. The section concludes with a description of our approach for

testing the sensitivity of the results to changes in the input assumptions

2 . 2 Loss Assessment

Figure 1 gives a schematic of the model used to assess upholstered

furniture fire losses. The model is given in the form of a probability

tree. The model parameters are listed across the top of the figure.

Each parameter can take on any one of several values represented by the

branches under that parameter. Probabilities assigned to the branches

represent the likelihood that the parameters will take on the particular

values

.

Each path through the tree represents a different type of upholstered

furniture fire, defined by the values of the parameters making up the

path. Associated with each path are expected losses, representing the

average losses for that type of fire. The probability for each path is

calculated by multiplying the probabilities of the branches making up

the path. Combining the losses associated with each path with the path
IS A IS FIRE RESPON- IS THERE A DISCOVERED EXTENT

IS SIBLE FUNCTIONAL BEFORE OF

IS FIRE IGNITION SOMEONE PERSON SMOKE LEAVING FIRE FLAME REPORTED? SOURCE HOME? AWAKE' DETECTOR? CHAIR' TYPE DAMAGE LOSSES

CIGARETTE

LEGEND

SM - SMOLDERING

SM/FL • SMOLDERING. THEN

FLAMING

FL - DIRECTLY FLAMING

C - CONFINED TO CHAIR

R - BEYOND CHAIR BUT CONFINED TO ROOM

>R - BEYOND ROOM

Figure 1. Probability Tree

6
probability allows us to construct the probability distribution of

average losses resulting from a single reported upholstered furniture

fire. The expected loss per reported fire is calculated by multiplying

each path probability by its associated level of loss and then summing.

The model parameters are initially set to reflect current conditions.

We then adjust the input probabilities to reflect the performance of the

various intervention strategies. The expected losses for each path are kept the same for the various strategies since the type of fire represented

by the path is unchanged. The model is exercised for each intervention

strategy to obtain the average losses per reported fire. These results

are then multiplied by the number of reported fires occurring under the

alternative (determined in a separate calculation) to give the total

annual U.S. losses under each intervention strategy.

The fire loss model serves as a vehicle for distinguishing the

clearly attractive decision alternatives from the less desirable ones. The model is not intended to predict exactly how each of the alternatives

will perform. Parameters are included in the model if they are judged

to be important in comparing the alternatives or in making basic assess- ments of the overall loss. Thus, for example, a parameter for the heat

release rate of the furniture is not included in the model because that

parameter has little direct effect on the comparison of the alternatives.

2.3 Cost Assessment

Several categories of cost must be taken into account in determining

the total societal cost of each intervention strategy. Some of the

costs are market-based and others are non-market related. Obvious

market costs are the added consumer expenditures imposed by the intervention strategy. These include the costs of the smoke detector purchases

and higher prices paid for furniture produced under the proposed standard.

However, in addition to increased consumer expenditures, there are other market costs associated with the higher prices which occur under

the proposed standard. These additional costs are due to the fact that

certain consumers are forced out of the market as the price is increased.

The fact that these consumers are no longer able to enjoy the benefits

of new upholstered furniture constitutes a cost to society. We defer

further discussion of how this cost is calculated until section 6.

Non-market costs are the societal costs not associated with consumer

purchases. Government expenditures for research and development or enforcement are examples of non-market costs. Other costs include the

societal cost of reduced market choice and the cost of less aesthetically

pleasing furniture, should that be an effect of an intervention strategy.

The total cost to society of an intervention strategy is the sum of

all costs incurred under that strategy.
2.4 Value Assignments

Since fire losses are measured in different units, e.g. numbers of

fatalities, numbers of injuries, and dollars of property loss, it is

desirable to transform these measures into common units to permit consistent comparison among alternative strategies. We convert numbers of

fatalities into equivalent dollars for this purpose, based on value

assignments representing the amount society is willing to spend to

prevent a single fire fatality. We multiply the number of injuries by

our estimate of the average cost of an upholstered furniture fire injury.

The nominal value assignments used in our analysis are given in section

3.1.2.

2.5 Dynamic Considerations

Most intervention strategies require a number of years for full

implementation. Thus, in analyzing the alternatives we must evaluate

them over some period of time. Our approach is to evaluate each of the

alternatives over the same time period, 1977 to 2010. We first evaluate

the losses before any of the alternatives are implemented. Then, for

each alternative we evaluate the losses for the year in which the

alternative is fully implemented. Losses for the intervening years are found by interpolation according to the rate at which the alternative is

implemented. Details on this process are given in section 5. For

simplicity we assume a constant U.S. population and we use constant 1977

dollars throughout the analysis. These simplifications should not

significantly affect the comparison of alternatives.

We use a present value method to compare the time varying patterns

of cost and loss under the different alternatives. The future values of

cost plus loss are discounted to the present time at a compound rate and

then summed. The resultant sum is called the present value of the cost

plus loss. The present value is a scalar measure that gives the present

worth of the time stream of cost plus loss.

2.6 Sensitivity Analysis

An important step in our approach is sensitivity analysis. The

alternatives are initially evaluated using nominal values or best

estimates for each of the input parameters. We then reevaluate the

alternatives using different values for the various input parameters.

If a change in the ranking of the alternatives occurs over a reasonable

range of a parameter, then additional effort may be required to refine

the estimate of that parameter. Sensitivity analysis is important in

guiding the model building and data gathering effort because it enables

us to focus our attention on the factors that most critically affect the

evaluation of alternatives

.
3. PRINCIPAL RESULTS

This section gives the principal results of our analysis. The

findings are presented with a minimum of derivation to emphasize the

performance and comparison of alternatives. Details on the assumptions,

data, and methodology are given in part two.

3.1 Current Losses

We first use the fire loss model to calculate upholstered furniture

fire losses under current conditions. This exercise serves to partially

validate the model and also provides a reference for comparing the

performance of the alternatives.

3.1.1 Expected Loss Per Reported Fire

Table 3 gives the expected losses per reported fire as calculated

from the model. We defer until section 4 a presentation of the input

data for calculating current losses. The table shows that, on the

average, 0.0276 persons are killed and 0.159 persons are injured in each

reported upholstered furniture fire under current conditions. The

average property damage is $4,190 per fire, consisting of $3,640 for

tangible property losses and $550 for intangible property losses.

Intangible property losses are defined as other than real property

losses, such as aesthetic damage, disruption of life style, and loss of

family mementos

.

3.1.2 Value Assignments

The various categories of fire loss are expressed in different

units. The multi-dimensionality of these outcomes gives a comprehensive

description of the loss , but makes it difficult to compare alternatives

when there is a mixed ordering of the outcomes. For example, it is not

apparent whether an alternative that results in one death and twenty

serious burn injuries is preferable to one that results in two deaths

and ten serious burn injuries.

To facilitate comparison of the alternatives and to ensure that

they are compared in a consistent manner, we introduce a set of explicit

value judgments. The value judgments assign a dollar equivalent to each

unit of loss. They allow us to convert the several dimensions of loss

into a single monetary equivalent. We recognize that determining a representative set of value assignments for all of society is a difficult

task and that there is much disagreement among different individuals on how these assignments should be made. Ignoring the value judgments,

however, will not obviate the problem, because value judgments are made,

2 Both fire fighter and civilian casualties are included in these figures.
Fatalities 0.0276 $300,000

Injuries 0.159 10,000

Property

Tangible

Intangible

Aggregate

Table 3. Expected Losses Per Reported Fire Under Current Conditions

Expected Loss

Category Number Value Assignment Monetary Equivalent

$ 8,290

1,590

3,640

550

$14,100

Results in part one of this report are given to three significant

figures or the nearest dollar.

Calculations may not check because of rounding.

either implicitly or explicity, every time a choice among public safety

alternatives is made. The value judgments are made explicit in this

analysis to ensure a consistent evaluation of alternatives and to allow

for an explicit examination of how the ranking of the alternatives

depends on the value judgments.

Table 3 gives the nominal value judgments used in this analysis.

We use $300,000 as the amount society is willing to pay to save a single

life, and $10,000 as the cost of an average reported fire injury. The

$300,000 figure is representative of amounts used in several public

safety studies [8,9,10] but it should be pointed out that figures have

been used ranging from $100 000 to $1 million per life saved [11,12,13].

The $10,000 injury figure is the amount cited by the Consumer Product

Safety Commission in their assessment of the possible economic impact of

the proposed standard [14] . We wish to emphasize that the value assignments used here are representative values only, and that the final

decision should be based on a set of assignments deemed appropriate by

the decision maker. Sensitivity studies are presented in subsequent

sections showing how the results change with changes in the value assignments.

The aggregate loss, given in table 3, is the total of the monetary

equivalents of the loss categories. The expected aggregate loss equals

$14,100 per reported upholstered furniture fire. Loss of life is the

major component of the loss, accounting for almost 60 percent of the

total dollars. Tangible property loss is the second most important

component, accounting for more than 25 percent of the total. Injuries

10
represent only about 10 percent of the loss. We emphasize that the

relative contributions of the different loss categories are dependent on

the value assignments for death and injury. Using the nominal value

assignments, table 3 shows that the greatest reduction in upholstered

furniture fire losses would come from those alternatives which are most

effective in reducing the number of fatalities

.

Total annual losses are determined by multiplying the losses for a single reported fire by the annual number of reported upholstered

furniture fires. As this important statistic is not reported directly,

we derive it in the following section.

3.1.3 Annual Number of Ignitions

Clarke and Ottoson [6] have estimated the fraction of fire fatalities

occurring in different categories of fires. Combining their estimates

with the total number of fire fatalities estimated by the U.S. Fire

Administration allows us to estimate the annual number of upholstered

furniture fire fatalitites. These calculations are given in table 4.

Table 4. Development of Annual Number of

Upholstered Furniture Fire Fatalities

Fire Category Annual Number of Fatalities

U.S. total 7500

Residential

0.72 x 7500 = 5400

Residential and furnishings

0.54 x 5400 = 2920

Residential and upholstered furniture

0.50 x 2920 = 1460

One-and two-family homes and apartments

and upholstered furniture

0.90 x 1460 = 1310

According to the U.S. Fire Administration there are currently 7,500

fire fatalities in the United States each year [2] . Multiplying by

0.72, the fraction of fire fatalities occurring in residences, as estimated by Clarke and Ottoson, gives an estimate of 5,400 residential fire

deaths per year. Of these, Clarke and Ottoson estimate that 54 percent

are the result of fires in which household furnishings are the first

item ignited. Furthermore, they estimate that in approximately half of

11
these cases, the first- to-ignite furnishings are pieces of upholstered

furniture. Applying these percentages to the 5,400 residential fatalities

gives 1,460 fatalities from upholstered furniture fires annually. Of

these 1,460 fatalities about 90 percent, or 1310 fatalities, occur in the

occupancy classes considered in this analysis (one- and two-family homes

and apartments)

.

We assume that essentially all fatalities occur in reported fires.

Thus, dividing the 1,310 fatalities by 0.0276, the expected number of

fatalities per reported upholstered furniture fire given in table 3,

gives an estimated 47, 500 reported upholstered furniture fires per year

in one- and two-family homes and apartments under current conditions.

Our estimates of the number of fatalities and the number of reported

fires (1,460 and 47, 500 respectively) are corroborated by recent testimony

before the Consumer Product Safety Commission by the U.S. Fire

Administration. Using their National Fire Incident Reporting System

(NFIRS) data for 1977, they estimate LJ500 residential upholstered

furniture fire fatalities and between 42, 000 and 61, 000 reported

structural upholstered furniture fires in that year [15]

.

3.1.4 Total Annual Losses Under Current Conditions

Table 5 gives the total annual losses from reported upholstered

furniture fires under current conditions. The results are obtained by

multiplying the expected loss figures given in table 3 by 47, 500, our estimate of the annual number of reported upholstered furniture fires.

As shown, the total annual expected losses include L310 fatalities, 7,570

injuries, $173 million in tangible property loss, and $26 million in

intangible property loss. The annual aggregate loss, which is the total

of the monetary equivalents, is $668 million.

Table 5. Total Annual Reported Upholstered Furniture

Fire Losses Under Current Conditions

a Total Annual Expected Losses

Category Number

Fatalities 1310

Injuries 7570

Property

Tangible

Intangible

Aggregate

Monetary Equivalent

(Millions of Dollars)

$394

76

173

26

$668

Calculations may not check because of rounding,

12
3.2 The No-Action Alternative

One possible intervention strategy is to take no action at all.

Even under this strategy, however, the losses will vary over time because

of two important trends. The first is a change in the construction and

composition of upholstered furniture. The second is the increased use

of smoke detectors in residences. Both of these factors will tend to

reduce upholstered furniture fire losses and must be taken into account

if we are to properly model the losses under the no-action alternative.

In assessing the losses under the no-action alternative, we first

define the trend we believe these forces will take. We then model the

losses for a year in which these trends have reached their "steady

state," or when the alternative has been "fully implemented." Finally,

we interpolate, according to the rate at which these trends occur, to

determine the losses for the intervening years. As discussed in

section 2, we assume no growth in the U.S. population. This assumption

should not significantly affect the relative comparison of alternatives.

All of the results are given in 1977 dollars.

3.2.1 Losses Under the Fully Implemented No-Action Alternative

An important trend in the upholstered furniture industry is the

replacement of cellulosic materials by thermoplastic fibers and urethane

foam cushioning materials. This trend is important because thermoplastic

upholstery materials tend to be more resistant to smoldering ignition.

However, once ignited, synthetic materials tend to result in larger

fires. For the purpose of this analysis, we assume that furniture

manufacturers will continue to use man-made materials at current usage

levels. Thus the furniture population will evolve toward a mix of

furniture with the same flammability characteristics as current furniture

production. Details on the fire characteristics of the currently produced

furniture population are given in section 5.1.

A second phenomenon affecting upholstered furniture fire losses is

the increased use of residential smoke detectors. The four model building

codes in use throughout most of the United States now require that at

least one smoke detector be installed in all new residential construction.

Current retail sales of smoke detectors are also growing rapidly. We assume that eventually 60 percent of the households in the United States

will have at least one smoke detector. However, the presence of a smoke

detector does not guarantee that it will function properly. In addition

to reliability problems, there are problems of lack of maintenance, such

as battery replacement, as well as actual misuse. In this analysis we

assume that at any point in time, 80 percent of the installed smoke

detectors will be operating properly. Thus, for the no- action alternative

we assume that eventually 48 percent (0.60 x 0.80) of U.S. households

will have one or more functional smoke detectors. (The sensitivity of our results to the assumptions concerning the installation level and

functional percentage is examined in section 7.3.)

13
Section 5.1 details how the fire loss model is adjusted to reflect

the new furniture population and the increased use of smoke detectors.

The resultant losses for the fully implemented no-action alternative are given in table 6. The table shows that total expected U.S. losses under

the no-action alternative are estimated to be $486 million per year for

a future year when the furniture population has been completely replaced

with furniture of the type currently produced and when the smoke detector

installation has leveled off at 60 percent. The aggregate loss is the

total of the monetary equivalent of 878 fatalities and 4,900 injuries, as well as $149 million in tangible property loss and $24 million in intangible property loss. Again, the monetary value assigned to loss of life

accounts for the majority of the aggregate loss (54 percent) . Tangible

property loss is again the second most significant contributor, at

31 percent.

Table 6. Total Annual Reported Upholstered Furniture Fire Losses

Under Fully Implemented No-Action Alternative

Category

Total Annual Expected Losses

Number

Monetary Equivalent

(Millions of Dollars)

Fatalities

Injuries

Property

Tangible

Intangible

Aggregate

878

4900

$263

49

149

24

$486

Calculations may not check because of rounding.

The total expected loss of $486 million under the fully implemented

no-action alternative compares with $668 million under current conditions

As detailed in section 5.1, the 27 percent loss reduction is primarily

the result of the increased use of smoke detectors. A small part of the

loss reduction is the result of the changes in the furniture population.

3.2.2 Losses Under the No-Action Alternative Over Time

The losses just calculated are for the case of the fully implemented

no-action alternative. However, since it will take a number of years

for the no-action alternative to become fully implemented, we must model

the losses for the intervening years. Section 5.1.2 details how the losses

14
are modeled over time. Our furniture replacement model predicts that it

will take 30 years, or until 2005, to replace virtually all of the current

furniture population with post-1975 furniture. For simplicity, we also

assume that the smoke detector installation will reach its saturation

level of 60 percent by 1980. The 1980 losses are determined in a separate

calculation. Losses for the remaining years are found by interpolation

based on the rates of smoke detector installation and furniture replacement.

Figure 2 shows the aggregate losses over time for the no-action

alternative from 1975 to 2010, the time frame of our loss analysis.

(The aggregate losses for the smoke detector alternative and the proposed

standard alternative, detailed in sections 3.3 and 3.4, are also shown

in the figure.) The current aggregate losses of $668 million per year

decline under the no-action alternative to $492 million per year by

1980. This decline is primarily due to the increased level of functioning

smoke detectors. The aggregate losses eventually level off at the $486

million annually cited in the previous section.

700

1— _eoo

-a 600

**_o

<A 500

1

00

00 400

o—J

LU1—

< 300

csLU

cc 200

100

NO ACTION

DETECTORS

PROPOSED STANDARD

1S75 1980 1985 1990 1995 2000 2005 2010

YEAR

Figure 2. Annual Aggregate Loss Under Three Alternatives

15
3 . 3 The Smoke Detector Alternative

A second alternative for reducing upholstered furniture fire losses

is to require the use of residential smoke detectors. Detectors are effective in providing early warning of fire. Thus, requiring their use

in residences should increase the number of upholstered furniture fires

that are discovered and contained while they are small and increase the

time available for escape. Several intervention strategies are possible

involving smoke detectors. However, to provide a reference on the

general effectiveness of smoke detectors, we consider an alternative

under which all U.S. residences are required to install at least one

smoke detector. We are not aware . of such a strategy being given active

consideration at this time, but the alternative, as defined for this

analysis, does provide a basis for comparing smoke detectors with other

intervention strategies

Our smoke detector alternative is directed toward requiring smoke

detectors in all residences that do not currently have detectors.

However, several communities already require detectors in existing

dwelling units. For example at this writing, Montgomery County, Maryland;

Minneapolis, Minnesota; San Carlos, California,- and Farmer's Branch,

Texas have legislated requirements for the installation of a smoke

detector in all homes. Many other communities such as Chicago, Illinois,

and Prince George's County, Maryland, are requiring smoke detectors in

most multifamily dwellings. Still other communities, although not

requiring detectors by law, have innovative plans for attaining high

installation levels. For example, Rock Island, Illinois, is purchasing

a smoke detector for each home to be installed by the local fire department. As noted earlier, smoke detectors are now required in the model

building codes for new construction. Thus, requiring smoke detectors in

all U.S. residences is a useful alternative for analysis.

3.3.1 Losses Under the Fully Implemented Smoke Detector Alternative

We assume that 90 percent of all U.S. homes will have smoke detectors

under the fully implemented smoke detector alternative. As before, we

assume that at any point in time 80 percent of the installed detectors

will be working. Thus, under the fully implemented smoke detector

alternative, we assume that 72 percent (0.9 x 0.8) of U.S. households

will have a functional smoke detector. Also, as under the no-action

alternative, we assume that the currently installed furniture population

will be replaced with a population that has the same burning characteristics as the currently produced furniture.

The fire loss model is used to determine the losses under the fully

implemented smoke detector alternative. The model parameters are adjusted

to reflect the added smoke detectors and changed furniture population and

the new numbers of ignitions and reported fire are computed. The expected

annual losses from reported fires determined in this way are given in

table 7.

16
Table 7. Total Annual Reported Upholstered Furniture Fire Losses

Under Fully Implemented Smoke Detector Alternative

Total Annual Expected Losses

Monetary Equivalent

Category Number (Millions of Dollars)

Fatalities 678 $203

Injuries 3960 40

Property

Tangible 131

Intangible 21

Aggregate $396

Calculations may not check because of rounding.

The table shows that the total annual upholstered furniture loss

under the fully implemented smoke detector alternative is $396 million.

This compares with a current loss of $668 million per year and an annual

loss of $486 million under the fully implemented no- action alternative.

There are 678 fatalities and 3,960 injuries expected annually as well as $131 million in tangible property loss and $21 million in intangible

property loss. Once again, the dollar contribution of loss of life

accounts for more than half of the aggregate total.

Whereas both the smoke detector and no-action alternatives offer

significant long range loss reductions relative to current levels of

loss, we note that the difference in loss between the two fully implemented alternatives is relatively small, $90 million. The reason is

that a significant smoke detector installation level is assumed under

the no- action alternative. The detector alternative addresses only the

marginal detector installation beyond the no- action level, increasing

the installation level of smoke detectors from 60 percent to 90 percent,

thus resulting in an increase from 48 to 72 percent in the level of

functional detectors.

3.3.2 Effectiveness of Smoke Detectors in Upholstered

Furniture Fires

For use in later calculations, we also determine the maximum

effectiveness of smoke detectors in reducing personal and property loss.

