9-i 

CHAPTER 9. SHIPMENTS ANALYSIS

 TABLE OF CONTENTS

9.1 INTRODUCTION ........................................................................................................... 9-1

9.1.1 Analyzed Product Classes, Market Sectors, and Market Segments ........................... 9-3

9.2 SHIPMENTS MODEL METHODOLOGY .................................................................... 9-4

9.2.1 Conceptual Framework of the Shipments Model ...................................................... 9-4

9.2.1.1 Lighting Demand Module .............................................................................. 9-6

9.2.1.2 Consumer Choice Module ............................................................................. 9-7

9.2.1.3 Price Learning Module .................................................................................. 9-9

9.2.1.4 The Coupled Model ..................................................................................... 9-11

9.2.2 Lamp Specific Modeling and Assumptions ............................................................. 9-11

9.2.2.1 Modeling Lighting Demand for New Construction and Renovations ......... 9-13

9.2.2.2 Modeling the Retirement of Lamps and Lamp-and-ballast Systems ........... 9-14

9.2.2.3 Incandescent Reflector Lamps: Turnover and Shipments ........................... 9-25

9.2.2.4 General Service Fluorescent Lamps: Turnover, Consumer Choice, and 

Shipments ..................................................................................................... 9-27

9.2.2.5 General Service Fluorescent Lamps: Market Shares and Stock Shares ...... 9-35

9.3 MODEL CALIBRATION AND INPUTS..................................................................... 9-36

9.3.1 Estimation of Historical Shipments and Initial Market Shares ................................ 9-36

9.3.2 Sources of Historical Shipments Data ..................................................................... 9-36

9.3.3 Subdivision of Historical Shipments by Sector, Product Class, and Technology ... 9-38

9.3.4 Consumer Choice Model Calibration ...................................................................... 9-39

9.3.5 Price Learning .......................................................................................................... 9-44

9.3.6 Lamp and Ballast System Assumptions ................................................................... 9-46

9.3.6.1 Ballast Substitution Assumptions ................................................................ 9-47

9.3.6.2 General Service Fluorescent Lamp Characteristics ..................................... 9-49

9.3.6.3 Incandescent Reflector Lamp Characteristics .............................................. 9-53

9.3.6.4 Lamp Usage Assumptions ........................................................................... 9-54

9.3.7 Rare Earth Costs ...................................................................................................... 9-58

9.4 ALTERNATIVE ANALYSES ...................................................................................... 9-59

9.4.1 Overview .................................................................................................................. 9-59

9.4.2 Light Emitting Diode Impact Determination ........................................................... 9-61

9.4.3 Alternative Incandescent Reflector Lamp Technology ........................................... 9-62

9.5 RESULTS ...................................................................................................................... 9-63

9.5.1 Results of Analyses of Candidate Standards Cases ................................................. 9-63

9.5.2 Results of the Alternative Analyses ......................................................................... 9-67
9-ii

LIST OF TABLES

Table 9.1.1 Candidate Standard Levels Assumed for Each Candidate Standards Case 

for Each of the Modeled Product Class Groupings ............................................. 9-2

Table 9.1.2 Product Class Groupings Used in the Shipments Model ..................................... 9-3

Table 9.2.1 IRL Options Used in Shipments Model ............................................................... 9-5

Table 9.2.2 GSFL Product Class Groupings and Lamp Options Used in Shipments 

Model ................................................................................................................... 9-5

Table 9.2.3 The Parameters and Time Units of the Weibull Distributions Used in the 

Shipments Analysis ............................................................................................ 9-15

Table 9.2.4 Scaling of Lamp Lifetime with Average Hours of Lamps Use per Start ........... 9-22

Table 9.2.5 Ballast Substitution Matrix ................................................................................ 9-29

Table 9.3.1 Fraction of Lamp Shipments Assumed to be from NEMA Members ............... 9-36

Table 9.3.2 Fraction of Ballast Shipments Assumed to be from NEMA Members ............. 9-37

Table 9.3.3 Input Data for Logit Parameter Calibration ....................................................... 9-40

Table 9.3.4 Logit Parameter Results from Calibration ......................................................... 9-41

Table 9.3.5 Bass Adoption Model Parameters ...................................................................... 9-41

Table 9.3.6 Ballast Acceptance Factors and Lifetime Reduction Factors ............................ 9-43

Table 9.3.7 Lamp Acceptance Factors .................................................................................. 9-43

Table 9.3.8 Data Extracted from Current Industrial Reports (CIRs) for Price Learning 

Analyses ............................................................................................................. 9-44

Table 9.3.9 Properties of Average Ballasts for Product Class Groupings ............................ 9-46

Table 9.3.10 Ballast Substitution Matrix: Retrofits and Renovations .................................... 9-48

Table 9.3.11 Properties of Representative GSFL Options: Baseline and All CSLs ............... 9-49

Table 9.3.12 GSFL Options for Different Ballast Types ........................................................ 9-50

Table 9.3.13 Properties of Representative GSFL Lamp-and-ballast Systems ........................ 9-51

Table 9.3.14 IRLs: Representative Properties for Baseline and CSL 1 Lamps ...................... 9-53

Table 9.3.15 Commercial Sector Annual Hours of Lamp Use and Starts per Day ................ 9-54

Table 9.3.16 Industrial Sector Annual Hours of Lamp Use and Starts per Day ..................... 9-55

Table 9.3.17 Residential Sector Annual Hours of Lamp Use and Starts per Day .................. 9-56

Table 9.4.1 Definition Alternative Analyses ........................................................................ 9-60

Table 9.4.2 Summary of Variable Assumptions for Best Estimate and Alternative 

Analyses ............................................................................................................. 9-60

Table 9.4.3 IRL Lamp Life Assumptions for Best-Estimate and Alternative 

Technologies that Meet a CSL 1 Standard ........................................................ 9-63

Table 9.5.1 Best Estimate of Cumulative Shipments of GSFLs and IRLs from 2017 – 

2046, for Each of the Candidate Standards Cases ............................................. 9-64

Table 9.5.2 Effects of Candidate Standards Cases on Cumulative Shipments 

Compared to Base Case for GSFLs and IRLs, Best Estimate ........................... 9-67

Table 9.5.3 Cumulative Shipments of GSFLs and IRLs from 2017 – 2046, for All 

CSL 1 and Max CSL, Alternative Analyses ...................................................... 9-68
9-iii

