8

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- i APPENDIX 8

- C. LIFETIME DISTRIBUTIO NS

TABLE OF CO NTENTS

8-C.1 INTRODUCTION

................................................................................................. 8-C-1

8-C.1.1 Product Lifetime

.................................................................................. 8-C-1

8-C.2 ESTIMATION OF SURVIV AL FUNCTION.

...................................................... 8-C-3

LIST OF TABLES

Table 8 -C.1.1 Room Air Conditioners: Product Lifetime Estimates and Sources ........... 8-C-2

Table 8 -C.1.2 Clothes Dryers: Product Lifetime Estimates and Sources ......................... 8-C-3

Table 8 -C.2.1 Lifetime Parameters ................................................................................... 8-C-5

LIST OF FIGURES

Figure 8 -C.2.1 Room Air Conditioners: Lifetime Function ............................................... 8-C-5 Figure 8 -C.2.2 Clothes Dryers: Lifetime Function ............................................................ 8-C-68

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- 1 APPENDIX 8

- C. LIFETIME DISTRIBUTIO NS

8- C.1 IN TRODUCTION

For each product class, DOE characterized the product lifetime using a Weibull probability distribution that ranged from the minimum to maximum lifetime estimates described

in chapter 8, Life Cycle Cost and Payback Period Analyses. The Weibull distribution is

recommended for application to lifetime data because it can be shaped to match low, average, and high values while still allow ing some probability of exceeding the high value. 1, 2

8-C.1.1 Product Lifetime

The product l ifetime is the age at which the product is retired from service. Appliance magazine provides estimates of the low, high, and average years of an appliance’s lifetime. The estimates, which are based on first -owner use of the product, represent the expert judgment of Appliance staff based on input obtained from various sources. DOE also identified other sources that give lifetimes for room air conditioners and clothes dryers (see Tables 8.C.1.1 and 8.C.1.2).

Because the basis for the estimates in the literature was uncertain, DOE developed a method using household survey data to estimate the distribution of room air conditioner and clothes dryer

lifetimes in the field

.8

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- 2 Table 8 -C.1.1 Room Air Conditioners: Product Lifetime Estimates and Sources
Typical Lifetime or Range (years) Source

Original Sources
Average = 9; Low = 7 Appliance Magazine, September 200 8 3

12.5 ASHRAE 2008 4

15 CEC 2005 5

12 European Rulemaking Draft Report 6

Average = 15; High = 20 NRDC 7

Other Sources

Lifetime Source

9 Appliance Magazine, 1997 ENERGY STAR Savings Calculator a

18 EnerGuide 2005 Natural Resources Canada, 2008 8

15 NA New Mexico Market Assessment, Itron 2006 9

18 NA Nebraska Public Power District 10

12 See endnote NYSERDA SBC

, 2002 11

9 NA RTF (Northwest), 2002 12

12.5 DOE TSD 1997 NCEP report, LBNL 2004 13

19 Aspen Memo,

2002 NYSERDA Deemed Savings Database: ENERGY

STAR 14

13 (TTW) DOE TSD 2005 NYSERDA Deemed Savings Database: ENERGY

STAR 13

Low = 8, High =16 NEMS Residential Demand Module, 2008 15

13 LBNL 2008 16

Average = 10

– 15,

Low = 8 –12, High

= 14 -18 LBNL 1994 17

10 Consortium for Energy Efficiency 18

10–12 American Council for an Energy Efficient Economy , 2007 19

NA means the data source is not stated in the reference.

a ENERGY STAR Savings Calculator, Products, Room AC. Efficient and conventional models.8

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- 3 Table 8 -C.1.2 Clothes Dryers: Product Lifetime Estimates and Sources
Typical Lifetime or R ange (years) Source

Original Sources
Average = 12; Low = 8; High = 15 Appliance Magazine, September 2008 3

15 CEC 2005 5

18 CALMAC 2000 20

Other Sources

Lifetime Source

Average = 12; Low = 8;

High = 15 Appliance Magazine, 2006 BTS Core Databook, 2007 21

18 EnerGuide 2005 Natural Resources Canada, 2007 22

18 DOE Framework Document Itron, Report to CEC, 2007

18 NA CEC Consumer Energy Center website

18 See endnote CEC Flex Your Power website

14 NA Nebraska Public Power website

18 NA New Mexico Market Assessment, Itron

2006 8

12 Nexant, PECI Questar Gas, Utah, from Deemed Savings Database, 2006

14 RTF (Northwest) CW/CD spreadsheet, 2008

NA means the data source is not stated in the reference.