The maximum effectiveness is determined by exercising the model twice:

with the probability of a functional smoke detector first set at 0.0 and

then set at 1.0. The difference in the two cases is 65 percent, 59

percent, and 45 percent reductions in deaths, injuries, and property

17
loss, respectively. These differences provide upper bounds on the

effectiveness of smoke detectors in reducing upholstered furniture fire

losses, since they compare zero percent reliability of the detectors with

100 percent reliability. These results are used in section 6.2 to allow

us to assign only a portion of the smoke detector cost to reducing

upholstered furniture fire losses. These results are also useful as an indication of the validity of the model, since they agree well with

predictions for upholstered furniture fire loss reductions made by

experts in fire detection [16]

3.3.3 Losses Under the Smoke Detector Alternative Over Time

We assume that the smoke detector alternative will take effect in

1980, and that the 90 percent installation rate will be reached by 1985.

Thus losses from 1975 through 1980 are identical to the losses under the

no-action alternative. As in the case of the no- action alternative, the

smoke detector alternative is not "fully implemented" until the year 2005

when the current furniture population is replaced with post- 197 5 furniture,

Losses for the years from 1980 until full implementation is achieved in

2005 are found by interpolation according to the rates at which the

furniture population is replaced and the smoke detectors are installed.

The losses for the years after 2005 are constant since it is assumed that

the furniture population and detector installation have reached their

steady state.

Figure 2 shows the aggregate losses over time for the smoke detector

alternative from 1975 to 2010. The current aggregate losses of $668

million per year eventually decline to $396 million annually. Almost all

of this decrease occurs by 1985 when the projected level of smoke detector

installation is reached. The continuing slight decline in losses between

1985 and 2005 is attributable to the continuing replacement of furniture.

3 . 4 The Proposed Standard Alternative

A third alternative considered for reducing upholstered furniture

fire losses is the proposed upholstered furniture standard currently

under consideration by the Consumer Product Safety Commission. The

proposed standard is intended to reduce smoldering ignitions in upholstered furniture, primarily those caused by cigarettes. Combinations of

upholstery and furniture construction that can be ignited by cigarettes

would not be permitted under the proposed standard.

Under the proposed standard, upholstery fabrics would be separated,

according to a stipulated flammability test, into four classes: A, B, C

and D. Class A fabrics are those that are most resistant to cigarette

ignition, and Class D fabrics are those that are least resistant. Some

reasonably simple modifications in the furniture construction, many of

which are now being implemented by the manufacturers voluntarily, would

18
allow most furniture to meet the proposed standard with Class A, B, or C

fabrics. These modifications include substituting vinyl welt cord for

braided cellulose and twisted paper welt cord, treating cotton batting

with boric acid, producing more smolder-resistant decking systems, and

using various wrappings on cushions. These techniques, however, will not

enable most constructions to comply with the proposed standard with the

majority of Class D fabrics.

Class D fabrics, which account for about 40 percent of the upholstery

fabrics now in use [17] , are primarily heavyweight cellulosic fabrics

such as jacquards and velvets. If the proposed standard is enacted, some manufacturers might cease using Class D fabrics, switching instead to

currently produced Class A, B, or C fabrics. Other manufacturers might

choose to add a needle punched aluminum foil barrier system to the arms,

backs, and cushions of the furniture. Such a system has been shown to be

effective at drawing heat away from the smoldering source, thereby reducing

the likelihood of a smoldering ignition. Some Class D fabrics could be

upgraded to Class A, B, or C by blending synthetic materials with the

cellulosic fibers. Another as yet unproven technique is to apply a microencapsulated sulfur backcoating to the Class D fabric, thereby

making it a Class A or B fabric. Other smolder inhibitors might also be

used in this manner.

3.4.1 Losses Under the Fully Implemented Proposed Standard Alternative

For the purpose of this analysis we assume that the foil barrier

method or a similar construction method will be used to make Class D

fabrics comply with the proposed standard. Because of such factors as poor quality control in the manufacturing process, loss of ignition

resistance due to soil and wear, use of slipcovers and noncompliant

reupholstering, we assume that only 80 percent of the furniture population

manufactured under the proposed standard will be in compliance. We also

assume, as in the no-action case, that 60 percent of U.S. households will

eventually have a smoke detector, of which 80 percent will be working at

any one time. Details for modeling these assumptions are given in section

5.3. The resultant losses are given in table 8.

Table 8 shows that the total annual upholstered furniture loss under

the fully implemented proposed standard is $157 million per year. There

are 259 fatalities and 1,560 injuries annually as well as $55 million in

tangible property loss and $9 million in intangible property loss. Once

again, the principal loss component is loss of life, accounting for half

of the total. The total annual loss under the proposed standard of $157

million is less than one-fourth of the $668 million current loss, less

than one-third of the $486 million loss under the fully implemented no- action alternative, and less than one-half of the $396 million loss under

the fully implemented detector alternative.

19
Table 8. Total Annual- Reported Upholstered Furniture Fire Losses

Under Fully Implemented Proposed Standard Alternative

with 80 Percent Compliance

Total Annual Expected Losses

Monetary Equivalent

Category Number (Millions of Dollars)

Fatalities 259 $ 78

Injuries 1560 16

Property

Tangible 55

Intangible 9

Aggregate $157

Calculations may not check because of rounding.

As shown in section 5.3, the losses under the fully implemented

proposed standard can be partitioned into those losses which are attributable to furniture that is compliant with the proposed standard and

those attributable to furniture that is not compliant. We find that $97

million or 62 percent of the total U.S. loss is due to the noncompliant

portion of the population. Furthermore, 176 of the 2 59 total expected

fatalities, or 68 percent, are from fires involving the 20 percent

noncompliant furniture. Thus it appears that the compliance rate may

significantly affect the overall effectiveness of the proposed standard.

A sensitivity study on the compliance level is presented in section

7.3.4.

3.4.2 Losses Under the Proposed Standard Alternative Over Time

In modeling the losses under the proposed standard over time, we assume that the standard takes effect in 1980. As for the no- action

alternative, we assume that 60 percent of all residences will have

purchased smoke detectors by 1980. Thus, the losses from 1975 to 1980 are the same as for the no-action case. Our furniture replacement model

predicts that it will take 30 years, from 1980 until 2010, to replace

virtually all existing furniture with furniture manufactured under the

proposed standard. The losses between 1980 and 2010 are found by interpolation, taking the appropriate weighted average of furniture that is

compliant and noncompliant with the proposed standard.

The annual aggregate losses expected under the proposed standard

alternative are shown in figure 2. The losses decline prior to 1980

because of the increased level of smoke detector installation and are

20
identical to the no-action alternative losses. After 1980, the

losses decrease as more and more furniture becomes compliant with

the proposed standard, eventually reaching the level of $157 million

annually

.

Figure 2 shows that the proposed standard alternative is the most

effective alternative for reducing fire losses. The detector alternative

is the next most effective at loss reduction. However, both of these

alternatives have measurable costs associated with the loss reduction.

We address these costs in the following sections.

3.5 Cost of Implementing the Intervention Strategies

This section summarizes our cost estimates for implementing the

various alternatives.

3.5.1 Cost of the No-Action Alternative

We assume that no costs are incurred under the no- action alternative.

Although smoke detectors are purchased under this alternative, these

purchases do not result from any action taken under this alternative.

Therefore, we do not include the currently projected detector purchases

as a cost. The zero cost of the no- action alternative provides a baseline for measuring the costs of the other alternatives.

3.5.2 Cost of the Smoke Detector Alternative

We assume that the effect of the smoke detector alternative is to

increase the installation level of smoke detectors from 60 to 90 percent.

Column 1 of table 9 gives the total consumer expenditures associated

with this increase in installation level. The total costs are based on

an average installed cost of $22 per detector and an average operating

cost of $1.80 per detector per year. We also assume a 10 percent annual

replacement rate. As discussed previously, we assume that the installation requirement will become effective in 1980 and that the 90 percent

installation level will be reached by 1985. Since we have assumed a constant U.S. population, we also assume that the number of U.S. households requiring detectors remains constant. Thus for the years 1985 and

beyond, only operating and replacement costs are required, as shown in

column 1.

3 Most of the detectors are assumed to be battery-operated with no associated installation cost.

21
Table 9. Cost of Smoke Detector Alternative

Annual Cost

(Millions of Dollars)

1975-9 $ 0.0

1980 102.8

1981 120.1

1982 137.3

1983 154.6

1984 171.9

1985 & beyond 86.4

Amount Allocated to Smoke Detector

Upholstered Alternative

All Required Furniture Fires Total

Year Smoke Detectors (29% of col. 1) (Col. 2 plus $1 million)

$ 0.0 $ 0.0

29.8 30.8

34.8 35.8

39.8 40.8

44.8 45.8

49.9 50.9

25.1 26.1

All costs, as well as losses, in this report are given in 1977 dollars.

The costs in column 1 of table 9 are the total direct consumer

expenditures associated with increasing the smoke detector installation

level from 60 percent to 90 percent. However, it is not appropriate

to assign all of these costs to the smoke detector alternative because

the benefits of the detectors also apply to fires other than upholstered

furniture fires. As discussed in section 6.2, we assign 29 percent of

the total detector costs to the upholstered furniture fire scenario

based on the fraction of lives smoke detectors could save in upholstered

furniture fires compared to all residential fires. The consumer expenditures allocated to the smoke detector alternative are given in column 2 of table 9.

Finally, implementation of the smoke detector alternative would

result in costs to the government for enforcement and education. We

include $1 million annually to reflect the portion of this cost attributable to upholstered furniture fires. The total annual cost of the

4

An alternative and more comprehensive approach would be to compare the

total costs of the required smoke detectors with the total benefits

derived from their use, whether they occur in upholstered furniture

fires or other types of fires. However, modeling the benefits of smoke

detectors in other residential fires would require a considerably larger

analytical effort than this project permits. Therefore we choose the

simpler approach of only modeling the costs and benefits associated with

upholstered furniture fires.

22
smoke detector alternative, obtained by adding $1 million to the upholstered furniture allocation, is shown in column 3 of table 9.

3.5.3 Cost of the Proposed Standard Alternative

The costing of the proposed standard alternative involves a number

of detailed assumptions and calculations. This section summarizes the

results of these computations. The reader is referred to section 6.3

for a detailed derivation of the cost estimates.

3.5.3.1 First-Year Cost of the Proposed Standard

For our initial analysis of the proposed standard alternative we assume that the standard will be met by the barrier method discussed

earlier. As detailed in section 6.3, we estimate that about 38 million

linear yards of Class D fabric would be underlaid with a foil barrier.

Labor, material, and inventory for applying the barrier would total

$103.7 million. We assign an additional $11.6 million for the necessary

treating of the cotton batting. Testing, record-keeping, and research

and development costs total an additional $21.3 million. Thus, we estimate the total first-year costs to the furniture manufacturer to be

$136.6 million. This represents an average cost of $6.83 per piece when

averaged over the total furniture production.

In a separate paper, C. Muehlhause [18] has calculated that due to

commissions and other markup effects, the first-year manufacturing costs

should be multiplied by a "market factor" of 1.5 to obtain the total

cost to society. Thus, the total first-year cost of the proposed

standard is $136.6 million x 1.5 + $1 million = $206 million, where $1

million is added to reflect enforcement costs. Although it is possible

that the aluminum foil barrier may affect the aesthetic quality of the

furniture, we assume that the barrier will be sufficiently well designed

to overcome any aesthetic problems. Therefore, aesthetics costs are not

included in this estimate.

3.5.3.2 Cost of the Proposed Standard Over Time

As discussed in section 6.3, we expect that the manufacturers' cost

of the proposed standard will decline over time. This decline is

anticipated because each Class D fabric must be separately tested with

each construction, and because an additional step is required in the

fabrication process when Class D fabrics are used. Many manufacturers

are expected to avoid this additional effort by substituting fabrics of

a higher class for Class D fabrics. We estimate that the usage. of Class

D fabrics will decline from 40 percent in 1980 to 20 percent in 1985.

There will be a corresponding reduction in the cost of applying the

barrier. We also assume that research and development will reduce the

23
cost of the barrier material by 50 percent within 5 years, and we eliminate the research and development costs after 1985. Although we project a decline in the use of Class D fabrics, we assume that many of

these fabrics will be replaced by similar fabrics of a higher class so that there would be no perceptible loss of market choice. Table 10

summarizes the initial and long-range costs of the proposed standard to

the furniture manufacturer.

Table 10. Summary of Manufacturers' Cost of the Proposed Standard

Annual Cost

(Millions of Dollars)

Component Initial Long Range

Barrier Installation

Material $ 39.9 $10.0

Labor and Handling 63.8 31.9

Cotton Batting Treatment 11.6 11.6

Testing and Recordkeeping 20.3 12.4

Research and Development 1.0 0.0

Total $136.6 $65.9

We assume that the proposed standard takes effect in 1980 and that

the cost reductions discussed above have occurred by 1985. The manu- facturers ' costs for 1981-1984 are found by linear interpolation. The

manufacturers' cost for all years after 1985 are set equal to the 1985

costs

The total annual societal cost of the proposed standard alternative

using the barrier method is given in figure 3. As with the first year,

the manufacturers' cost is multiplied by the market factor and then $1.0

million is added for the cost of enforcement. The market factor is

assumed to be 1.5 for the first five years, and then, due to long term

competitive adjustments in the upholstered furniture market, to decline

linearly over the next 10 years to a constant level of 1.2.

24
Figure 3. Annual Societal Cost of Proposed Standard

Using the Barrier Method

3.6 Cost Plus Loss Evaluation of the Three Intervention Strategies

The cost and loss results of the previous sections are combined in

this section to give the cost plus loss of each intervention strategy.

The costs and losses are summed by year for each alternative and the

results are given in figure 4. The cost plus loss criterion serves to

identify the most attractive intervention strategy from the standpoint

of society as a whole. Although distributional effects are not addressed

by this criterion, as discussed in section 2, the cost plus loss criterion

distinguishes the clearly promising alternatives from the less attractive

alternatives

.

3.6.1 Cost Plus Loss of No-Action Alternative

The cost plus loss of the no-action alternative is equal to the

total loss incurred under that alternative, because we define our accounting basis so that no costs are incurred under that alternative. Thus,

the cost plus loss declines from $668 million in 1975 to $492 million in

1980 and eventually levels off at $486 million per year after 2005. The

25
800

CO

re 700

o

-a

**—o

CO 600

C

o

E 500

CO

09O—

400

CO3—

1— 300

CO

o

o

NO ACTION

DETECTORS

PROPOSED STANDARD

200

100

1975 1980 1985 1990 1995 2000 2005 2010

YEAR

Figure 4. Annual Cost Plus Loss Under Three Alternatives

primary reason for the decline during the period 1975-1980 is the

increased use of smoke detectors. After this period, when smoke detectors

have reached their peak installation level, there is a slight decline in

cost plus loss due to the changing (more smolder- resistant) furniture

population.

3.6.2 Cost Plus Loss of Smoke Detector Alternative

The smoke detector alternative is assumed to take effect in 1980.

Thus, prior to 1980 the cost plus loss is the same as for the no-action

alternative. The cost plus loss curve for the detector alternative, as shown in figure 4, has a discontinuity in 1980, the first year that

costs are incurred. Between 1980 and 1985 the increased cost is offset

by the reduction in total losses, as evidenced by the "detector" curve

crossing the "no-action" curve. After 1985 the two curves are essentially

parallel with the smoke detector curve about $60 million below the "noaction" curve. The total cost plus loss to society under the smoke

detector alternative eventually levels off at $422 million annually.

26
3.6.3 Cost Plus Loss of Proposed Standard Alternative

The proposed standard is also assumed to take effect in 1980. The

cost plus loss under the proposed standard is coincident with the no- action alternative prior to 1980. There is a rather large increase in

cost plus loss in 1980 because the large cost of implementing the standard

is not offset by a significant loss reduction in that year. However,

due to the decreasing cost of the standard and its increasing effectiveness

as existing furniture is replaced by compliant furniture, loss reduction

begins to exceed the cost of the standard by about 1985, and the "proposed

standard" curve crosses the "no-action" curve. The total annual cost

plus loss under the proposed standard alternative continues to decline--

crossing the "detector" curve near 1988 and eventually leveling off at

$235 million annually.

3.6.4 Comparison of the Three Alternatives

Figure 4 shows that in the long run the proposed standard is the

most attractive strategy for reducing total societal cost plus loss.

However, in the early years the proposed standard is the least attractive

alternative because the cost exceeds the initial loss reduction. The

selection of the most attractive alternative therefore depends on the

issue of time preference—how much society is willing to pay today to

partake of benefits tomorrow.

Time preference is a difficult social issue involving a value

judgment on how much one generation should sacrifice to benefit succeeding

generations. There is a vast literature on the issue of time preference

[19,20] , and although there is not a consensus on how the problem should

be treated, many analyses have used discounting techniques to address

time related trade-offs.

Using a discounting approach, a time stream of the various costs

and losses is developed. Each of the future values of cost and loss is

then discounted to the present time at a compound rate reflecting the

decision maker's time preference. The resulting discounted values are summed and the sum is called the present value. The present value is a single number that summarizes the present worth of the particular time

stream. By comparing the present values of different time streams, the

time streams can be compared in a consistent manner. Discounting has

long been used in business to compare different investment plans.

Table 11 gives the present value of the cost plus loss of the three

alternatives discounted at an 8 percent real rate. We feel that this rate

represents a reasonable opportunity cost for consumer related expenditures.

The present values shown in the table are calculated over the period

1977-2010. The table shows that the present values of cost plus loss for

the detector alternative and the proposed standard are essentially equal

at approximately $6.0 billion. Both alternatives are preferred to the

27
no-action alternative on the basis of a total present value of cost plus

loss. The present value of the cost plus loss under the no- action

alternative is approximately $6.3 billion.

Table 11. Comparison of Three Alternatives

Present Value at 8% from 1977 to 2010

(Millions of Dollars)

Alternative Loss Cost Cost Plus Loss

No-Action $6330

Detector

Alternative 5650

Proposed Standard

(Barrier Method) 4840

$

300

1120

$6330

5950

5960

Although the proposed standard and detector alternatives result in

approximately the same present cost plus loss, they achieve that result

in different ways . The proposed standard achieves much greater loss

reduction, but it also costs significantly more to implement. Relative

to the no-action alternative, the proposed standard gives a loss reduction

in present value terms of $6.3 - $4.8 = $1.5 billion at a cost of $1.1

billion. The smoke detector alternative gives a loss reduction of $0.7

billion at a cost of $0.3 billion. The ratio of benefits to costs is

1.3 for the proposed standard and 2.2 for the detector alternative.

Thus, although the proposed standard gives a greater total loss reduction,

the reduction is achieved at a rate which is less efficient than the

rate under the detector alternative.

3.6.5 Reduction in Loss of Life Under the Three Alternatives

Table 12 gives the total expected number of upholstered furniture

fire fatalities under each of the three alternatives, as calculated from

the fire loss model. The numbers of fatalities are accumulated over the

period 1977 to 2010 without discounting. Relative to the no-action

case, the table shows that the smoke detector alternative saves 5,500

lives over this period while the proposed standard saves 12,900 lives.

Many analyses have evaluated public safety programs on the basis of

dollars spent per life saved. This is a meaningful measure if the

various expenditures and fatality reductions occur in the same period of

time. However, as discussed earlier, the costs and benefits of the

different upholstered furniture fire intervention strategies occur at

different points in time; therefore, it is not methodologically sound to

compare the total number of lives saved with the total program costs.

28
(One can calculate the present value of the program costs, and discount

the value assigned to lives saved, but it is not meaningful to discount

fatalities.) Nevertheless, as shown in table 13, it is possible to

derive upper and lower bounds for dollars spent per life saved.

Table 12. Total Number of Fire Fatalities from 1977 thru 2010

Under Three Alternatives

Alternative

Lives Saved Relative

Number of Fatalities to No-Action

No-Action

Detector Alternative

Proposed Standard

(Barrier Method)

30,800

25, 300

17,900

5,500

12 900 /

Table 13. Calculation of Upper and Lower Bounds on Expenditure

Per Life Saved Under Two Alternatives to No-Action from 1977 to 2010

Detectors

Proposed

Standard

Number of Lives Saved

Relative to No-Action

Accumulated Costs

Accumulated Property & Injury

Savings Relative to No-Action

Accumulated Fatality Directed

Expenditures Relative to

No-Action

5,500

$881,000,000

$845,000,000

$36,000,000

12,900

$3,008/000,000

$2,980,000,000

$28,000,000

Upper Bound on Expenditure per

Life Saved $161,000 $234,000

Lower Bound on Expenditure per

Life Saved $6,500 $2,200

Calculations may not check because of rounding,

29
Table 13 gives the total number of lives saved under the proposed

standard and smoke detector alternatives relative to no-action from 1977

thru 2010. An upper bound on the total expenditure per life saved is

obtained by dividing the total accumulated (undiscounted) cost of the

alternative (also given in the table) by the number of lives saved. The

table shows that the upper bound of the expenditure is $161,000 per life

saved under the detector alternative compared to $234,000 under the

proposed standard. However, because the entire costs of the alternatives

are assigned to life safety, this method of calculation neglects the

substantial reductions in injury and property losses, relative to no- action, which occur under the two alternatives. The monetary equivalents

of these reductions, are also shown in the table. By subtracting these

savings from the accumulated costs we obtain a lower bound on the expenditure per life saved. The lower bounds are $6500 per life saved for

the detector alternative and $2200 per life saved for the proposed

standard. These calculations provide upper and lower bounds on the cost

of life safety. However, we emphasize that neither of these ratios

addresses the issue of time preference, that is, the use of short-term

expenditures for future life safety.