LIST OF FIGURES

Figure 9.2.1 Schematic Representation of the Consumer Choice Model ................................ 9-8

Figure 9.2.2 Schematic diagram of the annual ballast turnover in the shipments model, 

including the effect of the consumer choice model and LED incursion. ........... 9-32

Figure 9.3.1 Generic lighting Bass diffusion curve................................................................ 9-41

Figure 9.3.2 IRL Learning Curve ........................................................................................... 9-45

Figure 9.3.3 GSFL Learning Curve........................................................................................ 9-45

Figure 9.3.4 Ballast Learning Curve ...................................................................................... 9-45

Figure 9.3.5 Inflation-Adjusted, Tri-band Phosphor REO Price Index for GSFLs................ 9-58

Figure 9.4.1 LED Incursion Curve Projections for GSFLs and IRLs, Best Estimate ............ 9-61

Figure 9.4.2 Lumen Capacity of GSFL, IRL, and Combined GSFL and IRL displaced 

by LED (Total LED), Best Estimate .................................................................. 9-62

Figure 9.5.1 Historical and Projected Shipments of GSFLs by Product Class Grouping, 

Best Estimate ..................................................................................................... 9-65

Figure 9.5.2 Historical and Projected Shipments for IRLs, Best Estimate ............................ 9-66
9-1

CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

 The U.S. Department of Energy (DOE) developed a consumer-choice-based model to 

estimate shipments of general service fluorescent lamps (GSFLs) and incandescent reflector 

lamps (IRLs). The model projects consumer purchases (hence shipments) based on sectorspecific consumer sensitivities to first costs and operating costs of lamps, as revealed by 

historical data. To account for non-economic consumer behaviors a technology diffusion model 

and a technology acceptance factor are superimposed on the shipments model. The model allows 

switching across product classes, where there is historical evidence that switching has occurred. 

Because of the complexity of the consumer-choice-based shipments analysis, the 

shipments model was executed as a separate computer model written in the Python language. 

The inputs and outputs of the shipments model were embedded in the national impact assessment 

(NIA) model, which is coded in a Microsoft Excel® spreadsheet which are available on 

regulations.gov, docket number EERE–2011–BT–STD–0006 at 

www.regulations.gov/#!docketDetail;D=EERE-2011-BT-STD-0006.

Shipments projections are a necessary input to calculations of the national energy savings 

(NES) and net present value (NPV) in the NIA, as well as to the manufacturer impact analysis 

(MIA). For each product class of lamps DOE projected the change in shipments that would occur 

under different candidate standards cases. Because the model accounts for product switching 

across compatible products, exploring the impact of a standard on any given product requires 

that the standard levels for all substitutable products be set as well. Accordingly, developing a 

candidate standards case (CSC) involves setting the assumed candidate standard level (CSL) for 

all analyzed product class groupings (as defined in section 9.1.1), using the CSLs defined in the 

engineering analysis (chapter 5 of this TSD). 

 In this preliminary analysis DOE defined four candidate standards cases to explore the 

potential range of energy savings, costs, and benefits obtainable from the standards. DOE first 

considered two CSCs: 

• the All CSL 1 CSC, in which the standards were assumed to be set at CSL 1 for all 

product class groupings, and ‘ 

• the Max CSL CSC, in which the standards were assumed to be set at the maximum CSL 

for each product class grouping. (In practice this is CSL 2 for 4-foot medium bipin

(MBP) GSFLs and CSL 1 for all other product class groupings.) 

DOE also considered a variation on each of these: 

• the All CSL 1 Except T5=Baseline CSC and 

• the Max CSL Except T5=Baseline CSC. 

 In these variations the T5 standard was kept at the existing standard level (the baseline) to 

test if this might result in a greater migration to T5s (which generally have higher efficacy than 
9-2

T8s)a and, therefore, in higher overall NES and NPV. Table 9.1.1 shows the assumed standard

levels for the modeled product class groupings (defined in the table and discussed in section 

9.1.1). The baseline and CSLs are as described in the engineering analysis (chapter 5 of this 

TSD). 

Table 9.1.1 Candidate Standard Levels Assumed for Each Candidate Standards Case 

for Each of the Modeled Product Class Groupings

Modeled Product 

Class Grouping

Base case 

(No new 

standards)

All CSL1 

Standard

Max CSL 

Standard

All CSL 1 

Except 

T5 = 

Baseline

Max CSL 

Except 

T5 = 

Baseline

GSFLs

4-foot MBP* Baseline CSL1 CSL2 CSL1 CSL2

8-foot SP** slimline Baseline CSL1 CSL1 CSL1 CSL1

8-foot RDC† HO †† Baseline CSL1 CSL1 CSL1 CSL1

4-foot T5, MiniBP SO ‡ Baseline CSL1 CSL1 Baseline Baseline

4-foot T5, MiniBP HO Baseline CSL1 CSL1 Baseline Baseline

IRLs

IRL Baseline CSL1 CSL1 CSL1 CSL1 * MBP = medium bi-pin, ** SP = single pin, † RDC = recessed double contact, †† HO = high output, and ‡

SO = standard output. 

 

To evaluate the impact of the candidate standards cases on shipments of the two

categories of lamps—GSFLs and IRLs—DOE calculated the difference between the standards 

case shipments and those of the corresponding base case for each product class grouping. All 

assumptions for a given standards case are identical to those of its corresponding base case, 

except that lamp options that do not meet the standard are excluded in the standards case. The 

cumulative impact of each CSC on shipments is determined by summing the annual impacts over 

the 2017 through 2046 analysis period. 

For each CSC, DOE calculated its best estimate of the impact of the CSC on shipments, 

broken down by product class grouping. In addition to the best estimate analyses, DOE ran

alternative analyses for three main purposes in this preliminary analysis: 

• Uncertainty Analysis: To gauge the importance of uncertainties in rare earth oxide (REO)

prices on GSFL prices and their impacts on shipments, NES, and the NPV, DOE ran 

model scenarios using high and low estimates of REO prices. 

• Impact Determination

 

a

 All lamp efficacy data used in the shipments analysis and the NIA reflect lamp operations at 35 oC, as developed 

in the engineering analysis (see chapter 5 of this TSD).