8- C.2 ESTIMATION OF SURVIV AL FUNCTION.

The Residential Energy Consumption Survey (RECS) records the presence of various appliances in each household, and places the age of each appliance into bins comprising several years. Data from the U.S. Census’s American Housing Survey (AHS), 23 which surveys all housing including vacant and second homes, enabled DOE to adjust the RECS data to reflect the

pre sence of appliances outside of primary residences. By combining the results of both surveys with the known history of appliance shipments (collected from Appliance magazine or directly from manufacturer trade associations), DOE estimated the percentage of appliances of a given age still in operation. This survival function, which DOE assumed has the form of a cumulative Weibull distribution, provides an average and a median appliance lifetime.

The Weibull distribution is a probability distribution commonl y used to measure failure

rates. b

b For reference on the Weibull distribution, see sections 1.3.6.6.8 and 8.4.1.3 of the NIST/SEMATECH e

- Handbook

of Statistical Methods

, < Its form is similar to an exponential distribution, which models a fixed failure rate, except

www.itl.nist.gov/div898/handbook/ >.8

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- 4 that a Weibull distribution allows for a failure rate that changes over time in a particular fashion.

The cumulative Weibull distribution takes the form:



# e x 

### xP **β**

**α**

**θ ** 

** **  ** **  ****

**−**

**−**



### = )( for x > θ and

P(x) = 1 for x ≤ θ

Where:

P(x) = probability that the appliance is still in use at age x ,

x = appliance age,

α = scale parameter, which would be the decay length in an exponential distribution, β = shape parameter, which determines the way in which the failure rate changes through time, and
θ = delay parameter, which allows for a delay before any failures occur.

When β = 1, the failure rate is constant over time, giving the dist ribution the form of a cumulative exponential distribution. In the case of appliances, β commonly is greater than 1, reflecting an increasing failure rate as appliances age.

RECS is DOE’s primary resource for appliance ages. For several appliances, including room air conditioners and clothes dryers, the survey asks respondents to identify the appliance’s

age as:

**•** less than 2 years old,

**•** 2 to 4 years old,

**•** 5 to 9 years old,

**•** 10 to 19 years old, or

**•** more than 20 years old.

**•** The RECS has been conducted every t hree or four years for the past several decades. For this analysis, DOE used the surveys conducted in 1990, 1993, 1997, 2001, and 2005. DOE used the AHS count of housing units that contain room air conditioners or clothes dryers to scale the

RECS data to b etter match the total installed stock. Table 8.C.2.1 shows the lifetime parameters for room air conditioners and clothes dryers.8

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- 5 Table 8 -C.2.1 Lifetime Parameters

Product Class Calculated Values Weibull

Parameters

Minimum

(years) Average (years) Maximum (years) Maximum percentile (%) Alpha (scale) Beta (shape)

Room Air Conditioner 3 10.5 30 97 7.47 1.00

Clothes Dryer 5 16.03 30 94 12.1 1.38

Figure 8 -C.2.1 Room Air Conditioners: Lifetime Function 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0%

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30Annual Retirement Rate8

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- 6 Figure 8 -C.2.2 Clothes Dryers: Lifetime Function8

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- 7 REFERENCES

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. 2005: pp. 13

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.

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. 2002. http://www.nyserda.org/02sbcappendixb.pdf

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- 8 13. Rosenquist, G., Energy Efficiency Standards and Codes for Residential/Commercial Equipment and Buildings: Additional Opportunities, July 2004, 2004. Lawerence Berkeley National Laboratory. Report No. LBID-2533.

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. http://www.cee1.org/resid/seha/rm

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. http://www.calmac.org/events/APX_F.pdf

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