3.7 Selected Sensitivity Studies

The results just presented depend on many assumptions. This section

examines the sensitivity of our results to changes in those assumptions.

Additional sensitivity studies are presented in section 7.

3.7.1 Loss of Life Dollar Assignment

It is difficult to assign a value to the amount society is willing

to spend to prevent a fire fatality, the so-called "value of life."

Figure 5 shows how the comparison of alternatives is affected by this value

The figure shows that if no value is placed on preventing the loss of

life, the most attractive alternative is the no-action alternative. At

a value of approximately $60,000 per life saved, the smoke detector

alternative becomes the most attractive strategy, and at approximately

$300, 000 per life saved, the proposed standard becomes the most attractive

alternative. The proposed standard is the most attractive strategy for

all values greater than $300,000 per life saved. At a value of $1 million

per life saved the proposed standard results in a reduction in present

value of cost plus loss of 7 percent over the detector alternative and

16 percent over no action. Thus, although the assignment of the value

of life is a difficult one, our sensitivity studies show that the smoke

detector alternative and proposed standard remain most attractive over a wide range of this parameter.

30
CO Nominal

assignment

1

100 200 300

LOSS OF LIFE DOLLAR ASSIGNMENT

(thousands of dollars)

400 500

Figure 5. Sensitivity of Results to Dollar Assignment on Loss of Life

3.7.2 Proposed Standard Using the Backcoating Method

We have postulated that for Class D fabrics, compliance with the

proposed standard would be achieved by using an aluminum foil barrier

under the fabrics. However, there is uncertainty on the particular

method or combination of methods that furniture manufacturers will

actually use to meet the proposed standard. Conceptually, we could

address our uncertainty on the method used to comply with the standard

directly. However, since the uncertainties are changing rapidly, we have chosen to designate the barrier method as the basic method for

complying with the proposed standard and to treat other compliance

methods as sensitivity studies. In this section we discuss the effectiveness of a promising alternative to the barrier method, which we call

the "backcoating method."

Two backcoating methods have been identified. Work at the Southern

Regional Research Center of the U.S. Department of Agricu] ture has indicated that many cotton upholstery fabrics may be upgraded from Class D

31
to Class B or C by proper choice of existing backcoating products [21]

The second backcoating method is based on research at the National

Bureau of Standards showing that the application of sulfur to textile

materials inhibits smoldering combustion. This method is still being

developed, but based on current laboratory work, we assume that a smolder

inhibitor such as microencapsulated sulfur could be applied to upholstery

fabrics in a backcoating. The backcoating would upgrade Class D fabrics

to either Class A or B. The backcoating method would also require the

boric acid based treatment for the underlying cotton batting to enable

constructions intended for use with Class B and C fabrics to meet the

proposed standard. To illustrate the proposed standard alternative

using the backcoating method we develop the losses and costs for the

microencapsulated sulfur process in this report.

Because of the different flammability characteristics of the furniture manufactured under the backcoating and barrier methods, the losses

under the backcoating method are separately modeled, as detailed in

section 5.3.2. The losses under the backcoating method are somewhat

larger than under the barrier method because the backcoating method is

less effective at reducing ignitions from flaming sources. Moreover, if

an ignition occurs, materials treated with a sulfur backcoating may tend

to result in larger fires. The cost of the backcoating method, detailed

in section 6.3, is significantly less than the barrier method cost

primarily because of reduced labor, materials, and handling.

Table 14 gives the present value of the cost plus loss for the

backcoating method, as well as for the other three alternatives already

investigated. Using our nominal assumptions on the cost and effectiveness

of this method, the table shows that the backcoating method of meeting

the proposed standard is the most attractive option. Although the

losses under the backcoating method are somewhat higher than under the

barrier method, the lower cost of the backcoating method more than

offsets this increase. However, we emphasize that a backcoating with

microencapsulated sulfur has not yet been used commercially, and the

results reported here are based on laboratory projections of effectiveness

only.

The total cost plus loss to society of a combination of both the

barrier method and the backcoating method using microencapsulated sulfur

or a comparably priced backcoating product would be very attractive

compared to any of the nominal alternatives. We regard the cost of the

barrier method as an upper bound on the cost of the proposed standard and

expect that other methods, more comparable in cost to the backcoatinq

method, would be developed if the proposed standard is promulgated by the

Consumer Product Safety Commission. Thus, the proposed standard alternative may be even more attractive than our nominal case suggests.

32
Table 14. Comparison of Proposed Standard (Backcoating Method)

with Three Nominal Alternatives

Present Value at 8% from 1977 to 2010

(Millions of Dollars)

Alternative Loss Cost Cost Plus Loss

Proposed Standard

(Backcoating)

Proposed Standard

$5060 $ 510

(Barrier) 4840 1120

Detector Alternative 5650 300

No-Action 6330

$5570

5960

5950

6330

3.7.3 Cost of the Proposed Standard Alternative

Our nominal cost estimate shows the barrier method to be a relatively

expensive way of meeting the proposed standard. Figure 6 shows how the

choice of alternatives is affected by the furniture manufacturers'

initial cost for the barrier method. The figure shows that the cost of

the proposed standard has a critical effect on the choice of alternatives.

A 40 percent increase in the cost would make the barrier method the least

attractive alternative, whereas a 30 percent decrease in the cost would

make the barrier method the most attractive alternative—even better

than our nominal estimate of the backcoating method. The sensitivity of our results to the cost of the backcoating method is discussed in section

7.4.1.

If further work is undertaken to refine our analysis, the cost of

the proposed standard is a major area to be addressed.

3.7.4 Cost of the Smoke Detector Alternative

Since there is relatively little uncertainty on the cost of installing smoke detectors, we postpone until section 7 our analysis of how

that cost affects the choice of alternatives. Instead, in this section

we examine how the choice of alternatives depends on the fraction of the

smoke detector costs allocated to the smoke detector alternative. The

reader is reminded that we assigned only a portion of the smoke detector

costs to upholstered furniture fires because smoke detectors are effective

in detecting other types of fires as well.

33
CM

05

OO

GOO

_I CO oo ro = o

"O

<•*— H- o

OOOO o

oo

Q_

o

—

/'

7

s/'

/'

/'

/'

/ S NO ACTION /

6

DETECTORS

/

/

./_ PROPOSED STANDARD - ./ ^ (BARRIER METHOD)

/

5 ~S NOMINAL ^ BARRIER METHOD

ESTI MATE

4 1 1

1

1 1 1 100 200

INITIAL MANUFACTURERS' COST

(millions of dollars)

300

Figure 6. Sensitivity of Results to Manufacturers' Cost of

Proposed Standard Using the Barrier Method

Figure 7 shows how the choice of alternatives is affected by the

percentage of smoke detector costs assigned to upholstered furniture

fires. As discussed in section 6.2, our nominal calculation assigns

29 percent of the costs to the upholstered furniture fire scenario

based on our estimate that 29 percent of the lives saved by detectors

would be in upholstered furniture fires. That calculation is based in

part on the assumption that smoke detectors could reduce loss of life in

all residential fires by 60 percent. If detectors would reduce life loss

in all residential fires by only 40 percent, then a larger percentage of

the fatalities avoided would be in upholstered furniture fires; hence the

allocation of costs would increase to 44 percent. Increasing the detector

34
CM

r»

r-» en

T—

C/5

C/3 o1 «/) GO TO

° .s co —

6 -

NO ACTION

PROPOSED STANDARD

(BARRIER METHOD!

Otf tc^Rt

oo

QNOMINAL

ASSIGNMENT

I I

10 20 30 40

PERCENT OF COSTS ASSIGNED

50 60

Figure 7. Sensitivity of Results to Percentage of Smoke Detector

Costs Assigned to Upholstered Furniture Fires

effectiveness to 70 percent would reduce the upholstered furniture fire

allocation of costs to 25 percent. The figure shows that over this range

of allocated costs, the smoke detector alternative is slightly more or

less attractive than our nominal evaluation of the proposed standard

using the barrier method. However, there is not enough difference

between those two alternatives to make one alternative clearly superior

to the other.

3.7.5 Annual Number of Ignitions and Fatalities

From table 4 we estimate that upholstered furniture fires currently

result in 1460 residential fire deaths per year of which 1310 are in one- and two-family homes and apartments. Other estimates on the magnitude

of the problem have been cited. Figure 8 shows how the comparison of

alternatives depends on the current magnitude of the problem. The

abscissa in the figure represents the total number of upholstered furniture

fire fatalities in all residential occupancies because that is the quantity

most commonly estimated. (Another quantity frequently estimated is the

number of residential upholstered furniture fire fatalities involving

smoking, which account for about 70 percent of the 1,460 residential

fatalities or 1,020 fatalities.)

35
12

° 10

CD

H- ° O c:o

100,000

IGNITIONS

200,000

1000 1500 2000

FATALITIES

2500 3000

Figure 8. Sensitivity of Results to Changes in the Total Annual Number

of Residential Upholstered Furniture Fatalities and the Annual

Number of Upholstered Furniture Ignitions in Residences

Figure 8 shows that the no-action alternative is the most attractive

if the current number of fatalities is less than 600. If the number of

fatalities is between 600 and 1,500, the smoke detector alternative is

preferable. The proposed standard is the preferred alternative if there

are more than 1,500 deaths per year. The figure also shows the effect of

changing our estimate on the number of upholstered furniture ignitions,

since in our analysis the number of ignitions is directly proportional

to the number of fatalities. Thus, large changes in the numbers of

fatalities or ignitions can change the choice of alternatives. However,

as discussed in section 3.1.3, our estimate has been well corroborated

and we do not expect it to change significantly.

3.8 Combination of Alternatives

Thus far we have examined how the smoke detector alternative and

proposed standard perform when implemented separately. Table 15 gives

36
the present value of the cost plus loss for the two alternatives implemented together. The cost of the combination program is the sum of the

costs of the two elements. The losses under the combination alternative

are calculated using the fire loss model. The table shows that the

combination alternative is preferable to any of the alternatives implemented singly. For both the barrier method and the backcoating method

of complying with the proposed standard, the present value of the cost

plus loss is about $100 million less under the combination alternative

than under the next best alternative.

Table 15. Comparison of Combination Alternatives

Present Value at 8% from 1977 to 2010

(Millions of Dollars)

Alternative Loss Cost Cost Plus Loss

Combination (Barrier) $4440

Proposed Standard (Barrier) 4840

Detector Alternative 5650

No-Action 6330

$1420 $5860

1120 5960

300 5950

6330

Combination (Backcoating)

Proposed Standard

(Backcoating)

4640

5050

810

510

5450

5560

37

Part Two

DETAILED DERIVATION OF RESULTS

4. DEVELOPMENT OF CURRENT LOSSES FROM FIRE LOSS MODEL

This section provides a detailed description of the upholstered

furniture fire loss model. The use of the model is demonstrated by

employing it to calculate losses under current conditions. Loss model

results for the various intervention strategies are given in section 5

4.1 Description of Fire Loss Model

4.1.1 Model Overview

Figure 9 gives a schematic of the fire loss model. As outlined in

section 2 , the model describes a number of different types of upholstered

furniture fires. The model parameters are listed across the top of the

figure. Beneath each input parameter are sets of branches representing

the different possible values of that parameter. Each path through the

tree represents a different type of upholstered furniture fire. The tree

is actually four times as large as it appears since the portion of the tree

associated with electrical ignition source is repeated for each of the

other three ignition sources. As shown, the model allows for more than

300 different kinds of upholstered furniture fires.

Associated with each path is a level of loss, represented by four

output variables on the right-hand side of the figure. Probabilities

are assigned to each branch representing the relative frequency of

occurrence of the branch values. Each branch probability assignment is

conditional on the values of the parameters preceding that branch . The

probability of a particular path through the tree is obtained by multiplying the probabilities of the branches making up the path. Combining the

path probability with the losses associated with the particular path

provides a probability distribution on losses resulting from a single

reported upholstered furniture fire. The expected losses per reported

fire are calculated directly from the probability distribution by multiplying each path probability by its associated loss values and then

summing over all paths through the tree.

The model is used by first setting the input parameters to reflect

current conditions. Then the model parameters are adjusted to reflect

the performance of the different intervention strategies. However, in

this section we will only be concerned with modeling the losses under

current conditions

.

4.1.2 Model Parameters

The model parameters are introduced according to the basic sequence

of ignition, fire development, and resultant loss. The model begins by

assuming that an ignition has occurred and then addresses whether the

fire is reported to the fire authorities. Since this analysis is only

41
IS A IS FIRE RESPON- IS THERE A DISCOVERED EXTENT

IS SIBLE FUNCTIONAL BEFORE OF

IS FIRE IGNITION SOMEONE PERSON SMOKE LEAVING FIRE FLAME REPORTED' SOURCE HOME? AWAKE' DETECTOR? CHAIR? TYPE DAMAGE LOSSES

FUNCTIONAL 1

FUNCTIONAL

FUNCTIONAL,!

J SM/FL

C DISCOVERED / R

1 FL

\ >R

C

y R

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\ >R

C NOT

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C DISCOVERED

/ R

F^

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R

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FATALITIES

INJURIES

TANGIBLE PROPERTY

INTANGIBLE PROPERTY

LEGEND

SM SMOLDERING

SM/FL - SMOLDERING, THEN

FLAMING

FL • DIRECTLY FLAMING

C - CONFINED TO CHAIR

R . BEYOND CHAIR BUT CONFINED TO ROOM

>R - BEYOND ROOM

Figure 9. Probability Tree for Assessing Losses Per

Upholstered Furniture Fire

42
concerned with reported fires, we consider only the losses that emanate

from the "reported" branch. The model then considers the ignition

source. For simplicity, the model delineates three of the most common

ignition sources: cigarettes (including pipes, cigars, and unspecified

smoking material), open flame, and electrical devices. All other ignition

sources are grouped into a fourth category called "other."

The second portion of the model characterizes the development of

the fire, given a reported ignition from a particular source. The model

first addresses whether anyone is at home at the time of ignition. If someone is at home, then the model addresses whether at least one individual is both conscious and physically capable of discovering and responding to the fire. If the individual is so capable, then he is classified

as "awake;" otherwise, he is classified as "not awake." The model also

considers whether there is at least one functional smoke detector in the

residence. Then, depending on whether someone is at home and awake and

on whether there is a functional smoke detector, the model addresses

whether the fire is discovered before or after it leaves the chair.

A fire is defined as "discovered" if its presence is observed

before it leaves the chair by someone who is physically capable of

responding to the fire. If the fire is observed after spreading from

the chair or it self-extinguishes, then it is classified as "not discovered. "

The fire is further characterized according to the fire type and

final extent of flame damage. The fire type gives the ignition and fire

sequence. Three fire types are considered: smoldering only, smoldering

then flaming and directly flaming (denoted by SM, SM/FL, and FL, respectively) . For simplicity, three levels of flame damage are considered:

confined to the chair, beyond the chair but confined to the room, and

beyond the room (denoted by C, R, and >R, respectively)

.

The third section of the model defines the losses for each path

through the tree. Four categories of loss are considered: loss of

life, injury, tangible property loss, and intangible property loss. The

various categories of loss are made dependent on extent of flame damage, on whether the fire is discovered before leaving the chair, and on whether

someone is at home at the time of ignition.

4.2 Probability Assignments for Current Conditions

The use of the fire loss model is best demonstrated by using it to

calculate losses for current conditions. Input data for the calculations

are derived from several sources. Wherever possible, we use statistical

5We use "chair" to refer to any piece of upholstered furniture,

43
data, such as provided bv the U.S. Fire Administration's National Fire

Incident Reporting System (NFIRS) , to develop the necessary probability

assignments. However, where statistical data are not available, we use expert judgment as that is the best information currently available.

The NFIRS data base is a key source of data for our analysis. At

the time we were carrying out the analysis, the data base consisted of

two years of reporting experience from parts of Ohio for 1976 and

California for 1975. The data include 2,742 incidents in one- and twofamily homes and apartments in which upholstered furniture was the first

item to ignite. Incendiary and suspicious fires were excluded from

consideration. It is clear that as more data become available or as the

understanding of upholstered furniture fires improves, it may be necessary

to revise our probability assignments and carry out a new evaluation of

the alternatives.

4.2.1 Ignition Source Probabilities

The probabilities on ignition source, given a reported ignition,

are taken directly from the NFIRS data base. Table 16 lists these

probabilities

Table 16. Ignition Source Statistics from 2742 Upholstered

Furniture Fires

Ignition Number of Probability

Source Occurrences of Occurrence

Cigarette 1771 0.7031

Open Flame 326 0.1294

Electrical 131 0.0520

Other 291 0.1155

Unknown 223

Based on 2519 fires for which the ignition source is unknown

4.2.2 Probabilities Leading to Discovery and Fire Type

The probability of a fire being discovered before leaving the chair

depends on a variety of factors including the type of fire and the

presence of individuals capable of discovering the fire. For the purpose

of this analysis, we make the probability of the fire being discovered

before leaving the chair dependent on the ignition source, whether

someone is at home and awake, and whether there is a functional smoke

detector

44
Statistical data do not exist on most of these parameters and so expert judgment must be used to assign the probabilities. The desired

probabilities are all conditional on the fire being reported. However,

most experts are inclined to assess the probabilities independently of

whether the fire is reported. We therefore introduce a second probability

tree to assist in translating the probability assignments from the class

of all fires (reported and unreported) to the class of reported fires

only. The new probability tree is called the auxiliary tree.

A schematic of the auxiliary tree is given in figure 10. The

auxiliary tree appears quite similar to the original probability tree

introduced in figure 9 except that two of the input parameters have been

dropped from the tree and the parameter designating whether the fire is

reported has been moved to the end of the auxiliary tree. In this

manner, the input parameters are made independent of whether the fire is

reported, yet the required probabilities can be derived for the class of

reported fires only. The ignition source and flame spread parameters

are not needed in the auxiliary tree because they are determined directly

from the NFIRS data base and are already conditional on the fire being

reported. We defer an example of the calculation of these probabilities

until all the probabilities for the auxiliary tree have been introduced.

As discussed in the following sections, separate auxiliary trees

are developed for each ignition source since many of the probabilities

are dependent on the ignition source. Figure 11 (A, B, C, and D)

summarizes the probability assignments for the auxiliary trees.

4.2.2.1 Is Someone Home?

The probability of at least one person being at home, given an ignition, is made dependent on the ignition source. To determine this

probability, we first estimate the probability of at least one person

being at home at a random time and then adjust the probability to reflect

the fact that there was an ignition of a particular type. From a separate

calculation not given here we estimate the probability of at least one person being at home at a random time to be about 0.75. However, the

probability of someone being at home, given that there is an upholstered

furniture ignition, is somewhat higher than this value because most

furniture ignitions are caused by direct human activity. Thus, we set

the probability of someone being at home at 0.95 and 0.99 for cigarette

and open flame ignitions, respectively, because nearly all those ignitions

occur when someone is at home. Electrical and other ignitions are less

dependent on someone being at home, so we set the probability of someone being at home, given those ignition sources, at 0.80 and 0.85,

respectively.

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4.2.2.2 Is a Responsible Person Awake?

Based on considerations of normal living patterns, we estimate in

a separate calculation that the probability of at least one person being

awake at a random time, given that someone is at home, is about 0.60. A

person is defined to be "awake" if he is physically awake and capable of

responding to a fire situation. Thus, young children, invalids, and

intoxicated persons are not considered "awake." However, the estimate

of this probability must be further conditioned to reflect the fact that

there has been an ignition. Since most upholstered furniture fires are associated with human activity, we increase our nominal estimate of at

least one person being awake to reflect the condition of an ignition

having occurred. We set the probability of someone being awake, given

an open flame ignition, at 0.95 because most of these ignitions are from

matches and lighters resulting in immediate ignition. For cigarette

ignition sources , we lower the probability of a responsible person being

awake to 0.80 because the person who was smoking may be infirm, intoxicated, or may have fallen asleep before the smoldering furniture ignition

occurred. Electrical and other ignitions are not as dependent on someone being awake, and so we set the probability of someone being awake, given

one of these ignitions, at 0.65, which is slightly higher than our unconditional probability estimate of someone being awake. It should be

recalled that all these estimates are conditional on someone being at

home. If no one is at home, then the probability that a responsible

person is awake is not defined.