: To determine the impacts of the expected growth of solid-state 

lighting (lighting using light emitting diodes (LEDs)) and of lighting controls on 

shipments, NES, and NPV, DOE ran scenarios both with and without the expected 

growth included in the best estimate scenario. 
9-3

• Alternative Technology Option: To test the potential impact of manufacturers responding 

to an IRL standard by developing higher-wattage, shorter-lived lamps, DOE ran a 

scenario in which representative products with these properties were added to the 

consumer choices. 

 This chapter reports the effects on shipments of all the CSCs and alternative analyses. 

(Chapter 10 of this TSD, which covers the NIA, describes the resulting effects on NES and 

NPV.) Section 0 presents the model methodology. Section 9.3 describes model calibration and 

inputs. Section 9.4 describes the alternative analyses. Section 9.5 presents the shipments 

projections for the GSFL and IRL base cases, standards cases, and alternative analyses. 

9.1.1 Analyzed Product Classes, Market Sectors, and Market Segments

 For the purposes of projecting future shipments, DOE modeled the product class 

groupings and sectors shown in Table 9.1.2. DOE aggregated product classes into a smaller set 

of product class groupings, constrained by the representative products identified in the 

engineering analysis (chapter 5 of this TSD) and by the lack of sufficient disaggregation of 

shipments data needed to determine market shares by product class (see, chapter 3 of this TSD). 

The properties of the representative products were assumed to reflect the product class grouping 

as a whole. Specifically, DOE used GSFL lamps with a correlated color temperature (CCT) less 

than 4,500K to be representative of those greater than or equal to 4,500K, and it used standard 

spectrum IRLs with diameters greater than 2.5 inches operating on less than 125 volts as 

representative of all covered IRLs. 

Table 9.1.2 Product Class Groupings Used in the Shipments Model

Product Class Grouping Sector

GSFLs Residential Commercial and Industrial

4-foot MBP X X

8-foot SP slimline X

8-foot RDC HO X

4-foot T5, MiniBP SO X

4-foot T5, MiniBP HO X

IRLs Residential Commercial

All IRLs X X

 DOE did not directly model shipments of 2-foot U-shaped lamps because of their 

relatively small market share. Following the procedure adopted in the 2009 GSFL-IRL 

rulemaking1, DOE scaled the results from the 4-foot MBP product class to approximate the NES 

and NPV of the 2-foot U-shaped product class. Specifically, it assumed that U-shaped lamps 

maintain a market share equivalent to 1/25th of the 4-foot MBP market, based on the ratio of the 

sum of shipments of 4-foot MBP T8s from 2006 – 2011 and the sum of 2-foot T8 U-shaped 

lamps during the same period reported by the National Electrical Manufacturers Association

(NEMA) (see chapter 3 of this TSD).
9-4

 For all product class groupings DOE aggregated across the commercial and industrial 

sectors, because of both the similar applications for these product classes and the relatively small 

contribution of the industrial sector. Residential usage of GSFLs was considered negligible for 

all lamp types except for 4-foot MBP lamps. 

In addition to modeling the representative products described previously, DOE 

incorporated T12 lamps into its shipments analysis. While new production of T12 lamps appears 

unlikely under the 2012 lamp efficiency standards, because of their relatively long lifetimes and 

their large historical market share, they still constitute a significant fraction of the existing 

lighting stock. Therefore, the shipments model addresses replacements for existing stock of T12 

lamps and ballasts with new T5 and T8 lamps and ballasts. Specifically, the model includes three 

additional T12 product classes: 4-foot MBP T12, 8-foot SP slimline T12, and 8-foot RDC HO

T12 lamps. DOE assumed that no new lamp-and-ballast systems would be shipped during the 

analysis period for any of these product classes, but DOE did model new shipments of T12 

lamps for the relamping of existing systems, as T12 lamps are available that are exempt from 

current standards.

In its projections of IRL shipments, DOE aggregated across all IRL product classes 

(standard- versus modified-spectrum, less than and greater than or equal to 125 V, and less than 

or equal to and greater than 2.5 inches in diameter). IRL products not directly modeled were 

scaled using 120V PAR-38 Standard Spectrum lamps, which constitute an estimated 56 percent 

of IRL covered products.b

9.2 SHIPMENTS MODEL METHODOLOGY 

DOE believes that the national impacts would be similar for other 

product classes not directly analyzed. By aggregating the product classes, DOE assumed that 

there would be no significant migration of shipments or stock between lamps in different product 

classes. As with the modeling of 4-foot MBP GSFL shipments, DOE aggregated commercial 

sector IRLs, analyzing residential lamps separately. 

 This section describes the conceptual framework of the model and the modeling 

assumptions. Model calibration and inputs are addressed in section 9.3. 

9.2.1 Conceptual Framework of the Shipments Model

 The shipments model estimates the changing market distributions of the covered lamps 

by product class grouping broken down by efficiency level for input to the NIA analysis. In its 

shipments and NIA modeling, DOE used the properties of the representative products identified 

in the engineering analysis (chapter 5 of this TSD) to represent the lamp options available to 

consumers at the different efficiency levels. Table 9.2.1 and Table 9.2.2 summarize the wattages 

and efficacies of representative IRL and GSFL options that meet the indicated efficiency levels 

in all product class groupings. Table 9.2.2 also includes lamp option identifiers (IDs) that are 

used in section 9.3 to further describe model assumptions about the properties of GSFL lamps 

 

b The 56 percent estimate is based on NEMA shipments from 2006 – 2011 (chapter 3).
9-5

and of lamp-and-ballast systems. As shown, in some cases, there are multiple representative 

lamps options for a given baseline or CSL. (For a complete listing of IRL properties, see Table 

9.3.14) A more complete description of the characteristics of these representative products is 

presented in section 9.3.6.2 and section 9.3.6.3. 