4.2.2.3 Is There a Functional Smoke Detector?

We assume that approximately 5 percent of U.S. residences had

functional smoke detectors in 1975 and 1976, the "current" period modeled.

We therefore set the probability of there being a functional smoke

detector at 0.05.

4.2.2.4 Is Fire Discovered Before Leaving Chair?

The probability of a fire being discovered before it spreads beyond

the initial piece of furniture ignited is made dependent on the ignition

source, on whether there is a functional smoke detector, and on whether

someone is at home and awake. If there is no functional smoke detector,

but someone is at home and awake, then the probability of the fire being

discovered before leaving the chair is set at 0.99 for open flame,

electrical, and other ignition sources, and 0.95 for cigarettes. If someone is at home but not awake, then the probability of the fire being

discovered before leaving the chair is set at 0.50 for all ignition

sources. If no one is at home, then the discovery probability is set at

0.01 for all ignition sources, reflecting the small chance that a neighbor

or passer-by will discover the fire before it leaves the chair.

51
If there is a functional smoke detector, the probabilities of the

fire being discovered before leaving the chair are the same for all

ignition sources. If someone is at home and awake, we assign a probability of 1.0 to the fire being discovered before leaving the chair.

If the detector is functional and if someone is at home but not awake,

then as shown in figure 12 we calculate the probability of the fire

being discovered before leaving the chair to be 0.83. As shown, this

assessment considers the probability that the person is either not

responsible (e.g., young or infirm) or intoxicated. If there is a functional smoke detector, but no one is at home, we assign a 0.02

probability that the fire will be discovered before it leaves the chair,

reflecting the small chance of the smoke detector alerting a neighbor or passer-by

PROBABILITY

OF DISCOVERY

GIVEN HOME,

IS FIRE NOT AWAKE

CHARACTERIZATION DISCOVERED AND FUNCTIONAL

OF PERSON BEFORE LEAVING PATH SMOKE

NOT AWAKE CHAIR? PROBABILITY DETECTOR

NOT RESPONSIB

0.1

DISCOVERED

H

0.0

NOT DISCOVERED

1.0

00

0.10

0.00

HOME,

NOT AWAKE,

FUNCTIONAL

RESPONSIBLE, BUT DISCOVEREDncorunaiDLt, dui i LEGALLY INTOXICATED 7 °

7 01 \ NOT DISCI0VERED

0.3

007

0.03

07

RESPONSIBLE AND

NOT INI

DISCOVERED

NilBLt HNU r

ITOXICATED J

8 \

0.95

NOT DISCOVERED

0.05

076

0.04

1.00

0.76

083

Figure 12. Calculation of Discovery Probability Conditional

on Home, Awake, and Functional Parameters

52
4.2.2.5 Fire Type

The fire type probability gives the likelihood that the fire only

smolders (SM) , smolders and then flames (SM/FL) , or flames only (FL)

To calculate the fire type probabilities, we introduce an intermediate

variable to characterize the initial ignition class. As shown in table

17, ignitions are classed as either initially smoldering or flaming.

The table shows that 100 percent of cigarette ignitions, 30 percent of

open flame ignitions, 70 percent of electrical ignitions, and 90 percent

of other ignitions are assumed to begin in a smoldering stage. The

remaining ignitions are assumed to begin in a flaming state.

Table 17. Probability Assignments on Ignition Class

as Function of Ignition Source

Ignition

Source

Ignition

Class

Ignition Class

Probability

Cigarette

Smoldering

Flaming

1.00

0.00

Open Flame

Smoldering

Flaming

0.30

0.70

Electrical

Smoldering

Flaming

0.70

0.30

Other

Smoldering

Flaming

0.90

0.10

As shown in figure 13, the fire type probabilties are made dependent

on ignition class and on whether or not the fire was discovered before

leaving the chair. A flaming ignition is assumed always to lead to a fire of type FL. A smoldering ignition, if discovered, leads to a fire

of type SM with probability 0.95 and of type SM/FL with probability of

0.05. If the fire is not discovered, then the SM probability is set at

0.08 and the SM/FL probability at 0.92.

To eliminate the intermediate parameter, ignition class, we combine

the information in figure 13 and table 17. For example, to calculate

the probability that a discovered fire resulting from an electrical

ignition source will smolder only, we first observe from table 17 that

there is a 70 percent chance of the ignition beginning in a smoldering

53
IS FIRE DISCOVERED

IGNITION BEFORE LEAVING FIRE CLASS CHAIR? TYPE

SM

DISCOVERED

{

0.95

SM/FL

0.05

NOT DISCOVERED

i

0.08

SM/FL

0.92

DISCOVERED FL

1.0

NOT DISCOVERED FL

1.0

Figure 13. Probability Assignments on Fire Type as Function

of Discovery and Ignition Class

state. From figure 13, we note that there is a 95 percent chance that a smoldering ignition will terminate in a smoldering state (SM) if the

fire is discovered before it leaves the chair. Therefore, the probability

that a fire type SM results from an electrical ignition source, given

discovery, is 0.70 x 0.95 = 0.66. 6 Similarly, the probability that the

fire will smolder and then flame (SM/FL) , given that it is discovered,

is 0.70 x 0.05 == 0.04. If a smoldering ignition from an electrical

source is not discovered, the probability of fire type SM is 0.70 x 0.08

= 0.06; the probability of SM/FL, given that it is not discovered, is

0.70 x 0.92 = 0.64. The probability of the fire type FL is the probability

that it begins flaming, or 0.30. Similar calculations are made for the

other ignition sources, the results of which are shown in the second

parts of figures 11A, B, C, and D.

Input probabilities are rounded to two decimal places subject to the

constraint that they sum to one

54
4.2.2.6 Is Fire Reported?

The terminal branches on the auxiliary tree are the probabilities

that the fire is reported to the fire department. These probability

assignments are based on expert judgment and, for all ignition sources,

they are made dependent only on the fire type and whether the fire is

discovered before leaving the chair. Thus, for example, the probability

of the fire being reported is assumed to be only 0.10 if the fire was discovered and only smoldered. But the probability of the fire being

reported is set at 0.95 if the fire ultimately flamed and was not

discovered before leaving the chair.

4.2.2.7 Calculation of Conditional Probabilities from Auxiliary

Probability Trees

The probabilities required for the original probability tree of

figure 9 are conditional on the fire being reported. The calculation of

these probabilities from the auxiliary tree is a multistep process based

on the definition of conditional probability.

As an example of how the conditional probabilities are calculated,

figure 14 is used to calculate, for cigarette ignitions, the probability

of someone being "not awake," given a reported fire with someone at

home. As shown, the probability of the fire being reported with someone

at home is found to be 0.214596. The probability of someone being at

home and not awake and of the fire being reported is the sum of the path

probabilities that comprise that event, or 0.092557. Thus, from the

definition of conditional probability, the probability of someone being

"not awake," given a reported cigarette ignition with someone at home,

is 0.092557/0.214596, or 0.431308. Similar calculations are made to

determine the other conditional probabilities. The resulting probabilities are given in the appendix.

7 . Intermediate calculations in part two of this report are shown to as many as 6 significant figures to maintain the relative differences among

the small probabilities and to minimize round-off errors. Final results,

however, are given in three significant figures. The exact calculations

shown in figure 14, as well as the other figures and tables in part two,

may not check because of rounding. For a more complete explanation of

"round-off" see appendix.

55
PATH PATH PROBABILITY

IS FIRE PATH PROBABILITY FOR REPORTED ISA IS THERE A DISCOVERED PROBABILITY FOR REPORTEO CIGARETTE FIRES RESPONSIBLE •FUNCTIONAL BEFORE FOR CIGARETTE CIGARETTE WITH SOMEONE

IGNITION IS SOMEONE PERSON SMOKE LEAVING FIRE IS FIRE IGNITION WITH FIRES WITH HOME AND

SOURCE HOME? AWAKE? DETECTOR? CHAIR? TYPE REPORTED? SOMEONE HOME SOMEONE HOME NOT AWAKE

FUNCTIONAL

FUNCTIONAL

| NOT HOME

\NOT REPORTED

DISCOVERED SM/FL / .60

.05 \N°T REPORTEO

\NOT REPORTED

NOT REPORTED

0.0 ^HOT REPORTED

\NOT REPORTED

DISCOVERED/ SMfl/FL f

05~VNOT REPORTED

\NOT REPORTED

.40 REPORTED

OB \NOT REPORTED

1.0 REPORTEO

H/FL /

NOT REPORTED

REPORTED -^riiNOT REPORTED

\NOT REPORTED

DISCOVERED/ 5M/FL /

05 \NOT REPORTED

\NOT REPORTED

"^NO

5M/FL /

.92 VNOT REPORTED

0.0 V

DISCOVERED

NOT REPORTED

NOT REPORTED

NOT REPORTED

NOT REPORTED

UlOT REPORTED

.92 \NOT REPORTED

rsriiNOT REPORTED

0.003610 0.003610 0032490

0.001140 0.001140

0.000760

0.0 0.0

0.0

0.065161

0.566445

0.020577

0.013718

0.0

0.0

0.0

0.002888

0.031551

0.001661

0.0

0000749 0.000749 0.000749 0006742

0.000237 0.000237 0.000237

0.000158 00 00 0.0 00

0,0 0.0 0.0

0.000129

0.001412 0001412 0.001412

0.000074

0.0

0.008574

0.077164

0.002708 0001805

0.0

0.0

0.0

0.007220

0.078879

0.004152

0.0

COLUMN TOTALSFigure 14. Portion of Auxiliary Tree for Cigarette Ignition Source

Used in Sample Conditional Probability Calculation

56
4.2.3 Extent of Flame Damage Probabilities

Statistics on the extent of flame damage for upholstered furniture

fires are taken directly from the NFIRS data base. However, the NFIRS

statistics are not conditioned on fire type or on "whether the fire is

discovered before leaving the chair. Since the latter two considerations

are important in the comparison of alternatives, the statistics must be

adjusted to make them dependent on fire type and the discovery parameter.

First, we consider the effect of fire type. If the fire type is SM

(smoldering only), we assume that the flame damage is confined to the

chair regardless of whether the fire is discovered. Therefore, as shown

in figure 15, we set the probability of the flame damage being confined

to the chair (C) at 1.0 for the fire type SM.

IS FIRE DISCOVERED EXTENT

BEFORE LEAVING FIRE OF FLAME PROBABILITY

CHAIR ? TYPE DAMAGE DISTRIBUTIONS

SM

1.0000

DISCOVERED SM FL

FL

SM

NOT DISCOVERED SM FL

=-R

0.8332

0.0682

0.0986

0.8332

0.0682

0.0986

1.0000

0.0000

0.6055

0.3945

FL

0.0000

0.6055

0.3945

Figure 15. Probability Distributions on Extent of Flame Damage

Conditional on Discovery and Fire Type

57
Table 18 gives the extent of flame damage for 2,497 of the 2,742

upholstered furniture fires contained in the NFIRS data base. The fires

in the data base include fires that only smoldered as well as fires that

ultimately flamed. The extent of flame damage for fires that ultimately

flamed can therefore be determined by adjusting the statistics to account

for the fires that never flamed. From the auxiliary trees (figure 11A-D)

,

we calculate that 24.3 percent of the reported fires, or approximately

606 of the 2,497 fires, never progress beyond the smoldering stage.

Subtracting the smoldering only fires from the "C" fires in the first

column of table 18 then gives the distribution on extent of flame damage

for fires that ultimately flame, as shown in the table.

Table 18. Statistics on Extent of Flame Damage for 2742

Upholstered Furniture Fires

Extent of

Flame Damage

Number of

Fires

Number of

Fires That

Ultimately

Flamed

Frequency of

Fires That

Ultimately

Flamed

C 1048 442 0.2337

R 860 860 0.4548

>R 589 589 0.3115

Unknown 245 —

Total 2742 1891 1.0000

Based on an estimated 1891 fires with known extent of flame damage that

ultimately flamed

Table 18 gives estimated frequencies on extent of flame damage for

reported fires that ultimately flame. However, the frequencies must be

further adjusted to account for their dependency on whether the fire is

discovered before leaving the chair. To calculate the required conditional probabilities we introduce the following notation:

P(x

x

,

P(x) = probability event x occurs

, . . ,x ) = probability events xn thru x all occur

n P(x/y) = probability

J event x occurs,

In

given that event y occurs

rep = fire is reported

flame = fire ultimately flames

C = flame damage is confined to chair

R = flame damage extends beyond chair but is confined to room

58
>R = flame damage extends beyond room

dis = fire is discovered before leaving the chair

dis = fire is not discovered before leaving the chair

Using the rules of conditional probability, we write:

P (C/rep, flame) = P (C/dis , rep, flame) P (dis/rep , flame) +

P (C/dis, rep, flame) P (dis/rep, flame) (1)

P (R/rep, flame) = P (R/dis , rep, flame) P (dis/rep, flame) +

P (R/dis, rep, flame) P (dis/rep, flame) (2)

P (>R/rep, flame) = P (>R/dis , rep, flame) P (dis/rep, flame) +

P (>R/dis, rep, flame) P (dis/rep, flame) (3)

Also, because the categories of flame damage have been defined to

be mutually exclusive and collectively exhaustive, we can write:

P (C/dis, rep, flame) + P (R/dis, rep, flame) + P (>R/dis , rep, flame) = 1 (4)

Equations (1) , (2) , (3) , and (4) provide four equations in six

unknowns. They can be solved uniquely if two more linearly independent

equations involving the unknown variables can be generated. To develop

two such equations, we assume that the flame damage must extend beyond

the chair if a flaming fire is not discovered before leaving the chair.

We also assume that the probability of a fire spreading beyond the room

is four times as great for undiscovered fire as for discovered fire.

Therefore, we can write:

P (C/dis, rep, flame) = (5)

P(>R/dis, rep, flame) = 4P (> R/dis , rep, flame) (6)

From the auxiliary trees, we calculate

P (dis/rep, flame) = 0.280

P (dis/rep, flame) = 0.720

Substituting these values, together with the values given in table 18,

into equations (1) through (6) , we obtain the probability distributions

shown in figure 15. As shown in the figure we assume that these probabilities on flame damage are valid for all fires that ultimately flame

that is, for fires of types SM/FL and FL. (We further assume that these

probabilities are valid for each of the ignition sources.)

59
4.3 Loss Assignments

Associated with each type of fire, or path through the tree, is an average level of loss. In this section we develop loss estimates for

each type of fire represented by the tree. The loss estimates are given

in terms of deaths, injuries, and tangible and intangible property loss.

In most cases, the loss estimates are developed from historical statistics,

adjusted by judgment to reflect dependencies not recorded in the statistics,

As a first approximation, we assume that the level of property loss

is dependent on whether the fire is discovered before leaving the chair

and on extent of flame damage. We assume that the level of injury and

death depends on whether anyone is at home, whether the fire is discovered

before leaving the chair, and on the extent of flame damage. It is

possible to construct a more detailed estimate of loss by introducing

more variables on which to condition the losses,, but the variables

selected here are sufficient for a preliminary comparison of alternatives.

Table 19 gives the average personal and tangible property losses

recorded for the 2742 fires in the NFIRS data base as a function of

extent of flame damage. Project team estimates for intangible property

losses are also given in the table. In order to make the values usable

under the assumptions made for the analysis, the fatality and injury

loss numbers must also be made dependent on whether someone is at home

and on whether the fire is discovered before leaving the chair. Since

statistical data do not exist for this dependency, expert judgment is

used to characterize it.

For example, we consider the number of fatalities from fires with

extent of flame damage beyond the room. Table 19 shows that on the

average 0.08489 persons were killed in a fire of this class. We would

expect this loss figure to be higher for fires in which someone was at

home and lower if no one was at home at the time of ignition. But

averaging over whether anyone was at home or not, the expected mortality

rate must be 0.08489 fatalities per fire. Thus,

P (home/rep, >R) L (home , rep, >R) +

P (home/rep, >R) L (Home", rep, >R) = L(rep,>R) = 0.08489 (14)

where

L(xIn,...,x ) = average loss given that events x

J- thru x all occur

home = someone is at home when ignition occurs

home = no one is home when ignition occurs

60
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The probabilities P (home/rep, >R) and P (home/rep, >R) are calculated

from the fire loss model (probability tree) . Thus, equation (14) is a single equation in two unknowns, and it can be solved if one more

independent equation involving L (home, rep, >R) and L (home, rep, >R) can be

developed. To provide this equation, we assume that the loss of life

for fires of class ">R" is 10 times greater for fires in which someone

is at home than in which no one is at home.

That is,

L (home, rep, >R) = 10L (home, rep, >R) (15)

From the fire loss model, we calculate that

P (home/rep, >R) = 0.7010

P (home/rep, >R) = 0.2990

Substituting these values into equations (14) and (15) , we obtain

L (home, rep, >R) = 0.11614

L (home, rep, >R) = 0.01161

These values must now be adjusted to reflect whether the fire is discovered before leaving the chair. Thus, we write

P (dis/home,rep,>R) L (dis , home, rep, >R) +

P (dis/home,rep,>R) L (dis , home , rep, >R) = L (home, rep, >R) (16)

P (dis/home,rep,>R) L (dis , home , rep, >R) +

P (dis/home,rep,>R) L (dis, home, rep, >R) = L (home , rep, >R) (17)

To uniquely solve (16) , another relationship between

L (dis, home, rep, >R) and L (dis , home , rep , >R) is required.

We assume that

L(dis, home, rep, >R) = 10L (dis , home, rep, >R) (18)

From the fire loss model, we calculate

P (dis/home,rep,>R) = 0.1265

P(dis/home,rep,>R) = 0.8735

62
Substituting these values into (16) and solving simultaneously with

(18) , we obtain

L(dis, home, rep, >R) = 0.01311

L(dis, home, rep, >R) = 0.13107

If no one is at home at the time ignition occurs, we assume that

the expected loss of life is the same for all fires whether or not the

fire is discovered before leaving the chair. Thus

L(dis, home, rep, >R) = L (dis, home, rep, >R) = L (home, rep, >R) = 0.01161

Similar calculations are made for loss of life in fires of flame

extent "R" and for injuries in fires of flame extent "R" and ">R" . Loss

of life for fires of flame extent "C" is only conditioned on whether

someone is home. For a fire that is not discovered before leaving the

chair, we assume that the probability that the flame damage is confined

to the chair is zero for reported fires, or P(dis/rep,C) = 0. Tables 20

and 21 list the assumptions used in subdividing the loss statistics into

finer categories.

Table 20. Assumptions Used to Condition Expected Fatality

Losses on Occupancy, Discovery and Extent of Flame Damage

Extent of

Flame Damage Relationship Between Fatality Loss Categories

C L (home, rep, C) = 20L (home, rep,C)

R

L (home, rep, R) = 20L (home, rep, R)

L (dis , rep, home, R) = 5L (dis , rep, home ,R)

L (dis , rep, home, R) = L (dis , rep, home ,R)

>R

L (home, rep, >R) = 10L (home , rep, >R)

L (dis, rep, home, >R) = 10L (dis , rep, home, >R)

L (dis , rep, home ,>R) = L (dis , rep, home ,>R)

Tangible and intangible property losses are made dependent on whether the fire is discovered before leaving the chair, using a method

similar to that outlined above. In subdividing the losses, we assume

that property losses in discovered fires with extent of flame damage "R"

and ">R" are §0 percent of the losses incurred in not-discovered fires.

63
Table 21. Assumptions Used to Condition Expected Injury

Losses on Occupancy, Discovery and Extent of Flame Damage

Extent of

Flame Damage Relationship Between Injury Loss Categories

C L (home, rep, C) = 10L (home, rep, C)

R

L (home, rep, R) = 10L (home, rep, R)

L(dis, rep, home, R) = 2L (dis , rep, home, R)

L(dis, rep, home, R) = L (dis , rep, home, R)

>R

L (home, rep, >R) = 5L (home, rep, >R)

L (dis, rep, home, >R) = 5L (dis , rep, home , >R)

L (dis, rep, home, >R) = L (dis , rep, home , >R)

Table 22 gives the resultant loss figures for each category of

loss.

4.4 Value Assignments

The fire loss model provides estimates for four categories of loss

deaths, injuries, tangible property loss, and intangible property loss.

In comparing the alternatives, we must compare the various units of loss

with the costs of implementing the alternatives. It is possible to

simultaneously compare the costs with the different units of loss , but

to facilitate the evaluation of the alternatives and to ensure that they

are compared on a consistent basis, this section introduces the explicit

value assignments for use in reducing the different outcome measures to

a common monetary scale. The monetary equivalent of the different

categories of loss may be interpreted as the amount society is willing

to pay to prevent a single loss of the particular category.

As discussed in section 3.1.2, we use a nominal value of $300 000

per life saved for our analysis. A sensitivity study to determine how

the choice among alternatives varies with this assignment is given in

section 3.7.1.