Table 9.2.1 IRL Options Used in Shipments Model

Lamp Option Nominal 

Wattage

Efficacy 

(lm/W)

Baseline 1 60 17.8

Baseline 2 60 18.3

CSL 1 55 20

Table 9.2.2 GSFL Product Class Groupings and Lamp Options Used in Shipments 

Model

Product Class

Grouping CSL

Lamp 

Option ID

Lamp 

Diameter

Nominal 

Wattage 

Efficacy 

(lm/W)

4-foot MBP Baseline L1.0.1 T8 32 89.2

CSL1 L1.1.1 T8 32 90.0

CSL2 L1.2.1 T8 32 95.4

L1.2.2 T8 28 96.0

L1.2.3 T8 25 93.0

8-foot SP 

slimline

Baseline L2.0.1 T8 59 98.2

CSL1 L2.2.1 T8 59 99.0

L2.2.2 T8 54 105.6

L2.2.3 T8 50 108.0

8-foot HO Baseline L3.0.1 T8 86 93.0

CSL1 L3.2.1 T8 86 95.3

T5 SO Baseline L4.0.1 T5 28 104.3

CSL1 L4.2.1 T5 28 109.7

L4.2.2 T5 26 111.5

L4.2.3 T5 25 116.0

T5 HO Baseline L5.0.1 T5 54 92.9

CSL1 L5.2.1 T5 54 97.3

L5.2.2 T5 50 100.0

L5.2.3 T5 47 102.1

Lamp-and-ballast interactions were explicitly addressed in the shipments model for two 

reasons. First, the existing ballast limits the lamp options available to consumers. Second, the 

ballast to which a lamp is paired affects its energy use, which in turn affects lamp and ballast 

shipments in the consumer choice module through its effect on operating costs. Therefore, the 

shipments model first computes ballast shipments before it calculates GSFL shipments. DOE 
9-6

estimated the national average energy consumption of GSFLs by modeling GSFLs in each 

product class grouping as if they were installed on a national average ballast (or one of several 

such ballasts in the case of 4-foot MBP lamps) with properties listed in Table 9.3.9. 

 

 The model has three main interacting elements: (1) a lighting demand module, which 

estimates the demand for GSFL and IRL lighting for each year of the analysis period; (2) a 

consumer choice module, which assigns shipments to product classes and efficacy levels based 

on consumer sensitivities to first costs and operation and maintenance costs; and (3) a price 

learning module, which projects future lamp and ballast prices based on historic price trends. To 

account for product switching, the consumer choice model consults lamp substitution matrices, 

which specify the allowable product choices that consumers have available (lamps or lamp-andballast combinations), depending on whether they are renovating lighting systems, installing 

lighting systems in new construction, or simply replacing lamps. Based on the estimated prices, 

the consumer choice model allocates the national lumen demand to the product class groupings 

and lamp options for each year of the analysis period, subject to the constraints of the standards 

case under consideration. 

9.2.1.1 Lighting Demand Module

A central assumption of the model is that the amount of light needed to fully light a space 

(lumen capacity demand per square foot, measured in units of lumens per square foot) is 

assumed to remain unchanged over the analysis period. That is, sector-specific lighting demand 

stays constant in terms of the total lumen capacity per square foot, where lumen capacity is the 

total maximum (non-dimmed) light output. However, total national lumen demand grows 

proportionally with floor area (residential, commercial, and industrial). Therefore, the total 

lumen demand was adjusted based on the sector-specific floor-space growth rates extracted from

Annual Energy Outlook 2012 (AEO 2012).

2

 

 While lumen capacity demand per square foot is expected to remain constant, DOE 

expects the demand for GSFL and IRL products to be eroded by increased penetration of solidstate lighting (i.e., lighting that uses LEDs for illumination) into the market. For its best-estimate 

(reference) scenarios, DOE assumed that LED penetration would match the LED incursions 

forecast for DOE’s Solid-State Lighting Program3, as described in section 9.4.2. 

At the same time that LED lighting is eroding GSFL and IRL lumen capacity demand per 

square foot, the increasing penetration of lighting controls is expected to erode the lumen-hour 

demand per year per square foot, by turning lights off or down when they are not needed or 

wanted. While that erosion in conventional lighting demand will mainly affect energy use and, 

therefore, the NIA, controls penetration can have an indirect effect on lamp shipments via its 

impact on lamp lifetime. DOE’s projection of lighting controls penetration over the analysis 

period is described in appendix 9A. The impacts on lamp lifetimes are described in section

9.2.2.2. 
9-7

9.2.1.2 Consumer Choice Module

 The consumer choice module constitutes the analytical heart of the shipments model. 

In each year of the analysis period the consumer choice model assigns the market share of new 

purchases (shipments) to each product class grouping, and to each CSL within each product class

grouping, subject to the lamp options (or lamp-and-ballast options, as appropriate) that are 

available to the consumer. The simplifying assumption of the model is that lamp efficacies exist 

only at the discrete levels defined by the CSLs in the engineering analysis. First cost and 

operations and maintenance (O&M) costs are the key variables that the model uses to ‘decide’ 

which option is selected, where consumer sensitivity to first costs and O&M costs are inferred 

from historical data. 

 For fluorescent lamps the shipments model accounts for the costs and energy savings of 

both the lamps and their associated ballasts. Ballast shipments are tracked separately from lamps 

shipments, because ballasts last longer than lamps, and they affect the choice of replacement 

lamps, but are generally purchased together with a lamp. (The model assumes that, when a 

ballast is replaced, the lamp (or lamps) is replaced with it.) For both the ballasts and the lamps, 

the consumer choice model is used to make the selection. When a ballast is replaced, the 

consumer choice module is first run to select the ballast type. The cost calculation assumes that 

the first cost for the ballast includes a lamp of average price for that ballast type, and it accounts 

for the ballast O&M costs (which include the labor cost of lamp replacement, given the average 

lamp lifetime for that ballast type). The consumer choice module is then rerun to select which 

specific lamp type is assigned to the ballast, based only on the lamps’ first costs and O&M costs. 

Details of the modeling are described in section 9.3.4. 

 DOE adopted an existing consumer choice model for this preliminary analysis that also 

had been used by DOE to project the penetration of solid-state lighting (SSL) into the U.S. 

lighting market.3 The model, also used by others,4,5

Figure 9.1.1

allocates market shares as an aggregate of 

many individual purchasing decisions. As shown in , the consumer choice module 

couples an econometric conditional logit model with a technology diffusion model, using a Bass 

diffusion curve,6

6

 which limits the technology adoption rate based on historical observations. The 

Bass diffusion curve captures barriers to market entry, like lack of consumer information, that 

diminish over time with consumer exposure to the growing market. As those barriers diminish, 

the product achieves a market share that is more nearly described by the economic factors 

captured by the logit model.