Injuries incurred during upholstered furniture fires cover a wide

range of types and severity. In a report commissioned by the Consumer

Product Safety Commission, Battelle Columbus Laboratories estimates the

cost of an average upholstered furniture fire injury at $8700 [22]

This figure represents the average costs of hospital and physicians,

rehabilitation, work loss, and legal fees for injuries to civilians (as

opposed to firefighters). Burn injuries, smoke inhalation, and other

injuries are averaged in this cost estimate. In this analysis we use a

64
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65
value approximately equal to this estimate, $10,000 per average fire

injury, although we recognize that this figure may not include an adequate

allowance for such indirect costs as pain and suffering. A sensitivity

study on this value assignment is given in section 7.1.2.

Tangible property losses are valued at the cost of the real property

involved as reported in the NFIRS data base. Intangible property losses

are valued at the average dollar amount one would be willing to pay to

forego such losses as aesthetic damage, disruption of life style, and

loss of family mementos. The tangible property losses, shown in table 19, are obtained directly from the NFIRS data base. For each extent of flame

damage class, the figure is the average direct property loss estimated

by the fire service for all upholstered furniture fires in that class.

The intangible property loss figures are project team estimates. Both

sets of figures, adjusted to make them dependent on the discovery parameter, are shown in table 22.

Table 23 gives the monetary equivalents for each of the categories

of loss. The table is constructed by multiplying the average number of

fatalities and injuries per fire (table 23) by their associated value

assignments. By construction, the losses are made dependent on extent

of flame damage, whether anyone is at home, and the discovery parameter.

The aggregate loss shown in the table is the sum of the monetary losses

associated with a particular category. There are 10 possible aggregate

loss levels, ranging from $458 to $58,832 per fire, depending on the

particular combination of conditioning variables.

4.5 Calculation of Losses Under Current Conditions

The probability estimates, loss outcomes, and value assignments

outlined above are used with the probability tree of figure 9 to calculate

the possible losses from a single reported upholstered furniture fire.

The calculations are made by determining the probability and losses

associated with each path through the tree. The probability of the path

is the product of the probabilities of the branches making up the path.

The losses are found from tables 22 and 23, depending on the level of

flame extent, occupancy, and discovery parameters. The probabilities of

the paths leading to the same loss are summed, and the results are presented in the form of a probability distribution on loss.

Table 24 gives the resultant probability distributions on aggregate

loss for a single reported upholstered furniture fire. The cumulative

probability is the probability that the expected losses will be less

than or equal to the amount shown. The cumulative probability distribution is also shown in graphical form in figure 16.

Measured in monetary terms , the average aggregate loss ranges from

approximately $460 to $58,800 per fire. There is a 54 percent chance

that the fire will have expected losses less than $4,500, and a 14 percent

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67
Table 24. Probability Distributions on Aggregate

Losses Under Current Conditions

Aggregate

Loss

(Dollars) Probability

$ 458 0.00031

2 204 0.41939

2 569 0.00001

3 077 0.10823

4 493 0.. 01447

11 864 0,22170

15 504 0.00001

16 071 0.02092

18 249 0.07051

58 832 0.14444

Cumulative

Probability

0.00031

0.41970

0.41971

0.52794

0.54241

0.76412

0.76413

0.78505

0.85556

1.00000

CJ

10,000 20,000 30,000 40,000 50,000 60.000 70,000

AGGREGATE LOSS [Dollars]

Figure 16. Cumulative Distribution on Aggregate Losses

Under Current Conditions

68
chance that losses will be $18,000 or more. The expected value of the

probability distribution is $14,100. Similar probability distributions

can also be constructed for each of the loss components. In this analysis,

however, our focus is on the expected values of these losses.

Table 25 gives the expected loss in each category. The table shows

that loss of life is the largest component of the aggregate loss accounting

for 59 percent of the total. Tangible and intangible property losses

are the second most important component, together accounting for 30 percent

of the expected loss. Injuries account for only 11 percent of the

expected aggregate loss. It should be recalled that these results are dependent on the value assignments made for death and injury, and that

changing the assignments could change the relative importance of the

different loss categories. The expected loss per reported fire is

multiplied by 47,500, the annual number of reported fires derived in

section 3.1, to obtain the total annual U.S. losses also shown in table 25.

Table 25. Reported Upholstered Furniture Fire Losses Under

Current Conditions

Expected Loss Per Fire Total Annual Expected Losses

Category Number

Monetary

Equivalent Number

Monetary Equivalent

(Millions of Dollars)

Fatalities

Injuries

Property

Tangible

Intangible

0.0276

0.159

$ 8,290

1,590

3,640

550

1312

7570

$394

76

173

26

Aggregate $14,100 $668

Obtained by multiplying the expected loss per fire by 47,500, the

annual number of reported upholstered furniture fires

4.6 Number of All Upholstered Furniture Fires Under Current Conditions

In this section we derive the number of "all" upholstered furniture

fires (both reported and unreported) under current conditions and the

corresponding ignition source distribution. These results are used in

section 5 to model the expected losses under the three alternatives.

We first calculate the probability that an upholstered furniture

fire is reported. From the definition of conditional probability, we

can write

69
t, / / x P(cig,rep) (7) P(crg/rep) =

p J;p)

P

and also

„, /

• » P(cig,rep) (8) P(rep/C1 g) = p(cig)

where

cig = ignition source is cigarette

Rearranging (8) we obtain

P(cig) =

l\

c ^'TMP\ < 9 > 3 P(rep/cig)

and substituting (7) into (9) yields

, . . P(cig/rep) P(rep) (10) iClg; P(rep/cig)

To determine the probability of an upholstered furniture fire being

reported, P(rep), we note that equations similar to (10) can be written

for the other ignition sources. Then, because the four ignition sources

are defined to be mutually exclusive and collectively exhaustive, we can write

P(cig) + P(open) + P(elec) + P(other) = 1 (11) or

or

where

P(cig/rep) P(rep) i P ( open/rep ) P ( rep

)

P(rep/cig) P (rep/open)

P(elec/rep) P(rep) P (other/rep) P(rep) (12)

P(rep/elec) P (rep/other)

" P(cig/rep) i P (open/rep)

_P(rep/cig) P (rep/open)

P(elec/rep)

+

P (other/rep)

] p = ± (13) P(rep/elec) P (rep/other)

open = ignition source is open flame

elec = ignition source is electrical

other = ignition source is other

70
The probabilities for each of the ignition sources conditional on the fire being reported are obtained directly from the NFIRS data base

as shown in table 16. The probabilities of the fire being reported, given

a particular ignition source, are determined from the auxiliary probability trees. Substituting these values into equation (13), we obtain

0.7031 0.1294 0.0520 0.1155

0.2579 0.4801 0.4807 0.3858 P(rep) = 1

or

P(rep) = 0.2938

The probability that the fire is reported is used to obtain the total

number of all upholstered furniture fires (both reported and unreported)

As detailed in section 3.1, based on the annual number of fire fatalities,

we estimate that there are 47, 500 reported upholstered furniture fires

annually. Dividing this estimate by 0.29 38, the probability that the

fire is reported, we obtain 161,600 upholstered furniture ignitions

annually under current conditions

For use in later calculations it is also useful to calculate the

unconditional ignition source probabilities, that is, the probabilities

of ignition source unconditional on whether the fire is reported. The

unconditional ignition source probabilities are obtained by substituting

the required values into equation (10) and similar equations for the

remaining ignition sources. We obtain the unconditional ignition source probabilities given in table 26. Multiplying each of the ignition source probabilities by 161,600, the total number of ignitions, we obtain the

total number of all fires (both reported and unreported) for each ignition

source shown in table 26.

Table 26. Ignition Source Distribution for All Fires

Under Current Conditions

Ignition

Source Probability

Current

Number of

Ignitions

Cigarette

Open Flame

Electrical

Other

0.8010

0.0792

0.0318

0.0880

129 442

12 799

5 139

14 221

Total 1.0000 161 600

71
5. DERIVATION OF LOSS RESULTS UNDER THREE

ALTERNATIVE INTERVENTION STRATEGIES

This section provides a detailed derivation of the losses under the

three intervention strategies. Many of the results have already been

summarized in section 3. They are repeated here along with the underlying input data and assumptions to provide complete documentation of

the results and their derivation.

5.1 Losses Under the No-Action Alternative

One intervention strategy for reducing upholstered furniture fire

losses is for the government to take no formal action at all. However, even under this strategy it is likely that upholstered furniture fire

losses will decline over time because of the increased installation of

smoke detectors and the current use of more smolder resistant materials

in furniture production. Since it will take a number of years for these

changes to take place, we model the losses under the no-action alternative

at a number of points in time. We begin by modeling the losses for the case in which the projected smoke detector level has been reached and

the current furniture population has been completely replaced with new

furniture. We call this the "steady state" or "fully implemented" case. We then develop the losses for the intermediate years.

5.1.1 Steady-State Losses Under the No-Action Alternative

To model the steady-state losses under the no-action alternative,

we first address the smoke detector installation. We assume that

eventually 60 percent of the homes in the United States will install at

least one smoke detector because of either concern for fire safety or local ordinances. Thus, in modeling the steady-state losses under the

no-action alternative we revise the probability of there being a functional smoke detector, in the fire loss model. The second trend addressed

in modeling the steady-state losses under the no-action alternative is a shift in the composition of upholstered furniture. Current (1975) fire

losses, developed in section 4, depend upon the flammability characteristics of the furniture currently in our homes, "the current furniture

population" or "pre-1975 furniture." Considerable quantities of cellulosic upholstery and cellulosic stuffing materials were used in the

construction of this furniture in past years. Many of these cellulosic

upholstery materials and fillings have now been replaced by thermoplastic

materials and polyurethane foam cushioning in current furniture production.

This is important since the thermoplastic materials tend to be more

smolder resistant. However, once ignited, the furniture being produced

now is likely to develop a larger fire because of the increased use of

polyurethane foam. We assume that under the no-action alternative the

current furniture population, of pre-1975 construction, will be replaced

by a new furniture population, of post- 1975 construction, similar in

72
flammability characteristics to furniture being produced now. Thus in

modeling the steady-state losses under the no-action alternative, we adjust the probabilities of ignition source, fire type, and extent of

flame damage to reflect the different flammability properties of the

post-1975 furniture. The other input probabilities, such as the probability of at least one person being home, remain the same as for current

conditions. The losses associated with a particular path through the

tree also remain the same as for current conditions.

5.1.1.1 Revised Functional Smoke Detector Probability

We assume that smoke detector usage will increase from the current

level of 5 percent functional to 48 percent functional, based on a 60 percent installation level with 80 percent of the detectors operational.

5.1.1.2 Revised Ignition Source Probabilities

Fire technology experts have estimated that smoldering ignitions

will be reduced by one-third when the current furniture population has

been completely replaced with new furniture, and also that there will be

a 10 percent reduction in the number of flaming ignitions. Using these

estimates, the revised number of ignitions and ignition source probabilities are calculated as shown in table 27. The table shows the

different combinations of ignition source and ignition class. The

column labeled "current number of ignitions" gives the number of fires

by source and initial ignition type for current conditions, derived from

tables 17 and 26. The second column gives the fraction of ignitions

that would still occur under the reduction factors discussed above. The

third column, the product of the first two columns, gives the number of

ignitions by source and type under the fully implemented no-action

alternative

.

The table shows that the total number of ignitions is projected to

decrease from 161,600 to approximately 111,000 ignitions per year. The

primary reason for the decrease in the total number of ignitions is the

projected one-third reduction in smoldering ignitions. (The assumption

of a constant U.S. population at the 1975 level is important to this

projection. Otherwise, the reduction would be in the same ratio 111,000:

161,600 but would have to be handled on a per capita basis.)

5.1.1.3 Revised Fire Type Probabilities

The fire type probabilities are the probabilities that the fire never leaves the smoldering state (SM) ; that the fire smolders and then

flames (SM/FL) ; or that it begins in a flaming state (FL) . As before,

we assume the fire type probabilities depend on the ignition class

73
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74
(whether the fire begins smoldering or flaming) and on whether the fire

is discovered before leaving the chair. Using the fire type dependencies

given in figure 13, the revised ignition class probabilities from table 27 are used to obtain revised fire type probabilities under the steady-state

no-action alternative. The calculations are given in fiaure 17. (No

calculations are given for cigarette ignition source since there is no change from current conditions .

)

5.1.1.4 Revised Probabilities for Extent of Flame Damage

Although the currently produced or "new" furniture is less likely

to ignite, there is evidence that once ignited, a larger fire than we expect under current conditions is likely. To model this phenomenon we

assume, based on discussions with fire research experts at the Center

for Fire Research, National Bureau of Standards, and the California

Department of Consumer Affairs, that only 60 percent of those fires

currently confined to the room will remain so confined. Using these

assumptions we compute the revised probability distribution on extent of

flame damage as shown in table 28. The intermediate distribution is

found by multiplying the current "C" probability by . 6 and assuming

that the remaining fires are "R" and ">R" in the same proportion as before. The revised probabilities are found by retaining the "C"

probability just calculated, multiplying the intermediate "R" probability

by 0.6, and then normalizing to find the probability of ">R. " As shown,

the probability of a discovered fire that ultimately flames being confined

to the chair declines from 0.83 to 0.50. The probability of such fires

spreading beyond the room increases from 0.10 to 0.38.

5.1.1.5 Calculation of Steady-State Losses

Under No-Action Alternative

The fire loss model is used to calculate the steady-state lossesunder the no-action alternative. Except for the ignition source, fire

type, extent of flame damage, and functional smoke detector probabilities,

the input probabilities to the fire loss model are the same as for

current conditions. The outcome assignments for a particular path

through the tree are kept the same as for current conditions since we

are using constant dollars throughout the analysis.

The revised input probabilities are used with the original auxiliary

trees of figure 10 to recalculate the required loss model probabilities

conditional on the fire being reported. The revised probability of a fire being reported, also determined from these calculations (described

in section 4), is found to be 0.272 compared to 0.294 for current conditions. The revised conditional probabilities, along with the revised

flame extent probabilities, are used with the main tree of figure 9 to

calculate the steady-state losses resulting from a single reported

upholstered furniture fire under the fully implemented no-action alternative.

75
IGNITION SOURCE IGNITION CLASS

IS FIRE DISCOVERED

BEFORE LEAVING

CHAIR ?

FIRE TYPE

REVISED

FIRE TYPE

PROBABILITY

OPEN FLAME

SMOLDERING

0.2419

FLAMING

DISCOVERED

NOT DISCOVERED

SM

0.95

v SM FL

0.05

SM

0.08

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FL 0.7581 1.00

0.2298

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0.0194

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0.7581

SM

ELECTRICAL

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FLAMING

DISCOVERED

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0.95

SM FL 0.05 SM

0.08 SM FL 0.92

FL 0.3655 1.00

0.6028

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0.3655

SM

OTHER

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FLAMING

DISCOVERED <095 SM FL

NOT DISCOVERED <

0.05

SM

0.08 SM/FL

0.92

FL

0.8266

0.0435

0.0696

0.8005

0.1299 0.1299 1.00

Figure 17. Calculation of Revised Fire Type Probabilities

Under No-Action Alternative

76
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77
Table 29 gives the resultant probability distributions on aggregate

loss for a single reported upholstered furniture fire under the fully

implemented no-action alternative. A graph of the cumulative probability

distribution is given in figure 18. The range of possible losses is the same as under current conditions, from $460 to $58,800, but the likelihood

of the different values has changed. Whereas there is 0.14 probability

of the total losses per fire exceeding $58,800 under current conditions,

there is a 0.17 probability of that occurring under the steady-state no- action alternative. The expected aggregate loss, given a reported

ignition, is $16,100 compared to $14,100 for current conditions.

Table 29. Probability Distributions on Aggregate Losses

Under No-Action Alternative

Aggregate

Loss

(Dollars) Probability

Cumulative

Probability

$ 458

2 204

2 569

3 077

4 493

11 864

15 504

16 071

18 249

58 832

0.00041

0.40808

0.00003

0.06962

0.03412

0.09470

0.00009

0.10498

0.12201

0.16596

0.00041

0.40849

0.40852

0.47814

0.51227

0.60697

0.60706

0.71204

0.83404

1.00000

Table 30 gives the expected losses by category. To obtain the

total annual losses, the number of reported fires is calculated as the

product of the number of ignitions and the probability of the fire being

reported, or 111 000 x 0.272 = 30,200. By multiplying this number by

the loss per reported fire, the total expected losses are obtained. The

table shows that total annual U.S. losses under the steady-state no- action alternative are $486 million, compared to $668 million under

current conditions. More than half of the $486 million in aggregate

loss is due to loss of life. The total number of fatalities under the

fully implemented no-action alternative is 878 compared to 1312 under

current conditions. Thus the combined effect of the increased smoke

detector installation level and the more smolder-resistant furniture

population is to reduce total expected U.S. losses occurring in residential

upholstered furniture fires by $182 million per year.

78
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Figure 18. Cumulative Distribution on Aggregate Losses

Under No-Action Alternative

Table 30. Reported Upholstered Furniture Fire Losses

Under Fully Implemented No-Action Alternative

Expected Loss Per Fire Total Annual Expected Losses

Category

Monetary Monetary Equivalent

Number Equivalent Number (Millions of Dollars)

0.0291 $ 8 720 878 $263

0.162 1 620 4900 49

4 930 149

800 24

$16 100 $486

Fatalities

Injuries

Property

Tangible

Intangible

Aggregate

Obtained by multiplying the expected loss per fire by 30,200, the

annual number of reported upholstered furniture fires

79
5.1.2 No-Action Alternative Losses Over Time

It will take a number of years for the losses under the no-action

alternative to reach the steady-state level just calculated. We assume

that the smoke detector installation level will increase from its 1977

level of 5 percent functional to the steady-state level of 48 percent

functional by 1980. It will take many more years for the furniture

population to be completely replaced. Both of these effects must be

modeled if we are to model the losses over time under the no-action

alternative

Our approach is to calculate the losses for an intermediate year

and then to obtain the losses in the intervening years by interpolation.

We choose 1980 as the intermediate year because that is when the voluntary

smoke detector level is assumed to rea'ch its steady-state value. In

calculating the losses for 1980 we divide the 1980 furniture population

into furniture that was made before and after 1975 (i.e., currently

installed furniture and currently produced furniture) . The expected

losses in 1980 can therefore be calculated by determining the losses for

each population group with the smoke detector level at its steady-state

value and then averaging according to the relative size of each group.

We have already calculated the losses for the post-1975 population

(currently produced furniture) in which the smoke detector installation

is at the steady-state level (table 30) . The losses for the pre-1975

furniture population are calculated by using the fire loss model to

determine the losses for the case in which the furniture population is

the currently installed population and in which the smoke detector

installation rate has reached its ultimate level of 60 percent (48 percent

functional) . This is done by using the fire loss model with the probability and outcome assignments developed for current conditions in

section 4 except that the probability of a functional smoke detector is

set to 0.48. The losses resulting from these calculations are given in

table 31.

In order to determine the relative fraction of pre-and post-1975

furniture in 1980 we need to model the upholstered furniture replacement

pattern. Based on work done at the University of Maryland, we assume

that furniture lifetimes are normally distributed [22] . We assume a mean lifetime of 17 years and standard deviation of 3.3 years.

Using a constant annual future production, based on our constant

population assumption, and past production data, we derive the resultant

furniture replacement pattern shown in figure 19. Since upholstered

furniture production will likely increase in the years to come, the

mix of furniture may change more rapidly than predicted by this model.

A sensitivity study on the furniture replacement pattern is given in

section 7.2.1.

80
Table 31. Total Annual Losses for Currently Installed Furniture

Population Assuming 60 Percent Installation Level of Smoke Detectors

Category

Total Annual Expected Losses

Number

Monetary Equivalent

(Millions of Dollars)

Fatalities

Injuries

Property

Tangible

Intangible

Aggregate

932

5590

$280

56

138

21

$495

o

_i

O

o

Figure 19. Furniture Replacement Rate Curve

81
The figure shows that according to our replacement model 30 percent

of the 1975 furniture population will be replaced by post- 1975 vintage

furniture by 1980. Taking a weighted average of the losses for the preand post-1975 populations as given in tables 30 and 31 gives the expected

losses for the year 1980. The calculations are shown in table 32.

Losses for the years 1981 through 2004 are found by interpolation,

by obtaining the fraction of pre- and post-1980 furniture for each year

from figure 19 and then taking the appropriate weighted average of the

corresponding losses. The expected losses for the years between 1975

and 1980 are estimated by simple linear interpolation. Losses for the

year 2005 and all subsequent years are set equal to the steadv-state

losses (table 30)

Figure 20 gives the resultant losses over time. The figure shows

the current losses of $668 million declining to $492 million by 1980 and

finally leveling off at $485 million per year by 2005. The steep decline

in the early years is due to the installation of smoke detectors during

the period 1975 to 1980.