While the technology diffusion model captures how product adoption increases over 

time, there are non-economic reasons for consumer preferences that persist over time and that are 

not captured in this model; this analysis uses an acceptance factor to capture these deviations 

from economic factors. For example, economic factors do not fully explain consumers’ persistent 

preference for 4-foot T8 lamps over 8-foot T8 lamps, which might be explained by aesthetics and 

greater ease in handling. In this preliminary analysis, the logit calibration was based on aggregate 

data from T8 and T5 lamps and was used to represent how consumers respond to price. The 

acceptance factors were used to calibrate the consumer choice module to how the actual market 

shares of the product class groupings considered in the shipments model differed from the logitbased predictions, which had been based on the aggregate T8 and T5 datasets. For example, the 
9-8

acceptance factor was used to reflect the much larger market share of 4-foot, rather than 8-foot, 

T8 lamps. The logit and diffusion model elements are described in more detail in this section; the 

acceptance factor calibration of the consumer choice model is detailed in section 9.3.4. 

Figure 9.2.1 Schematic Representation of the Consumer Choice Model

 The Conditional Logit Model. The conditional logit model calculates the probability that 

a consumer will purchase product j, (Pj)—based on a logistic curve probability function of the 

form:

Pj(z) = ezi

∑ e n zi i=1

Eq. 9.1 

Where: 

 

Pj(z) = the probability a consumer will purchase product j among n possible options, and

 z = the ‘logit’, which is defined as follows: 
9-9

zj = βFC ∗ FCj + βOM ∗ OMj

Eq. 9.2

Where:

βFC = consumer sensitivity to first cost,

FCj = first cost of product option j, 

βOM = consumer sensitivity to operations and maintenance cost, and

OMj = operations and maintenance cost of product option j. 

The regression coefficients (beta values), which represent the consumers’ sensitivity to 

first cost (βFC) and O&M cost (βOM), are determined from a logistic regression that fits historical 

shipments, first costs (FC), and O&M costs (OM) to the logistic curve. Sections 9.2.2.3 and

9.2.2.4 describe how first costs and O&M costs are handled for the two categories of lamps and 

for ballasts. 

The Bass Technology Diffusion Curve. The Bass diffusion curve sets the maximum 

market share the model will allocate to an individual product class grouping, given the 

technology diffusion rate for lighting products. If the consumer choice module initially allocates 

a market share that is too large according to the diffusion curve, the excess share is sent back to 

the consumer choice module to be reallocated with that particular product option eliminated from 

the choice matrix. 

 A Bass adoption curve is a 2-parameter diffusion curve widely used to describe how new 

products enter into markets. The two parameters, CE and CI, represent external and internal 

influences, respectively, on markets; see Bass6 and Pacific Northwest National Laboratory

(PNNL)

16 for more details. If the fraction of the market is zero at time = 0, the Bass diffusion 

curve is expressed in the following way:

MS(t) = 1 − e−(CE+CI)t

1 + �

CI

CE� e−(CE+CI)t

Eq. 9.3 

Where:

MS(t) = market share at time t, 

t = time since the product was introduced to the market (yr), 

CE = the coefficient of external influence, and

CI = the coefficient of internal influence. 

9.2.1.3 Price Learning Module

As described previously, the consumer choice model uses product prices as inputs. 

Consistent with current practice, DOE has adopted a ‘price learning’ model to project product 

prices over the analysis period.

7,8

 As originally defined, price learning reflects systematic 

decreases in manufacturing costs resulting from cumulative production experience. When price 
9-10 

learning analyses are considered on an industry-wide basis, rather than at the manufacturer level, 

and when they include learning effects downstream of production (for example, increased 

efficiencies in product distribution), the price learning curve is typically referred to as an 

experience curve, but it takes the same mathematical form. Consequently a broad range of cost 

and price metrics have been used to quantify learning rates for appliances and equipment (see, 

for example, Weiss et al., 2010, Table A1).9

Historical data are used to estimate the learning impact by fitting the data to a learning 

curve of the following form: 

p(X) = pinit ∗ X−b

Eq. 9.4 

Where: 

p(X) = the price of a particular product as a function of cumulative production (2011 

dollars), 

pinit = the initial price of the product at the time of market introduction (2011 dollars), 

X = cumulative production (total shipments) of the product from the time of its market 

introduction (number of units), and 

 b = a positive constant known as the learning rate parameter.

 As described in section 9.3.5, DOE used historical price and shipments data from the 

U.S. Census to determine the cumulative historical production and prices of lamps and ballasts 

sold into the U.S. market and, thus, to calibrate the learning rate parameter b. 

Eq. 9.4 can be used to obtain a projection for the price of lamps or fluorescent ballasts in 

each year, p(y), if the cumulative production is written explicitly as a function of time: 

X(y) = � s(v)

y−1

v=yinit

Eq. 9.5

Where:

 

X(y) = the cumulative production (total shipments) of a product between the year of its 

introduction and year y (number of units), 

y = the current year,

v = the vintage, or year, in which a product was shipped to market, 

yinit = the year of the product’s market introduction, and 

s(v) = the shipments in vintage year v (number of units; see Eq. 9.35, Eq. 9.38, and Eq. 

9.43) 
9-11 

Eq. 9.4 and Eq. 9.5 can then be combined to compute a price learning factor:

PLF(y) = � X(y)

X(2011)

�

−b

Eq. 9.6 

Where:

 

PLF(y) = the price learning factor in year y, and 

all other variables are defined in Eq. 9.4 and Eq. 9.5. 

 

The price learning factor is then used to calculate the price of any lamp option in any 

year, given its 2011 price, as determined in the engineering analysis (see chapter 5 of this TSD), 

using the following equation: 

p(y) = PLF(y) × p(2011) 

Eq. 9.7 

 

Where:

 

p(y) = the price of a particular lamp option in year y, 

p(2011) = the price of a particular lamp option in 2011, and 

PLF(y) is as defined in Eq. 9.6. 

9.2.1.4 The Coupled Model

 The shipments model uses the price learning rate and cumulative production information 

described in the previous section to calculate the price of each product in any year of the 

analysis, given the additions to the cumulative production estimate by the shipments model up to 

that point. Accordingly, the model proceeds step-wise each year to calculate product shipments 

based on prices and O&M costs via the demand and consumer choice modules. It then calculates 

the following year’s product prices based on that year’s shipments. 

9.2.2 Lamp Specific Modeling and Assumptions

 DOE projected the annual shipments of GSFLs and IRLs by computing the lighting 

demand for new construction and lighting renovation, as well as the lighting demand for 

replacement of failed lamps in each year, to obtain the total demand for new lighting shipments:
9-12 

D(y) = DNCR(y) + DF(y)

Eq. 9.8 

Where:

y = the year of the analysis periodc

D(y) = the total lighting capacity demand for new shipments in year y (lm), 

, 

DNCR(y) = the total lighting capacity demand for new construction and lighting 

renovations (lm), and

DF(y) = the national lumen capacity demand for replacement of failed lamps and lampand-ballast systems (lm). 

 DOE then apportioned this demand among the various technology options via the 

consumer choice module to determine the shipments of each product class grouping or 

technology option in each year. 

 Given values for the retirements and new shipments in year y, as well as the total stock in 

year y-1, the stock of lamps or lamp-and-ballast systems in year y can be calculated as:

S(y) = S(y − 1) − R(y) − F(y) + s(y)

Eq. 9.9 

Where:

S(y) = the national stock of lamps or lamp-and-ballast systems in year y (number of 

units), 

R(y) = lamps or lamp-and-ballast systems retired for lighting renovations in year y

(number of units), 

F(y) = lamps or lamp-and-ballast systems that fail (or are removed for scheduled 

relamping) and are replaced in year y (number of units), and

s(y) = the total shipments of new lamps or lamp-and-ballast systems in year y (number of 

units). 

Eq. 9.9 requires the stock to be initialized at the beginning of the analysis period. The 

technique for initializing the stock model is described in section 9.1.1. For the purposes of 

computing the NES in the NIA (chapter 10 of this TSD), however, it is not necessary to compute 

the total installed stock of lamps and lamp-and-ballast systems in the United States. The only 

portion of the stock that is relevant to this calculation is made up of lamps shipped during or after 

the compliance year of the standard being considered, yrule. For this analysis, DOE refers to that 

relevant portion of the stock as the operating stock shipped during the analysis period

(OSSDAP). The OSSDAP in each year, denoted S′

(y), can be computed from Eq. 9.9 with the 

assumption that S′

(yrule − 1) = 0. 

 

c The time variable y in this analysis is a discrete variable representing the year of the analysis period. Throughout 

the remainder of this preliminary analysis, however, quantities that depend on y will be written in the form D(y), 

which is more typically used for functions of a continuous variable, rather than the usual subscript form that is 

conventionally used for discrete variables Dy. This is done for the sake of avoiding confusion with other subscripts 

used in the notation.
9-13 

 A complication to this basic picture arises in the case of projecting GSFL shipments. The 

choice of a fluorescent lamp by a consumer depends on the ballast to which the lamp will be 

coupled. If a consumer is replacing a lamp on an existing ballast, the lamp must be compatible 

with the ballast. Therefore, the GSFL part of the shipments model must account for the 

shipments and stock, throughout the analysis period, of ballasts that can be coupled to the 

analyzed product class groupings. DOE therefore models GSFL shipments in two steps: first, a 

turnover model for ballasts is computed to project ballast shipments and stock using the 

equations described previously; then, the lamp shipments and stock are derived from the ballast 

projection by computing the lamp-replacement probability on the projected stock of ballasts. 

With that caveat, the equations described previously are the fundamental equations 

underlying the shipments and stock modeling in this analysis. The remainder of this section will 

be devoted to computing the various components of these equations for IRLs, GSFLs, and for 

fluorescent ballasts as a preliminary step to computing the GSFL shipments and stock.

9.2.2.1 Modeling Lighting Demand for New Construction and Renovations 

 To project the lighting demand for new construction, DOE assumed a constant demand 

for lighting capacity per square foot of floor space (lm/ft2 at maximum lamp output), so that 

overall lighting demand grows at the same sector-specific annual growth rate as floor space.

Thus, the annual lighting demand for new construction (DNC) in a particular sector is given by: 

DNC(y) = K(y0)[(1 + γ)y−y0 − (1 + γ)y−y0−1]

Eq. 9.10 

Where:

 

DNC(y) = the total lighting capacity demand for new construction (lm), 

K = the total lighting capacity (lm at maximum output) of the installed stock in the sector 

being analyzed (lm), 

yo = the initial year of the model, and

γ = the sector-specific, 25-year (2010-2035) average floor space growth rate projected by

AEO2012. 

 In addition, DOE assumes that a fixed percentage of the lamp stock in each year is 

removed from service for renovations or lighting retrofits. The number of lighting units (IRLs or 

fluorescent lamp-and-ballast systems) removed for renovations in year y is then: 

R(y) = S(y − 1)fren

Eq. 9.11 

Where:

 

R(y) = stock removed for renovation in year y (number of units), 

S(y − 1) = total installed stock (number of units) in year y-1 (computed in the following 

sections for IRLs and for fluorescent ballasts), and 
9-14 

fren = fraction of the stock retired for renovations in each year. 

 This is added to the new-construction demand to yield the total lighting demand for new 

construction and renovation: 

DNCR(y) = DNC(y) + R(y)Λ

Eq. 9.12 

Where:

DNCR(y) = total lighting capacity demand for new construction or renovation in year y

(lm), and 

Λ = maximum lumen output of the lamp or lamp-and-ballast system being considered

(lm/unit). 

DOE takes the fraction fren to be 3% of the total commercial and industrial stock and 1% of the 

total residential stock, following the assumptions used in the 2011 fluorescent ballast 

rulemaking.10

Table 9.1.2

 Shipments projections for GSFLs and IRLs are computed independently for the 

sectoral breakdowns indicated in .

9.2.2.2 Modeling the Retirement of Lamps and Lamp-and-ballast Systems 

DOE determined the lighting demand for replacement shipments in a given year by 

computing the number of shipments from previous years that would be expected to retire in that 

year. DOE based its model for the retirement of lamps and ballasts on the Weibull distribution. 