O

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1975 1980 1985 1990 1995 2000 2005

YEAR

Figure 20. Annual Aggregate Loss Under No-Action Alternative

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5.2 Losses Under the Smoke Detector Alternative

A second intervention strategy for reducing upholstered furniture

fire losses is the enactment of federal legislation requiring smoke

detectors in all U.S. residences. The effect of this strategy would be

to increase the steady-state smoke detector installation level from our assumed 60 percent rate to some higher installation rate, depending on the level of compliance. Therefore, our approach in modeling the losses

under this alternative is to assume a new steady-state installation

level and to change the functional smoke detector probability accordingly.

Since this alternative has no impact on the furniture itself, we assume

the same furniture evolution under this alternative as under the no- action alternative. Thus, the probability assignments for loss model

parameters related to upholstered furniture fire behavior are the same

as for the no-action case.

5.2.1 Revised Input Probabilities

We assume that 90 percent of all residences will eventually comply

with the smoke detector requirement. Even though the requirement is for

all residences to have detectors, we assume that a small fraction, 10

percent, will never comply because of ignorance, lack of concern, or out-right disobedience. We also assume that 80 percent of the installed

detectors will be operational. Thus, the steady-state probability of

there being a functional smoke detector is set at 0.90 x 0.80 = 0.72.

The furniture population under the smoke detector alternative is

the same as for the no-action alternative. Therefore, the probabilities

of ignition source, fire type, and extent of flame damage are as given

in tables 27 and 28 and figure 17. The probability assignments for the

other parameters as well as the outcome assignments remain unchanged.

5.2.2 Calculation of Steady-State Losses Under

Smoke Detector Alternative

The revised probabilities are used as inputs to the fire loss model

to obtain the steady-state losses under the detector alternative. The

method used is the same as for the no-action alternative as described in

section 5.1.1.5. The resultant probability distributions of losses per

reported upholstered furniture fire are given in table 33. A graph of

the cumulative distribution is given in figure 21. The figure shows

that there is a 0.13 probability of the losses per fire exceeding $58,800

compared to a 0.17 probability under the fully .implemented no-action

alternative. The expected aggregate losses are $13,900 per reported

fire. The revised probability that the fire is reported, also calculated

from the fire loss model, is 0.256 compared to 0.272 for the no-action

alternative

84
Table 33. Probability Distributions on Aggregate Losses Under Smoke Detector Alternative

Aggregate Cumulative

Loss Probability Probability

(Dollars)

$ 458 0.00051 0.00051

2 204 0.44489 0.44540

2 569 0.00004 0.44543

3 077 0.07394 0.51937

4 493 0.03693 0.55631

11 864 0.07280 0.62911

15 504 0.00012 0.62922

16 071 0.11362 0.74284

18 249 0.12958 0.87242

58 832 0.12758 1.00000

10,000 20,000 30,000 40.000 50,000 60,000 70,000

AGGREGATE LOSS IDollars]

Figure 21. Cumulative Distribution on Aggregate Losses

Under Smoke Detector Alternative

85
Table 34 gives the expected loss by category. The total number of

reported fires, 28,400, is obtained by multiplying the number of ignitions

expected in the steady-state no- action alternative furniture population,

111,000, by the probability that the fire is reported, 0.256. This is

again used to obtain the total annual expected losses of $396 million as shown in the table. The loss of life component again accounts for more

than half of the aggregate losses. There are 678 fatalities annually

compared to 1312 under current conditions and 878 under the steady-state

no-action alternative. The total U.S. losses of $396 million compare to

$486 million under the steady-state no-action alternative and $668

million under current conditions. Thus the effect of increasing the

smoke detector installation level from 60 to 90 percent is to reduce

total U.S. losses occurring in residential upholstered furniture fires

by about $90 million per year.

Table 34. Reported Upholstered Furniture Fire Losses Under

Fully Implemented Smoke Detector Alternative

Expected Loss Per Fire

Monetary

Category Number Equivalent

Fatalities 0.0239 $ 7, 160

Injuries 0.139 1,390

Property

Tangible 4,630

Intangible 750

Total Annual Expected Losses

Monetary Equivalent

Number (Millions of Dollars)

678

3960

Aggregate $13,900

$203

40

131

21

$396

Obtained by multiplying the expected loss per fire by 28,400, the

annual number of reported upholstered furniture fires

5.2.3 Losses Under the Smoke Detector Alternative Over Time

In modeling the losses over time for the smoke detector alternative

we assume that the program takes effect in 1980 and that it takes until

1985 for the detector installation to reach its projected level of 90

percent. Losses for the years 1977 to 1980 are the same as for the no- action alternative. Losses for the years between 1985 and 2005 are based on the changing furniture population (figure 19) and are found in

the same manner as those for the no- action alternative. The calculations

for the years from 1980 through 1985 take into account both the changing

furniture population and the increased level of smoke detector installation. The losses for the years after 2005 are constant and equal to the

2005 steady-state losses (table 34)

86
Figure 22 gives the resultant losses over time for the smoke detector

alternative. The figure shows total U.S. losses declining from the

current level of $668 million per year to $396 million. Most of the

loss reduction occurs by 1985 when the projected level of smoke detector

installation has been reached. The continuing slight decline in losses

between 1985 and 2005 is attributable to the continuing replacement of

the furniture population.

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Figure 22. Annual Aggregate Loss Under Smoke Detector Alternative

5.3 Losses Under the Proposed Upholstered Furniture Standard

A third intervention strategy is the proposed upholstered furniture

standard currently under consideration by the Consumer Product Safety

Commission. The proposed standard, described in detail in section 3, is

intended to eliminate combinations of fabric and furniture construction

that are vulnerable to cigarette ignition. We consider two methods for

meeting the proposed standard. We first consider the use of a needlepunched aluminum foil barrier for use in dissipating the heat build-up

from dropped cigarettes. We then consider the use of a backcoating

87
containing microencapsulated sulfur to make upholstery fabrics more

smolder resistant. The backcoating method is considerably less expensive

than the barrier method, but has yet to be tested and demonstrated under

commercial conditions. Our purpose in modeling a second method of

compliance with the standard is to give some consideration to new technology which might allow compliance at a lower cost.

5.3.1 The Barrier Method for Meeting the Proposed Standard

We first evaluate the effectiveness of the barrier method under

full compliance and then we assume a level of compliance for evaluating

the losses under this alternative.

5.3.1.1 Full Compliance

The primary effect of the proposed standard is to reduce smoldering

ignitions from cigarettes and other ignition sources. Since the barrier

has been designed to prevent cigarette ignitions, we assume that all

cigarette ignitions will be eliminated if full compliance is obtained.

We assume that smoldering ignitions from electrical and other sources

will be reduced by 80 percent.

The treated cotton batting used in conjunction with the aluminum

foil barrier provides some protection from flaming ignitions. We assume

that flaming ignitions from open flame and electrical sources will be

reduced by 30 percent. However, since open space heaters, a major

component of "other" ignition sources, are a relatively large heat

source, we assume that flaming ignitions from other sources will be

reduced by only 20 percent under the barrier method.

The revised ignition source probabilities are calculated as shown

in table 35. The calculations are analogous to the calculations for the

no-action alternative, except that we have used the reduction factors

appropriate for the proposed standard. The table shows that the probability of the ignition source being a cigarette declines from 0.80

under current conditions to 0.0 under the barrier method with full

compliance. The total number of ignitions is projected to decline from

the current level of 161,600 ignitions per year to approximately 11,800

ignitions per year under the barrier method with full compliance.

Table 35 also provides the basis for computing the new fire type

probabilities. These calculations are also analogous to those for the

no-action alternative. The results for three ignition sources are summarized in table 36. No results are shown for cigarette ignitions

since that ignition probability is zero.
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89
Table 36. Probability Distributions on Fire Type Under Fully

Implemented Proposed Standard (Barrier Method)

with 100 Percent Compliance

Is Fire Discovered Probability

Ignition Before Fire Type Under

Source Leaving Chair? Standard

SM 0.0000

Discovered SM/FL 0.0000

Open Flame FL 1.0000

SM 0.0000

Not Discovered SM/FL 0.0000

FL 1.0000

SM 0.3799

Discovered SM/FL 0.0200

Electrical FL 0.6001

SM 0.0320

Not Discovered SM/FL 0.3679

FL 0.6001

SM 0.6577

Discovered SM/FL 0.0346

Other FL 0.3077

SM 0.0554

Not Discovered SM/FL 0.6369

FL 0.3077

Since most of the construction materials will be similar under both

the proposed standard and the steady-state no-action alternatives, we use the same extent of flame damage probabilities for the two cases. Thus,

the extent of flame damage probabilities under the proposed standard with

full compliance are as given in table 28. We also use the same 0.48

functional smoke detector probability for the two cases, because the

proposed standard has no special provision for_ enhancing the installation

of smoke detectors . The other probability assignments remain the same as those for current conditions

The revised probability assignments as just presented are used in

the fire loss model to calculate the loss distributions for a single

reported upholstered furniture fire under the proposed standard using

the barrier method with full compliance. The results are given in

table 37. A graph of the cumulative distribution is given in figure 23.

Although the possible values of loss are the same as those for current

90
Table 37. Probability Distributions on Aggregate Losses Under Proposed Standard Using the Barrier Method

with 100 Percent Compliance

Aggregate Cumulative

Loss Probability Probability

(Dollars)

$ 458 0.00044 0.00044

2,204 0.39957 0.40001

2,569 0.00008 0.40009

3,077 0.04946 0.44955

4,493 0.08931 0.53886

11,864 0.03614 0.57500

15,504 0.00025 0.57525

16,071 0.27474 0.84999

18,249 0.08668 0.93667

58,832 0.06333 1.00000

10.000 20.000 30.000 40.000 50.000 60,000 70,000

AGGREGATE LOSS SDollars)

Figure 23. Cumulative Distribution on Aggregate Losses

Under Proposed Standard Using the Barrier Method

91
conditions, ranging from $460 to $58,800, the figure shows that the

likelihoods of the different outcomes have changed substantially under

the proposed standard. Whereas there was a . 14 probability of a fire

with expected losses exceeding $58,800 under current conditions, there

is only a 0.063 probability of such a fire occurring under the proposed

standard. The expected aggregate loss, given a reported ignition, is

$11,600, compared to $14,100 under current conditions.

Table 38 gives the expected losses per reported fire for the proposed standard using the barrier method with full compliance. The

expected fatalities per reported fire are now 0.0162 compared to 0.0276

under current conditions . The table shows that the monetary value of

the expected fatality loss is approximately equal to the expected tangible

property loss, each accounting for about 42 percent of the aggregate

losses

Table 38. Reported Upholstered Furniture Fire Losses Under

Fully Implemented Proposed Standard (Barrier Method)

with 100 Percent Compliance

Expected Loss Per Fire

Monetary

Category Number Equivalent

Fatalities 0.0162 $ 4,860

Injuries 0.112 1,120

Property

Tangible 4,820

Intangible 790

Total Annual Expected Losses

Monetary Equivalent

Number (Millions of Dollars)

104

719

Aggregate $11,600

$31

7

31

5

$74

Obtained by multiplying the expected loss per fire by 6,430, the annual

number of reported upholstered furniture fires

Although the total number of ignitions declines under the proposed

standard using the barrier method with full compliance, the probability

of an ignition being reported increases. The reason is that a higher

percentage of fires that do occur under the proposed standard are serious,

The probability that the fire is reported is calculated to be 0.546.

Thus an expected 6,430 of the 11,800 fires under the barrier method with

full compliance will be reported. Total expected annual losses are found by multiplying the expected loss per reported fire by the expected

number of reported fires. The results, also shown in table 38, give an expected total annual loss of $74 million under the fully implemented

proposed standard using the barrier method with full compliance.

92
5.3.1.2 Partial Compliance

Several factors, including the use of slipcovers, noncompliant

upholstering, poor manufacturing quality control, and loss of ignition

resistance due to soil and wear, make it unlikely that the proposed

standard will ever achieve full compliance. Therefore, in this section

we investigate the effectiveness of the barrier method assuming that

only 80 percent compliance is achieved.

In modeling the partially compliant case, we assume that the non- compliant furniture is equivalent in burning characteristics to the

currently produced furniture assumed under the no-action alternative.

Thus the expected losses for a particular compliance level are found by

taking a weighted average of the losses from the fully compliant proposed

standard furniture population and the no- action furniture population.

The calculations are shown in table 39.

The table shows that the total annual losses are $157 million for

the 80 percent compliant case, compared to $74 million for the fully

compliant case. Furthermore, the 20 percent noncompliant furniture

population contributes 62 percent of the aggregate loss, 68 percent of

the fatalities, 63 percent of the injuries, and 55 percent of the property

loss as well as 54 percent of the reported fires and 70 percent of the

ignitions . Thus achieving a better compliance level than 80 percent

would appear to affect the expected losses. A sensitivity study on the

compliance level is presented in section 7.4.3.

5.3.1.3 Losses Over Time

It will take a number of years for the proposed standard to become

fully implemented, even at the 80 percent compliance level. The reason

is that, according to our furniture replacement model shown in figure

19, it takes about 30 years for essentially all of the furniture to be

replaced. The losses over time are modeled in the same way for the

proposed standard as for the no-action alternative. The only difference

is that the furniture replacement is assumed to begin in 1980 when the

standard takes effect, rather than in 1975 when the currently produced

or post-1975 furniture replacement begins. Also, at any point in time

only 80 percent of the post-standard furniture is assumed to be compliant.

Figure 24 gives the losses over time for the proposed standard using

the barrier method with 80 percent compliance.

8

The furniture replacement model used for post-1975 furniture in modeling

the no-action alternative is also used for post-1980 furniture produced

under the proposed standard.

93
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Alternative Using the Barrier Method

5.3.2 The Backcoating Method for Meeting the Proposed Standard

A second possible method for meeting the proposed standard is to

apply a backcoating to upholstery fabrics. As discussed in section

3.7.2 it is possible that existing backcoating products could be used;

however, in this section we consider the use of a backcoating containing

microencapsulated sulfur. Although this method has been demonstrated in

the laboratory, it has not been tested under field conditions and there

is some question as to whether it is a feasible alternative. We investigate the effectiveness of the sulfur backcoating method, assuming that

it performs as demonstrated under laboratory conditions.

As with the barrier method, we investigate the effectiveness of the

backcoating method assuming full compliance with the proposed standard

before considering the case of partial compliance.

95
5.3.2.1 Full Compliance

The primary effect of the sulfur backcoating is to reduce the

incidence of smoldering ignitions. Based on laboratory experience

accumulated to date, we assume that all smoldering ignitions from

cigarettes, open flame and electrical sources are eliminated. We assume

a 50 percent reduction in smoldering ignitions from other sources. The reason is that many of the "other" ignition sources, such as space

heaters with a sustained heat source, may eventually volatize the sulfur

in the backcoating.

Laboratory experience to date indicates that sulfur treated fabric

may be slightly more susceptible to flaming ignitions than untreated

fabrics. To reflect this phenomenon, we increase the incidence of

flaming ignitions by 10 percent.

The revised ignition source probabilities using the above assumptions

on likelihood of ignition are calculated as shown in table 40. The

calculations are analogous to those performed for the barrier method.

Also given in the table is the annual number of ignitions occurring

under the proposed standard using the sulfur backcoating method with

full compliance. The table shows that the expected number of ignitions

under the backcoating method with full compliance is approximately 19, 500

ignitions per year, compared to 11,800 under the barrier method and

111,000 under the steady-state no-action alternative. The revised

probability distributions on fire type are shown in table 41. Since

smoldering ignitions are expected only for the "other" category, only

this category is shown. Again, the method of computation parallels that

previously presented.

In modeling the proposed standard using the barrier method, we assume that the extent of flame damage probability distributions are the same as under the steady-state no-action alternative, since the

furniture populations in both cases have similar constructions using

similar amounts of polyurethane foam. However, the extent of flame

damage probabilities must be adjusted to model the backcoating method,

because of the propensity of sulfur-backed materials to burn more

intensely. We use the same adjustment method as used for the no- action

alternative (shown in table 28). However, in this case we use adjustment

factors of 0.5 instead of the 0.6 factor used for the no-action alternative. Table 42 gives the distributions on extent of flame damaqe for

current conditions, no-action and the proposed standard using the

backcoating method.

The probability of a functional smoke detector is set at 0.48, the

same as that for the no-action alternative and the barrier method of

meeting the proposed standard. All of the other probability assignments

are the same as those for current conditions.

96
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97
Table 41. Probability Distributions on Fire Type Under Fully

Implemented Backcoating Method of Compliance with Proposed Standard

Is Fire Discovered Probability

Ignition Source Before Fire Under

Leaving Chair? Type Backcoating Method

SM 0.7634

Discovered SM/FL 0.0402

Other

FL 0.1964

SM 0.0643

Not Discovered SM/FL 0.7393

FL 0.1964

Table 42. Probability Distributions on Extent of Flame Damage

for Current Conditions, No-Action, and Fully Implemented

Proposed Standard (Backcoating Method)

Is Fire

Discovered

Before

Leaving

Chair?

Extent of

Flame Damage

Extent of Flame Damage Probability

Current

Conditions No-Action

Proposed Standard

(Backcoating)

Discovered

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0.0986

0.4999

0.1227

0.3774

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0.1193

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0.3945

0.0000

0.3633

0.6367

0.0000

0.3028

0.6972

98
The above assumptions on ignition, fire type, and extent of flame

damage are used in conjunction with the fire loss model to calculate the

possible losses resulting from a single reported upholstered furniture

fire under the proposed standard using the backcoating method with full

compliance. The resulting distributions are given in table 43.

Table 43. Probability Distributions on Aggregate Losses

Under Proposed Standard Using the Backcoating Method

Aggregate

Loss

(Dollars)

Probability

Cumulative

Probability

$ 458

2,204

2,569

3,077

4,493

11,864

15,504

16,071

18,249

58,832

0.00039

0.33848

0.00007

0.04279

0.08431

0.03240

0.00029

0.32811

0.09854

0.07461

0.00039

0.33887

0.33895

0.38174

0.46605

0.49845

0.49874

0.82684

0.92539

1.00000

The expected losses per fire are given in table 44. The probability

of an ignition being reported is calculated to be 0.528. Thus an expected

10,300 of the 19,500 fires under the backcoating method with full

compliance will be reported. As shown in the table, the total annual

expected losses under the backcoating method with full compliance are calculated to be $13 100 x 10 300 = $135 million.

5.3.2.2 Partial Compliance

As with the barrier method, we assume that in practice only 80

percent of furniture will be compliant with the proposed standard using

the backcoating method. Total expected losses for this case of partial

compliance are found by taking a weighted average of the results for the

fully compliant case and the no-action alternative. The computations

are given in table 45. As shown in the table, total annual losses for

the 80 percent compliant case are $205 million, compared to $97 million

for the fully compliant case.

99
Table 44. Reported Upholstered Furniture Fire Losses Under

Fully Implemented Proposed Standard (Backcoating Method)

with 100 Percent Compliance

Category

Expected Loss Per Fire

Number

Monetary

Equivalent

Total Annual Expected Losses

Monetary Equivalent

Number (Millions of Dollars)

Fatalities 0.0181

Injuries 0.122

Property

Tangible

Intangible

Aggregate

$ 5,430

1,220

5,540

920

$13,100

186

1250

$ 56

13

57

10

$135

Obtained by multiplying the expected loss per fire by 10,300, the

annual number of reported upholstered furniture fires

5.3.2.3 Losses Over Time

Losses over time under the backcoating method are calculated exactly

as for the barrier method. The resulting aggregate loss is given in

figure 25. The figure also shows how these losses compare with the

losses under each of the three nominal alternatives.

100
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700

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NO ACTION

PROPOSED STANDARD

(BACKCOATINGj

PROPOSED STANDARD

[BARRIER METHOD]

1975 1980 1985 1990 1995

YEAR

2000 2005 2010

Figure 25. Annual Aggregate Losses Under Proposed Standard Using

the Backcoating Method and Three Nominal Alternatives

102
6. DERIVATION OF COST RESULTS

This section gives a detailed derivation of the costs of implementing

each intervention strategy. The basic cost estimates were summarized in

section 3, but without detail on the individual cost elements. This

section provides that detail.

6.1 No-Action Alternative

We define the costs of the no-action alternative to be zero, since

it is the baseline against which the other alternatives are compared.

Actually costs are incurred under this alternative, such as expenditures

for voluntary and locally required purchases of smoke detectors. But

since these expenditures are made under .all of the alternatives, we set

the costs equal to zero to keep the cost accounting simple. This simplification does not affect the relative evaluation of the alternatives.