The probability that a particular unit survives to a time t after its initial installation is:

wS(t) = �exp �− �t − d

λT �

k

� , t > d

1, t ≤ d

Eq. 9.13 

Where:

wS(t) = the probability that a unit survives to time t after its initial installation,

t = the time since installation, in units of either hours or years, which is always 

nonnegative, 

T = a characteristic lifetime for the lamp or ballast, in the same units as t,

d = a delay parameter specifying the minimum lifetime of the unit, in the same units as t, 

k = a parameter controlling the shape of the distribution, and 

λ= a parameter controlling the characteristic retirement age.

The specific parameters and time units that DOE used to specify the survival probability 

of different lamps and ballasts are summarized in Table 9.2.3. Their derivations are described

later in this section.
9-15

Table 9.2.3 The Parameters and Time Units of the Weibull Distributions Used in the 

Shipments Analysis

Product Time 

Units

Delay 

parameter 

d

Weibull 

shape 

parameter k

Weibull 

scale 

parameter λ

Characteristic 

Lifetime T 

IRL Hours 0 4.26 1.02 Lamp life hours

(Table 9.3.14)

GSFL Hours 0 5.50 1.10 Lamp life hours

(Table 9.3.13)

Fluorescent ballast –

Residential Sector

Years 2.00 2.50 1.02 15.0

Fluorescent ballast –

Commercial Sector

Years 1.50 5.00 1.04 12.6

Fluorescent ballast –

Industrial Sector 

Years 0 5.00 0.92 10.3

It is more computationally useful in many cases to utilize the probability that a lamp 

retires during some well-defined time interval—during the tenth year of its life, say, or the 

5,000th hour of its operation. In this discussion, the probability that a unit retires between time t-1 

and time t is written as:

wR(t) = wS(t − 1) − wS(t)

Eq. 9.14 

Where:

wR(t) = the probability that a unit retires between time t-1 and time t, 

wS(t) = the survival probability defined in Eq. 9.13, and

t = the time since installation as defined following Eq. 9.13. 

IRL Retirement. As described previously, the Weibull retirement distribution for IRLs 

depends on the characteristic lifetime, T, of the IRL. To determine T for the purposes of the 

shipments modeling, the rated lifetime for each lamp option given in the engineering analysis 

(chapter 5 of this TSD) is adjusted to account for the impact of dimmers on lamp life. Operating 

an incandescent lamp dimmed (i.e., at reduced wattage) increases lamp lifetime, often by a 

significant factor. 

 To account for this, DOE made use of the dimmer-related correction factors discussed in 

appendix 6A of this TSD. DOE assumes that operating a lamp on a dimmer will lead to a 20% 

reduction in energy consumption on average; this corresponds to a factor of 3.94 increase in 

lamp lifetime for individual incandescent lamps. DOE assumed that 29% of residential IRLs and 

5% of commercial IRLs operate on dimmers and that these fractions are constant with time.d

 

d Growth in controls penetration for IRLs in the model is assumed to be purely in switch-based controls, not in 

dimmers, and growth is assumed to occur only in the commercial sector.
9-16 

These fractions imply that the national average lamp lifetimes in each sector increase by 85% 

and 15%, respectively. Therefore, in the shipments analysis, DOE adjusts upward by these 

amounts the estimated lifetime from the engineering analysis for IRLs.

DOE used the Weibull retirement distribution to compute an IRL survival function that is 

defined as a function of the total hours of lamp use (see Table 9.2.3). Thus, computing the lamp 

failures in each year required transforming the survival function from a function of the hour h to 

a function of the year a of a particular lamp’s lifetime. DOE did this by convolving the Weibull 

retirement distribution, Eq. 9.14, with the same sector-specific hours-of-use distribution, f(u), 

that was used in calculating the life-cycle cost (LCC) (chapter 8 of this TSD)e

PR(a) = � wR(h)f(h/a)

hmax

h=0

:

Eq. 9.15 

Where:

PR(a) = probability of lamp retirement in year a of lamp’s life, 

wR(h) = the Weibull retirement function, as defined in Eq. 9.14, 

a = the lamp’s age (yr), 

h = the total time that the lamp has been operated (hr), 

hmax = the maximum expected lifetime of a lamp (hr), and 

f(h/a) = hours of use distribution f(u) evaluated at the value u=h/a. 

To parameterize the Weibull distribution in Eq. 9.15, DOE uses the parameters determined from

laboratory testing of incandescent lamp failure rates.

11 These parameters are listed in Table 9.2.3. 

From the probability function, Eq. 9.15, one can calculate the average lamp lifetime 

measured in years, L, with all parameters defined as in Eq. 9.15: 

L = � aPR(a)

∞

a=0

Eq. 9.16 

It is also possible to use that probability function to compute the expected lamp failures 

in year y, given a time series of historical shipments spanning the maximum expected age 

reached by any lamp, amax: 

 

e In principle this distribution should be adjusted to account for the increasing penetration over the analysis period of 

switch-based controls, like timers and occupancy sensors, in the commercial sector. However, the impact of this 

effect is relatively small (typically around 15% on average across all shipments if controls reduce usage by 30%) 

and will have a negligible impact given the very short lifetimes of commercial IRLs, so DOE neglects this effect in 

its shipments analysis. However, the impact on energy consumption of switch-based controls is accounted for in the 

NIA.
9-17 

FIRL(y) = � PR(y − v)

y−1

v=y−amax

sIRL(v)

Eq. 9.17 

Where:

FIRL(y) = failures of IRLs in year y (number of units), 

y = current year,

v = vintage, or year, of shipments, 

amax = maximum expected lamp lifetime (yr), 

PR(y − v) = probability of lamp failure in year a=y-v of a lamp’s lifetime, and

sIRL(v) = shipments that occurred in a particular vintage (number of units). 

 DOE uses the equations just defined, along with historical shipments data, to compute the 

lamp failures that require replacement in each year. The lighting capacity demand that must be 

met to replace these failed lamps is then: 

 

DF,IRL(y) = FIRL(y)ΛCL

Eq. 9.18 

Where:

DF,IRL(y) = lighting capacity demand to replace failed lamps in year y (lm), 

FIRL(y) = lamp failures in year y (number of units), 

Λ = maximum lumen output of the lamp being considered (lm/unit), and 

CL = a lifetime correction factor.

The lifetime correction factor CL = max(L, 1), where L is the lamp lifetime in years (Eq. 