6.2 Smoke Detector Alternative

The principal costs of the smoke detector alternative are the costs

of purchasing and maintaining the required smoke detectors. We assume

that the impact of this intervention strategy will be to increase the

detector installation level from 60 to 90 percent over a five year

period. Assuming a constant population of 72 million households during

the time frame of this analysis [23], we calculate that 0.30 x 72 = 21.6 million first time purchases will be made under the detector

alternative. We assume that detectors have an average lifetime of ten

years and thus we assume that 10 percent of the installed detectors will

be replaced in any given year.

9

We assume that the average purchase cost of a detector is $20. We assume an average $2 installation cost for all detectors, based on $20

installation costs for house-wired detectors and zero installation costs

for battery operated detectors, the latter of which are expected to make

up 90 percent of all detectors by 1980. We also assume an annual maintenance cost of $1.80 per detector based on battery replacement costs or

an equivalent amount of electricity for house current detectors.

(Although some detectors now require the considerably more expensive

mercury batteries, the $1.80 figure is based on the expectation that

essentially all smoke detectors manufactured after 1980 will use the

less expensive 9 volt alkaline batteries.)

9

All cost estimates are in 1977 dollars.

103
Table 46 gives the costs of the required smoke detector purchases

for several selected years. The costs include initial year purchases as well as replacement and maintenance costs. The table shows that the

annual costs begin at $102.8 million, reach a maximum of $171.9 million

in 1984, and then level off at $86.4 million for 1985 and beyond.

Table 46. Annual Cost of Required Smoke Detectors

Cost

(Millions of Dollars)

Year

Initial

Installation

Operation

and

Maintenance Replacement Total

Upholstered

Furniture

Fire

Allocation

1975-9 $ 0.0 $ 0.0 $ 0.0 $ 0.0 $ 0.0

1980 95.0 7.8 0.0 102.8 29.8

1981 95.0 15.6 9.5 120.1 34.8

1982 95.0 23.3 19.0 137.3 39.8

1983 95.0 31.1 28.5 154.6 44.8

1984 95.0 38.9 28.0 171.9 49.9

1985 & beyond0.0 38.9 47.5 86.4 25.1

The total costs associated with the required smoke detector purchases

are given in column 4 of table 46. However, it is not appropriate to

assign all these costs to the smoke detector intervention strategy for

reducing upholstered furniture fires, because smoke detectors impact on many types of residential fires. We allocate a fraction of the total

costs according to the relative impact that smoke detectors have in

upholstered furniture fires compared to other residential fires.

Our approach is to allocate the costs according to the relative

fraction of deaths prevented in upholstered furniture fires versus other

types of residential fires. We assume that a properly installed and

operating smoke detector in every residence could reduce the loss of

life in all residential fires by about 60 percent. The 60 percent

figure is based on estimates of a 41 percent reduction in fatalities by

McGuire and Roscoe [25] , a 71 percent reduction in fatalities by Halpin,

Dinan and Deters [26] , and a report from the Ontario Housing Corporation

[26] that smoke detectors "discovered" 85 percent of the fires which

occurred in their dwellings. We calculate in table 2 that there are currently 4860 fire deaths in one- and two-family dwellings and thus we

104
estimate that detectors could save about 0.60 x 4,860 = 2,920 lives per

year. We also calculate in section 3.3.1 that smoke detectors would

reduce the loss of life in upholstered furniture fires by about

65 percent. Based on our current estimate of 1310 upholstered furniture

fire fatalities per year, we therefore estimate that detectors would

save about 0.65 x 1310 =850 lives per year in upholstered furniture

fires. We therefore estimate that 850/2920 = 29 percent of the smoke

detector life savings will be from upholstered furniture fires.

Therefore, as shown in column 5 of table 46, we assign 29 percent of the

total smoke detector costs to the smoke detector alternative.

The total societal cost of the smoke detector alternative must

include governmental costs for enforcement and education. We include

annual costs of $1 million to reflect the portion of this cost attributable to upholstered furniture fires. The total annual cost of the

smoke detector alternative is therefore obtained by adding $1 million to

column 5 of table 46.

6.3 Proposed Upholstered Furniture Standard

We assume that regardless of the compliance mechanism, the proposed

standard will result in an increase in the cost of manufacturing upholstered furniture. This increased cost will in turn be passed on to the

consumer, augmented to a certain extent by the effects of commissions

and other middleman costs. To the extent that consumer purchases are sensitive to upholstered furniture prices, some consumers will be forced

out of the market. The costs of the proposed standard, therefore,

include the increased manufacturing and marketing costs as well as the

societal costs of forcing certain consumers out of the market.

6.3.1 Cost of the Barrier Method

6.3.1.1 Initial Cost to Furniture Manufacturers

The costs of the barrier method to the furniture manufacturers in

the first year are summarized in table 47. A primary cost of this

method is the cost of the labor and materials for installing the aluminum

foil barrier. We estimate that about 190 million linear yards of

upholstery fabric will be used in 1980, the first year the standard is

assumed to be in effect. We assume that about 40 percent, or 76 million

linear yards, will be Class D fabric, the fabric type requiring the

barrier. We assume that the barrier will be used only on those portions

of the furniture where a cigarette might fall — about 50 percent of the

furniture's covered area. Therefore, about 38 million linear yards of

aluminum foil barrier will be required to meet the standard. At an estimated cost of $1.05 per linear yard, we calculate the total cost of

the barrier material to be $39.9 million the first year the standard is

in effect.

105
Table 47. Manufacturers' First Year Cost of the Proposed

Standard Using the Barrier Method

Component

Initial Cost

(Millions of Dollars)

Barrier Installation

Material

Labor

Handling

$ 39.9

55.8

8.0

Cotton Batting Treatment 11.6

Testing

Furniture Manufacturers

Fabric Manufacturers

15.2

2.7

Recordkeeping

Furniture Manufacturers

Fabric Manufacturers

1.5

0.9

Research and Development 1.0

Total $136.6

Based on discussions with furniture manufacturers we estimate that

the labor costs for installing the barrier may range from $3.50 to

$10.30 for sofas and $2.50 to $6.70 for chairs. Taking a weighted

average of the midpoints of these estimates, according to the relative

fraction of sofas and chairs, gives an average labor cost of $5.37 per

piece of upholstered furniture. To account for employer payroll expenses

such as social security and insurance contributions, we use a factor of

1.3 to give an effective labor cost of $6.98 per piece of upholstered

furniture. Assuming an annual upholstered furniture production of

20 million pieces, of which 40 percent are made from Class D fabrics, we obtain a total annual labor cost of $55.8 million for the first year the

standard is in effect.

Added inventory and handling costs will be incurred as a result of

using the barrier method to meet the proposed standard. We assume that

these costs equal 20 percent of the materials costs, or $8.0 million the

first year the standard is in effect.

In addition to the costs of applying the barrier, there are the

costs of treating the cotton batting with a boric acid based material.

The cotton batting must be so treated to make furniture with Class B, C,

and D fabrics meet the standard. We assume that it will be more efficient

106
to treat all of the cotton batting with boric acid than to keep two

separate inventories, one for Class A fabrics and another for the other

fabrics. At an annual volume of 116 million pounds of batting and at a treatment cost of 10 cents per pound, we therefore estimate the initial

year cotton batting treatment costs at $11.6 million per year.

Testing costs are also imposed by the proposed standard. The tests

involve both mock-up tests and fabric tests. For furniture construction

to be used with Class A, B, or C fabrics, mock-up tests must be conducted

using the least ignition-resistant fabric to be used with that construction. The mock-up tests may be pooled by the manufacturers. We assume

an average of 12 mock-up tests per year for each of the 1,369 furniture

manufacturers [28] for use with their Class A, B, and C fabrics. At an average mock-up testing cost of $50 per test, we therefore calculate the

mock-up testing costs for Class A, B, and C fabrics to be $0.8 million

the first year the standard is in effect.

Class D fabrics entail more mock-up testing. Each fabric must be

tested with each furniture construction. We assume that 72 000 Class D

fabrics will be tested on an average of four mock-up constructions. At

$50 per test, the Class D fabric mock-up testing costs are therefore

$14.4 million for the first year the standard is in effect.

The total mock-up testing costs are the sum of the testing costs

for all four fabric classes, or $15.2 million. We assume an additional

record-keeping cost to the furniture manufacturer of $5 per test or

$1.5 million in the first year.

The fabric manufacturers must also test their fabrics to determine

their classification. We assume an annual volume of 180, 000 fabric

tests per year. At an average cost of $15 per test, we obtain a fabric

testing cost of $2.7 million. We assume an additional record-keeping

cost to the fabric manufacturers of $5 per test, or $0.9 million annually.

We assume that industry will invest in research and development to

reduce the costs of meeting the standard. We assign $1 million per

year to reflect these costs.

The total cost of using the barrier method to meet the proposed

standard is the sum of the above costs, or $136.6 million the first year

the standard is in effect. Dividing $136.6 million by 20 million, our estimate of the number of furniture pieces produced in one year, we obtain an average cost of $6.83 per piece. However, the average cost

for a furniture piece upholstered with Class D fabric is $15.81, whereas

the average cost for a piece upholstered with Class A, B, or C fabric is

only $0.84.

107
6.3.1.2 Adjustment for Market Effects

We have estimated that the upholstered furniture industry will

incur an additional cost of $136.6 million per year to meet the proposed

standard using the barrier method. In a simple economic world, we could

assume that these costs are the total societal costs of the proposed

standard. However, the real economic world is more complicated and

there are more costs to be taken into account before a truer measure of

the total societal cost is obtained. In particular, several factors

combine to make the price increase of the furniture in the short run greater than the per-unit cost of the added manufacturing costs. These

factors include inventory and financing charges incurred by distributors

and commissions to salesmen. As the manufacturing costs increase, so do

these other costs. Coupled with the higher price of the furniture is a reduction in demand and loss of benefit to persons who no longer participate in the market. The total societal cost of the proposed standard

is the net of the increase in price and the loss of consumer benefit.

Economists term this cost the change in social surplus.

C. Muehlhause of the National Bureau of Standards has prepared a detailed paper relating the change in social surplus to the change in

manufacturers' costs [18]. A result of this work is that the total

societal costs of the proposed standard are equal to 1.5 times the

initial increase in manufacturing costs. Multiplying the $136.6 million

cost increase by 1.5 and adding an additional $1 million per year for

enforcement we obtain $206 million for the total societal cost of the

proposed standard in the first year.

6.3.1.3 Cost of the Barrier Method Over Time

We calculate that the barrier method will cost $206 million the

first year the standard is in effect. However, due to adjustments in

the furniture market, we believe that these costs will decrease over

time. There has been a shift away from the use of Class D fabrics over

the last few years. Because of the considerably higher cost of using

Class D fabrics under the proposed standard as shown above, we believe

this trend away from Class D fabrics would be accelerated by the proposed

standard as manufacturers shift to fabrics that do not require the

barrier underlay. Also, there would be competitive adjustments in the

marketplace, resulting in lower mark-ups of the manufacturers' costs.

To model the changing costs over time, we assume that the use of

Class D fabrics will decrease from 40 percent of the total upholstery

fabric market in 1980 to 20 percent in 1985. We assume that this shift

results in no loss of consumer choice because much of it represents

natural evolution in the marketplace or changes in the fabrics that are imperceptibly small to the casual user. We also assume that research

and development will result in new barrier materials that cost half as much as the first-year barrier materials.

108
Table 48 gives the initial and long-run manufacturing costs of the

barrier method. As shown, the long-run cost of the barrier material is

reduced by 75 percent because of lower usage and lower unit cost. The

labor, handling, mock-up testing, and manufacturers' record-keeping

costs are also reduced because of the decreased use of Class D fabrics.

The cotton batting treatment costs and the fabric manufacturers' testing

and record-keeping costs remain unchanged in the long run because these

activities must still be performed. We eliminate the long-range research

and development costs because we assume that the early efforts were successful in developing less expensive barrier materials.

Table 48. Manufacturers' Annual Cost of Proposed Standard

Using the Barrier Method

Cost

(Millions of Dollars)

Component Initial Long Range

Barrier Installation

Material $ 39.9 $10.0

Labor 55.8 27.9

Handling 8.0 4.0

Cotton Batting Treatment 11.6 11.6

Testing

Furniture Manufacturers 15.2 8.0

Fabric Manufacturers 2.7 2.7

Record-keeping

Furniture Manufacturers 1.5 0.8

Fabric Manufactuers 0.9 0.9

Research and Development 1.0 0.0

Total $136.6 $65.9

Table 48 shows that the long-run manufacturers' costs are less than

50 percent of the initial year cost, $65.9 million versus $136.6 million.

The primary reason for the cost reduction is the decreased use of Class D

fabrics, which results in significantly lower material and labor costs.

109
We assume that the initial year manufacturers' costs will occur in

1980 and that the long-run costs will be reached by 1985. The costs for

the intermediate years, 1981-1984, are found by linear interpolation.

As before, we must adjust the manufacturers' cost to account for subsequent marketplace adjustments. We use the same market factor of 1.5 to

make this adjustment for the first 5 years. We then linearly reduce the

market factor to a long-range value of 1.2 over the next 10 years to

represent the long-run competitive adjustments of the producers and

sellers

Table 49 gives the total societal cost of using the barrier method

to meet the proposed standard for four selected years. Costs for intermediate years are found by linear interpolation. The total societal

costs are calculated by multiplying the manufacturers' costs by the

market factor for the particular year and adding $1 million for the

cost of enforcement. The table shows that the total initial year cost

of $206 million decreases to a long-range value of $80 million.

Table 49. Total Annual Societal Cost of Proposed Standard

(Barrier Method)

Cost

Year (Millions of Dollars)

1980 $206

1985 100

1990 90

1995 & beyond 80

6.3.2 Backcoating Method for Meeting the Proposed Standard

A second possible method for meeting the proposed standard is to

apply a smolder inhibiting backcoating to Class D fabrics. The technique

has yet to be used commercially but it appears promising on the basis of

laboratory work. In this section we develop the cost of the "backcoating

method" under the assumption that a microencapsulated sulfur backcoating

could be used to inhibit smoldering combustion. We expect that this cost

is similar to the cost of using other types of backcoating products to

upgrade Class D fabrics.

The principal costs for this method are the backcoating costs and

sulfur treatment. Many of the Class D fabrics are already backcoated

for reasons not related to f lammability . However, we estimate that

about 45 percent or 34.2 million linear yards of the Class D fabrics

must be backcoated in order to utilize the sulfur process. Backcoating

costs average $0.30 per linear yard, giving a cost of $10.3 million for

additional backcoating.

110
Based on discussions with industry sources we estimate that adding

microencapsulated sulfur to the backcoating will cost about 14 cents per

linear yard of treated fabric. This must be added to the backcoating of

all Class D fabrics. We therefore estimate the sulfur treatment cost

for the 76 million yards of Class D fabrics to be $10.6 million.

We use the same cotton batting treatment costs as those for the

barrier method, because the same treatment is used and the same amount

of batting is treated under both methods.

Application of the sulfur backcoating to Class D fabrics will

transform them into Class A or B fabrics. Under this method there would

no longer be any Class D fabrics. Thus the mock-up testing costs to the

furniture manufacturer are simply the costs of testing the furniture

constructions with prototype fabrics A, B, and C — or $0.8 million, as previously calculated. As before, record-keeping costs are assumed to

be $5 per test. However, because there are fewer mock-up tests conducted

under the backcoating method, record-keeping costs are reduced to

$0.1 million.

We assume that the fabric testing and record-keeping costs for the

backcoating method will be the same as for the barrier method because each

fabric must still be tested. Therefore, we use the same $2.7 million

fabric-testing and $0.9 million record-keeping costs.

Table 50 summarizes the annual manufacturers ' cost of the backcoating method. The table shows a total annual manufacturers' cost of

$37.0 million, compared to an initial cost of $136.6 million for the

barrier method. The primary reason for the lower cost is the reduced

cost of materials, labor, and testing.

Table 50. Manufacturers' Annual Cost of Proposed Standard

Using the Backcoating Method

Component

Cost

(Millions of Dollars)

Sulfur Treatment

Additional Backcoating

Cotton Batting Treatment

Testing

Furniture Manufacturer

Fabric Manufacturer

Record-keeping

Furniture Manufacturer

Fabric Manufacturer

$10.6

10.3

11.6

0.8

2.7

0.1

0.9

Total $37.0

111
We assume that the backcoating method costs to the furniture manufacturers are constant over time. As with the barrier method, we apply

a market factor to the manufacturers ' cost to determine the total societal

cost of the sulfur method. We use the same market factors: 1.5 during

the first 5 years declining to 1.2 over the next 10 years.

Table 51 gives the total annual societal cost of both the backcoating

and barrier methods of meeting the proposed standard. The total annual

societal costs are calculated by multiplying the manufacturers 1 cost by

the appropriate market factor and adding $1 million per year for enforcement. The table shows that the backcoating method costs are significantly

less than the barrier method costs, although the difference decreases

in time. In the long term, the total annual societal costs are $80.1 million for the barrier method and $45.4 million for the backcoating

method.

Table 51. Annual Societal Cost of Proposed Standard

Cost

(Millions of Dollars)

Year Barrier Method Backcoating Method

1980 $205.9 $56.5

1985 99.9 56.5

1990 90.0 51.0

1995 & beyond 80.1 45.4

112
7. SENSITIVITY ANALYSIS

Our nominal results are based on several key assumptions. This

section tests the sensitivity of our results to changes in those assumptions. Some sensitivity studies have already been reported in section 3. This section summarizes those results as well as a number of other more

detailed studies not yet reported.

7.1 Sensitivity to Value Assignments and Time Preference

Key to the evaluation of benefits are the value assignments and

discounting parameters used to convert benefits into present monetary

terms. This section tests the sensitivity of our results to changes in

these parameters. In these sensitivity studies, as in the rest of the

section, we only vary the value of the parameter in question. All other

parameters are kept at their nominal values. (We also have the capacity

to perform multi-variate sensitivities if they are deemed useful.)

7.1.1 Value of Life

In section 3 we examine the sensitivity of our results to changes

in the amount society is willing to spend to save a human life. Although

it is very difficult to assign a value to this parameter, the sensitivity

analysis shows that the smoke detector and proposed standard alternatives

are the most attractive alternatives over a rather broad range of values,

from $60,000 to $400,000 per life saved. At values above $400,000 per

life saved, the proposed standard is clearly the most attractive alternative. However, at values close to zero, the no-action alternative is the

favored strategy.

7.1.2 Cost of a Fire Injury

Based on work by the Consumer Product Safety Commission, our nominal

results assume a $10,000 cost for an average fire injury. One might argue

that a higher value should be used since the $10,000 figure does not

include such indirect losses as pain and suffering. Figure 26 shows how

our results depend on the cost assigned to an average fire injury. At

value assignments close to zero, the three alternatives are essentially

equivalent. At values in the range of our nominal assignment, $10,000,

the smoke detector and proposed standard alternatives are the most

attractive. As the value increases significantly above $40,000 per fire

injury, the proposed standard increasingly becomes the most attractive

option.

113
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BARRIER METHOD)

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J i

, 1 1

20,000 40,000 60,000 80,000 100,000

INJURY VALUE ASSIGNMENT [Dollars]

Figure 26. Sensitivity of Results to Injury Value Assignment

114
7.1.3 Discount Rate

In comparing future benefits and costs with present benefits and

costs we use a discounting approach to discount future values to their

present equivalents . The discount rate is the compound rate at which

the future benefits and costs are discounted. The higher the discount

rate, the more current benefits are valued relative to future benefits.

Figure 27 shows how our results depend on the discount rate. At

low discount rates, close to zero, the proposed standard is definitely

the most attractive alternative. The reason is that the early implementation costs of the proposed standard are offset by the future benefits,

since these benefits are discounted very little. But as the discount

rate increases to our nominal value of 8 percent and higher, the smoke

detector alternative becomes the most attractive alternative because

it offers benefits almost as soon as the costs are incurred.

7.1.4 Planning Interval

Our nominal analysis is limited to a 34-year planning interval,

1977 to 2010. We terminate the analysis at 2010 because all of the

alternatives would be fully implemented by that time. However, extending

the analysis beyond 2010 would increase the total accumulated benefits

at relatively little additional cost for each alternative.

Figure 28 shows the present value of the cost plus loss at 8 percent

plotted against the final year of the planning interval. Although the

total cost plus loss depends on the planning interval, the comparison

of the alternatives is little changed by varying the final year over a rather broad range from 2000 to 2030.

7.2 Furniture Population Parameters

The rate at which the furniture population is replaced and its

flammability properties are important factors in evaluating the effectiveness of the different alternatives. This section examines the sensitivity

of our results to these parameters.

7.2.1 Furniture Replacement Pattern

Our nominal results depend on the assumption that the furniture

lifetimes are normally distributed with a mean and standard deviation

of 17 and 3.3 years, respectively. Using past production data and a constant annual future production, we obtain the curve shown in figure 29.

Subsequent to the completion of our work, Lane and Koecher of the

University of California have developed a different furniture replacement

curve [28]. Their curve, which is also reproduced in figure 29, is

115
18

NO ACTION

NOMINAL

VALUE

.8 .12 DISCOUNT RATE

.16 .20

Figure 27. Sensitivity of Results to Choice of Discount Rate

116
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PROPOSED STANDARD

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DETECTORS

NOMINAL

YEAR

1990 2000 2010

FINAL YEAR

2020 2030

Figure 28. Sensitivity of Results to Planning Interval

117
Figure 29. Comparison of Lane-Kocher and Nominal

Furniture Replacement Curves

118
based on past production data and future demand predicted by their

model. The figure shows that essentially all of the furniture population

is expected to be replaced in about 15 years compared to 30 years

under our nominal assumptions.

Table 52 gives the comparison of alternatives using the two different

furniture replacement curves. The table shows that the comparison of

alternatives is quite sensitive to the assumptions concerning furniture

replacement rate. Our nominal results show that the smoke detector

and proposed standard alternatives are approximately equivalent. But

if we assume that the population is replaced according to the Lane-Kocher

model, then the proposed standard is clearly the most attractive strategy.

The reason is that the benefits from the proposed standard are realized

much earlier, thereby offsetting the early implementation costs. The

results of this sensitivity study indicate that further research directed

toward determining the appropriate furniture replacement model should

be included in any refinements of this analysis.

Table 52. Comparison of Nominal Results with Results Obtained

Using Lane-Kocher Furniture Replacement Curve

Present Value at 8% from 1977 to 2010

(Millions of Dollars)

Alternative Using Lane-Kocher Curve

Loss Cost Cost Plus Loss

Nominal Case

Cost Plus Loss

No-Action $6310 $

Detector

Alternative 5640 300

Proposed Standard

(Barrier Method) 4480 1120

$6310

5940

5600

$6330

5950

5960

10

To model our three alternatives we make the simplifying assumption that

the curve Lane and Kocher developed for replacement of pre-1979 furniture

with post-1979 furniture is valid for both pre- and post-1975 furniture

and pre- and post-1980 furniture.

119
7.2.2 Smolder Resistance of Currently Produced Furniture

In modeling the natural evolution of the furniture population under

the smoke detector and no-action alternatives, we assume that the

population would evolve toward a mix of materials equivalent in fire

properties to the currently produced furniture population. We further

assume that the incidence of cigarette ignitions would be reduced by

one third when the furniture population was completely replaced. This

latter assumption is a critical one because it governs the extent to

which upholstered furniture fires will be reduced under the no-action

alternative.

Figure 30 shows how varying the estimated reduction in cigarette

ignitions alone affects the choice of alternatives. The sensitivity

study is conducted over a range from 50 to 90 percent of the cigarette

ignitions remaining, compared to our nominal value of 67 percent. If some unforeseen technology in furniture manufacturing would take the

parameter out of this range, then the cost of the proposed standard

would have to be reassessed. The figure shows that the smoke detector

alternative is the most attractive for remaining fractions less than our nominal two thirds value. For larger values the proposed standard is

most attractive. The findings are reasonable since the proposed standard

would be much more cost effective in replacing easily ignited furniture

than in replacing furniture that is already resistant to cigarette

ignition.

7.3 Parameters Governing the Smoke Detector Alternative

The performance of the smoke detector alternative depends on the

number of detectors installed as well as the fraction of installed

detectors that are operational. This section examines the sensitivity

of our results to changes in these parameters, as well as changes in the

purchase cost of the smoke detectors themselves

7.3.1 Smoke Detector Installation Level Under No-Action

Our nominal analysis assumes that voluntary and locally mandated

installation of smoke detectors would reach an ultimate level of

60 percent. Figure 31 shows how the comparison of alternatives is

changed by varying this installation level from 40 to 70 percent. The

figure shows that even at a 70 percent installation level, the proposed

standard and smoke detector alternatives are superior to the no-action

alternative. Of course, the lower the voluntary and locally mandated

installation level, the less attractive the no-action alternative becomes.

120
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Figure 30. Sensitivity of Results to Reduction

in Cigarette Ignitions Under No-Action

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Figure 31. Sensitivity of Results to Smoke Detector

Installation Level Under No-Action

Although this sensitivity analysis assumes a fixed installation

level of 90 percent under the mandatory smoke detector alternative, the

figure shows that the cost plus loss of the smoke detector alternative

varies with the no-action installation level. The reason is that as we vary the level of voluntary and locally mandated installation, the costs

and loss reduction attributable to the mandatory smoke detectors also

vary.

7.3.2 Smoke Detector Installation Level Under Federal Mandate

Our nominal analysis of the smoke detector alternative assumes that

a 90 percent installation level would ultimately be achieved under the

mandatory smoke detector program. Figure 32 shows how the comparison of

alternatives changes by varying the assumed installation level under the

mandatory program from 70 to 100 percent. The figure shows that the

smoke detector alternative is slightly preferred at ultimate installation

levels above 90 percent, but the proposed standard is most attractive

at lower levels. However, there is little significant difference between

these two alternatives over the range of installation levels investigated.

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Figure 32. Sensitivity of Results to Smoke Detector

Installation Level Under Detector Alternative

7.3.3 Fraction of Operational Smoke Detectors

Figure 33 shows how the fraction of smoke detectors that is assumed

to be operational affects the comparison of alternatives. Our nominal

assumption is that 80 percent of all detectors would be properly operating.

The figure shows that the smoke detector alternative is the most attractive if the fraction of operational detectors rises much above 80 percent.

For operational percentages much less than 80 percent the proposed

standard is the most attractive. However, in none of the cases is there

such a significant difference among the alternatives that one is clearly

the most attractive

.

7.3.4 Smoke Detector Purchase Cost

In section 3 we estimate the installed cost of a typical smoke

detector to be $22 per unit. Table 53 shows the comparison of our nominal results with two values of cost per installed detector. The

table shows that varying the cost from $10 to $30 per installed detector,

has essentially no effect on the comparison of alternatives. As in our nominal analysis, these sensitivity results assume that 29 percent of

the total smoke detector costs are assigned to the smoke detector

alternative.

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PERCENT OPERATIONAL

100

Figure 33. Sensitivity of Results to Percentage of

Properly Operating Smoke Detectors

124
Table 53. Sensitivity of Results to Cost Per Installed Smoke Detector

Present Value at 8% from 1977 to 2010

Cost

Per

(Millions of Doll ars)

Alternative Detector

(Dollars)

Loss Cost Cost Plus Loss

$10 $5650 $ 190 $5840

Detector

Alternative 22 5650 300 5950

30 5650 370 6020

No-Action 6330 6330

Proposed Standard

(Barrier) 4840 1120 5960

nominal cost

7.4 Parameters Affecting the Proposed Standard

The performance of the proposed standard is dependent on the cost

of the standard and the ultimate level of compliance. This section

presents several sensitivity studies to explore the dependence of our results on these factors.

7.4.1 Manufacturers' Cost of the Proposed Standard

Figure 34 shows how the choice of alternatives is affected by the

furniture manufacturers' initial cost for both the barrier method and

the backcoating method. As discussed in section 3.7.3, the figure shows

that the comparison of alternatives is quite sensitive to the manufacturers' cost for the barrier method. If the cost is greater than our nominal value of $136 million for the first year, then the smoke detector

alternative is most attractive. On the other hand, if the manufacturers'

cost is less than our nominal value, then the proposed standard is

clearly most attractive. On the other hand, figure 34 shows that the

initial manufacturers' cost of $37.0 million for the backcoating method

would have to more than double to make this compliance method less

attractive than no-action.

We wish to point out that the difference in the vertical intercepts

in figure 34 is due to the different expected losses under the two

compliance methods. The difference in the .slopes of the two lines is

due to the different assumptions concerning the behavior of the manufacturers' costs over time.

125
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1

1 1 M 1 1 100 200

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(millions of dollars]

300

Figure 34. Sensitivity of Results to Manufacturers' Cost

of Proposed Standard Under Two Compliance Methods

126
7.4.2 Market Factor for Assessing Total Societal Cost of

Proposed Standard

In assessing the total societal cost of the proposed standard we multiply the manufacturers' cost by a market factor. The market factor was derived to account for the effects of middleman charges and decreased

consumer participation in the market. Table 54 shows how the comparison

of alternatives depends on the market factor. The market factor of 1.7

corresponds to the mark-up currently being applied to the total manufacturing cost of the upholstered furniture. The 1.2 factor represents

the mark-up associated with such fixed costs as sales commissions.

Although the absolute value of the cost plus loss of the proposed

standard varies with the market factor, the table shows that the choice

of alternatives is not significantly affected by the value of the market

factor.

Table 54. Sensitivity of Results to Market Factors

Market Factors

Present Value at 8% from

1977 to 2010

(Millions of Dollars)

Alternative Initial Long Range Loss Cost Cost Plus Loss

1.2 1.2 $4840 $ 960 $5800

Proposed 1.5

a 1.2a 4840 1120 5960

Standard

(Barrier)

1.5 1.5 4840 1200 6040

1.7 1.2 4840 1230 6070

1.7 1.7 4840 1360 6200

No-Action 6330 6330

Detector

Alternative 5650 300 5950

nominal values

7.4.3 Compliance Level

Our nominal analysis assumes that 80 percent of the furniture

manufactured under the proposed standard would be compliant. Reasons

for non-compliance include the use of slipcovers, aging, the use of

improper materials or techniques, or outright disregard for the standard.

Figure 35 shows how the performance of the barrier method of meeting the

proposed standard depends on the compliance level. Two curves are given

in the figure. One assumes that the total cost of attempting to meet

the standard is constant, and only the compliance varies. This curve would correspond to the case where aging or deteriorated materials have

affected the complaince level. The other curve assumes that the total

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costs of the standard vary with the compliance level. This curve would

correspond to the situation where there has been no attempt at all to

meet the standard. In the fixed cost case, for compliance levels higher

than 80 percent the proposed standard is most attractive, while the

detector alternative is most attractive for compliance levels less than

80 percent. On the other hand, for the varying cost case the proposed

standard and detector alternatives are essentially equal and preferred

to no action.

7.5 Summary of Sensitivity Results

We have examined the sensitivity of our results to many different

assumptions and parameter values in this section and also in section 3.7.

We have seen that under a great variety of conditions the differences

between the proposed standard and detector alternative are small. Within

reasonable ranges on most parameters they remain together more attractive

than no action.

Two sensitivity studies indicate areas where future attention should

be focused. The first is the cost of the proposed standard (section 3.7.1

and 7.4.1) and the second is the furniture replacement pattern (section

7.2.1) . If the cost of the proposed standard should prove to be significantly higher than our nominal estimate, then the smoke detector alternative is the most attractive alternative followed by no action. However, we expect that such a significant increase in this cost estimate is

unlikely. On the other hand, if the cost of the proposed standard proves

to be significantly lower than our nominal estimate or the furniture

replacement is considerably faster than our model predicts, then the

proposed standard is the most attractive alternative. With regard to the

furniture replacement pattern, if essentially all existing furniture could

be replaced in 15 years, compared to our nominal estimate of 30 years,

then the proposed standard is the most attractive strategy.

129
ACKNOWLEDGEMENTS

We are grateful for the information and assistance provided us by a number of organizations and individuals throughout this project. In

particular, we wish to thank the technical staff of the Center for Fire

Research of the National Bureau of Standards (NBS) , particularly

James Winger, Richard Bright, Richard Custer, Sanford Davis, Joseph

Loftus, Harold Nelson, and William Parker. We also wish to thank the

National Fire Data Center at the U.S. Fire Administration, Gordon Damant

of the California Department of Consumer Affairs, E. L. Briggs, Jr. of

the Southern Furniture Manufacturers Association and the many other

individuals in the furniture manufacturing, fabric manufacturing and

chemical industries who provided data used in the analysis. We are grateful to John Lyons, Director of the National Engineering Laboratory,

NBS, and Frederic Clarke, Director of the Center for Fire Research,

for their enthusiastic support of this work. We also wish to thank

Scott Olmsted and Ellen Leaf of SRI International and Marjorie Hastedt

and Nancy Wilson of NBS for their contributions to the project,

Carl Muehlhause of NBS for his economic analysis in support of the

project, and Joan Rosenblatt of NBS for her helpful suggestions on improving this report.

130
REFERENCES

[1] Buchbinder, B. , Helzer, S.G. and Offensend, F. Preliminary Report

on Evaluating Alternatives for Reducing Upholstered Furniture Fire

Losses, Nat. Bur. Stand. (U.S.), NBSIR 77-1381 (Nov. 1977).

[2] Highlights of Fire in the United States: Deaths, Injuries, Dollar

Loss, and Incidents at the National, State and Local Levels.

National Fire Prevention and Control Administration, Department of

Commerce (U.S.) June 1978.

[3] Barrager, S.M. , Judd, B.R. and North, D.W. The Economic and Social

Costs of Coal and Nuclear Electric Generation. A discussion paper

prepared for an Environmental Workshop held at the MITRE Corporation,

May 27-28, 1975. March 1976. Available from the Superintendent

of Documents, U.S. Government Printing Office, No. 038-000002937.

[4] Thompson, G.I. and Chatterjee, P. Priorities at the Federal Highway

Administration. Federal Highway Administration, Washington, D.C.

Aug. 1976.

[5] Recommendations for a Synthetic Fuels Commercialization Program.

Report submitted by the SYNFUELS Interagency Task Force to the

President's Energy Resources Council. Nov. 1975. Available from

the Superintendent of Documents, U.S. Government Printing Office,

No. 041-001-00111-3.

[6] Clarke, F.B. Ill and Ottoson, J. Fire Death Scenarios and Fire

Safety Planning, Fire Journal, Vol. 70, No. 3, 20-22, 117-118

(May 1976)

.

[7] Loftus, J.J. Back-up Report for the Proposed Standard for the

Flammability (Cigarette Ignition Resistence) of Upholstered

Furniture, PFF 6-76, Nat. Bur. Stand. (U.S.), NBSIR 78-1438,

(June 1978)

.

[8] Faigin, B.M. 1975 Societal Costs of Motor Vehicle Accidents.

National Highway Traffic and Safety Administration,. Department of

Transportation (U.S.) Dec. 1976.

[9] Are Government Programs Worth the Price. Business Week, p. 114-115.

June 30, 1975.

[10] "PHOENIX" Examines Two Recent FRS Publications, Hazards to

Occupants on the Upper Floors of Dwelling, Fire, Vol. 70, No. 872 r 451-2 (Feb. 1978)

.

131
[11] Hirshleifer, J., Bergstorm, T. and Rappaport, E. , Applying CostBenefit Concepts to Projects Which Alter Mortality, School of

Engineering and Applied Science, University of California, Los

Angeles, California, UCLA-ENG-7478 (NSF Grant GI-39416) (Nov. 1974).

[12] Hornblower, M. , Placing Dollar-and-Cent Value on Life, The

Washington Post, Al-2 (Nov. 29, 1976).

[13] McConnaughey , J., Economic Impacts of Building Codes, NBS-NCSBCS

Joint Conference on Research and Innovation in the Building

Regulatory Process - Proceedings, (Providence, R.I., Sept. 1976)

National Bureau of Standards Special Publication 473 (June 1977)

[14] Prunella, W.J., Upholstered Furniture: Preliminary Assessment of

the Possible Impact of the Proposed Cigarette Ignition Standard,

Working Paper, Bureau of Economic Analysis, Consumer Product Safety

Commission (Nov. 1976)

[15] Schaenman, P.S. and Tovey, H. , Upholstered Furniture Fires: The

Magnitude of the Problem. Testimony for Consumer Product Safety

Commission, Washington, D.C. (Dec. 1977).

[16] Private communication: R. Bright, Center for Fire Research,

National Bureau of Standards.

[17] The UFAC Report, Presented to the Consumer Product Safety Commission

on July 15, 1976 by the Upholstered Furniture Action Council, H8

[18] Muehlhause, CO'., A Cost/Benefit Framework for Consumer Product

Safety Standards, Journal of Research of the National Bureau of

Standards, Vol. 83, No. 5, Sept. -Oct. 1978.

[19] Arrow, K. J. , The Rate of Discount for Long-Term Public Investment,

Ashley, H. , Rudman, R.L. and Whipple, C. (eds) , Energy and the

Environment: A Risk Benefit Approach (Pergamon Press, New York)

113-140.

[20] Grant, E.L. and Ireson, W.G., Principles of Engineering Economy

(The Ronald Press Company, New York, 1970).

[21] Donaldson, D.J., Smolder Resistant Cotton Upholstery Fabrics,

Natural Fibers Textile Conference, Atlanta, Georgia, Sept. 26-28,

1978.

[22] Stacey, G.S., Analysis of Costs of Accidents Associated with

Cigarette Ignition of Upholstered Furniture, Draft Working Paper

to Bureau of Economic Analysis, Consumer Product Safety Commission,

Battelle, Columbus Laboratories (Aug. 16, 1976).

132
[23] Dardis, R. and Thompson, R. , Cost-Benefit Analysis of

Proposed Flammability Standard for Upholstered Furniture,

R. Bruce LeBlanc, Proceedings of the 1978 Symposium on Textile

Flammability, New York, N.Y. April 19-20, 1978, 93-102.

[24] Projections of the Number of Households and Families: 1975 to

1980, Population Estimates and Projections, Current Population

Reports, U.S. Department of Commerce, Bureau of the Census,

Series P-25, No. 607 (Aug. 1975).

[25] McGuire, J.H. and Ruscoe , B.E. , The Value of a Fire Detector in the

Home, Fire Study No. 9, National Research Council of Canada,

Division of Building Research, Ottawa, Ontario, Canada (Dec. 1962).

[26] Halpin, B.M., Dinan, J.J. and Deters, 0. J. , Assessment of the

Potential Impact of Fire Protection Systems on Actual Fire

Incidents, Johns Hopkins University, Applied Physics

Laboratory (EPP TR 35) Laurel, Maryland (Oct. 1977)

.

[27] Smoke Detectors in Ontario Housing Corporation Dwellings, Ontario

Housing Corporation, Toronto, Ontario, Canada (January 1978)

.

[28] 1972 Census of Manufacturers, Industry Series, Household Furniture,

U.S. Department of Commerce, Bureau of the Census, MC72(2)-25A

(March 1975)

.

[29] Lane, S. and Kocher, L. , Preliminary Results from a Study of the

Economic Effects of the Proposed Flammability Standard for

Upholstered Furniture, American Council on Consumer Interests,

Proceedings -of the 24th Annual Conference, Chicago, 111.,

April 19-22, 1978.

133
APPENDIX

Conditional Probabilities for Current Conditions

This appendix is provided for the convenience of the reader

who wishes to work through the fire loss calculations detailed in

sections 4 and 5.

Figure 36, A, B, C, and D, gives the fire loss model probabilities

for each ignition source under current conditions. These probabilities,

conditional on the fire being reported to the fire service, are calculated

from the auxiliary trees (figure 11) as described in section 4.2.2.7.

Together with the probabilities given in table 16 and figure 15 and the

loss assignments given in tables 23 and 24 the probabilities shown in

the figure are input to the fire loss model (figure 9) to determine the

current losses per reported upholstered furniture fire.

To the reader who is working through the details of the calculations,

we wish to point out that there may be some very minor discrepancies in our reported values on some parameters. Calculations were performed by

full scale computer, hand calculator, and pencil and paper with varying

numbers of significant figures. Intermediate roundoffs were made when

the calculation mode was changed. None of the resulting discrepancies

have any significance in the final results of the analysis presented in

this report.

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138
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS Tech. Note 1101

a.Gov't Accession No, 3. Recipient's Accession No.

4. TITLE AND SUBTITLE Decision Analysis of Strategies for Reducing

Upholstered Furniture Fire Losses

5. Publication Date June 1979

6. Performing Organization Code

7. AUTHOR(S) Susan Godby Helzer, Fred L. Offensend,

Benjamin Buchbinder

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

1ft, Project/Task/Work Unit No. 751-3679

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, zip) 13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

|

| Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or less tactual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) Decision analysis is used to evaluate alternative strategies for

reducing residential upholstered furniture fire losses. Three alternatives

are evaluated: no-action, mandatory smoke detector installation, and

the proposed upholstered furniture standard under consideration by the

Consumer Product Safety Commission. Quantitative models are developed

to assess fire losses and costs under each alternative. The alternatives

are evaluated on the basis of minimizing the total cost plus loss to

society over time. Subject to the assumptions set forth in the report,

the analysis shows that the detector alternative and the proposed standard

are essentially equivalent and preferred to the no-action alternative.

The proposed standard is more effective in saving lives , whereas the

detector alternative is less costly to implement. The sensitivity of

the results to key assumptions and input parameters is tested. The

results are shown to be particularly sensitive to the cost of the proposed

standard, the loss of life value assignment, and the upholstered furniture

replacement pattern.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons) ._-,.—. , -. ... -.. , Building fires; cost-benefit analysis; costs; decision analyses;

fire losses; furniture; hazard analysis; probability; residential buildings;

sensitivity analysis; smoke detectors; standards; upholstered furniture.

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