9.16), is necessary to account for lamps with average lifetimes shorter than one year, which will 

yield multiple shipments per fixture per year, which will not be operated simultaneously. The 

total lighting demand is then DIRL =DNCR,IRL + DF,IRL (where DNCR,IRL is the demand for IRLs in 

new construction and renovations) . In practice, DOE computes the demand independently for 

each of the three lamp options considered in the engineering analysis for IRLs (Baseline 1, 

Baseline 2, and CSL 1). 

Fluorescent Ballast Retirement. To compute the demand associated with the 

replacement of retired ballasts, DOE follows the ballast retirement model used in the 2011 

fluorescent ballast rulemaking10. The probability of a ballast’s retirement from the stock during 

year aB of its lifetime is described by a Weibull distribution: 
9-18 

PBR(aB) = wR(aB)

Eq. 9.19 

Where:

PBR(aB) = the probability that a ballast retires from the stock in the aB

th year since its 

installation,

wR(aB) = the Weibull retirement distribution given in Eq. 9.14, and

aB = the ballast’s age (yr). 

The probability that a ballast survives to be aB years old is also described by the appropriate 

Weibull function: 

PBS(aB) = wS(aB)

Eq. 9.20 

Where:

PBS(aB) = the probability that a ballast survives for aB years after installation, 

wS(aB) = the Weibull survival distribution given in Eq. 9.13, and

aB = the ballast’s age (yr). 

 For ballasts, DOE used a retirement and survival probability defined as a function of 

ballast age, rather than hours of use as for lamps, for consistency with the 2011 fluorescent 

ballast rulemaking analysis. In that analysis, DOE used the sector-specific model parameters 

given in Table 9.2.3, which are the same model parameters used for the present analysis. To 

model the commercial and industrial sectors jointly in this analysis, DOE used a weighted 

average of the parameters for the commercial and industrial sector when modeling each product 

class, according to the relative distribution of each class among the two sectors, as given in Table 

4.1 of DOE’s 2010 Lighting Market Characterization (LMC). 12

The retirement model for ballasts was developed in the ballast rulemaking from studies 

that measured the actual lifetimes of fluorescent ballasts in the field. Thus, DOE assumed that it 

includes the effect both of ballasts that fail and of ballasts that are retired for renovations. The 

number of ballasts that are removed from the stock due to failures and renovations in each year is 

given by: 

FB(y) + RB(y) = � PBR(y − v)

y

v=y−aB,max

sB(v)

 Eq. 9.21 

Where:

FB(y) = ballast failures in year y from the product class being considered (number of 

units), 

RB(y) = ballasts retiring in year y from the product class being considered (number of 

units), 
9-19 

y = the model year,

v = the vintage, or year, of shipment, 

aB,max = the maximum expected ballast age (yr), 

sB(v) = shipments in vintage year v (number of units), and

PBR(y − v) = probability of ballast retirement in or before year y − v of the ballast life, 

as defined in Eq. 9.19. 

Because renovations are already accounted for as a fixed fraction of the total stock in the 

computation of DNCR above, this portion of the demand must be subtracted from the total demand 

for replacing retired ballasts to yield the total demand for replacing failed ballasts: 

DF,B(y) = (FB(y) + RB(y))ΛB(y) − SB(y − 1)frenΛB(y − 1)

Eq. 9.22 

Where:

DF,B(y) = the lighting demand to replace failed ballasts in year y from the product class 

being considered (lm), 

ΛB(y) = the average lumen output of installed ballasts (lm/unit) (This depends on the 

distribution of installed lamps among the various efficiency levels and technology 

options, computed in section 9.2.2.5.), 

SB(y − 1) = stock of ballasts in the product category being considered in year y-1

(number of units) (Eq. 9.38), and 

fren = fraction of the stock retired for renovations in each year. 

GSFL Retirement. As is the case with IRLs, the GSFL survival function depends on the 

GSFL Weibull retirement function, Eq. 9.14, which in turn depends on the characteristic lamp 

lifetime, T. In the case of IRLs, lamp lifetimes were corrected for the effect of lighting controls, 

before being used by the Weibull function in the shipments model. In the case of GSFLs, the 

effect of lighting controls is different and more complicated. Increased use of lighting capacity 

under lighting controls in the commercial and industrial sectors has the effect of shifting lighting 

systems to programmed start ballasts more rapidly, because fluorescent lighting control systems 

generally include these ballasts. GSFLs operating on programmed start ballasts tend to last 

longer than those operating on instant start ballasts. Other effects of lighting controls include 

increased lamp lifetime due to decreased operating hours as well as decreased lamp lifetimes due 

to increased switching. DOE assumes the net effect of these two approximately cancel out and 

considers only the lamp lifetime increase caused by the programmed start ballast itself. This 

requires no adjustment of GSFL lifetimes obtained from the engineering analysis (chapter 5 of 

this TSD) for the shipments modeling, given that the model explicitly addresses the shift to 

programmed-start ballasts caused by controls, and the model then selects the lamp lifetime 

appropriate to the ballast it is coupled with (see Table 9.3.13).

DOE believes that a certain fraction of GSFLs in the commercial and industrial sector are 

subject to scheduled group relamping, in which all lamps within a space are replaced 

simultaneously when they have reached a predetermined fraction of their rated lifetime (in 

hours). DOE assumed that group relampings occur, on average, when lamps reach 85% of their 
9-20 

rated lifetime. To account for this effect, DOE computed the characteristic lamp lifetime by 

adjusting the GSFL life hours in chapter 5 of this TSD, according to the following equation. 

T = TRated(1 − 0.15fGR)

Eq. 9.23 

Where:

TRated = the rated lamp lifetime, in hours, and 

fGR = the fraction of lamps that are subject to group relamping. 

 DOE used the group relamping fractions reported in the 2011 ballast rulemaking10 for 

this preliminary analysis. To simplify the model, DOE also assumed that, for each ballast type, 

all lamps coupled to that ballast have the same rated lifetime, TRated, and that this is given by the 

lifetime of the baseline lamp option, which was taken to be representative of all lamps in the 

product class grouping. 

 DOE uses the ballast shipments and stock projections as the basis to compute the 

shipments and stock of GSFLs. To do this, DOE developed a relamping schedule, Prelamp(aB), 

which represents the probability that a ballast has a new lamp installed when it is aB years old 

(provided that it survives to that age). DOE assumes that old lamps are disposed of upon ballast 

retirement so that all new ballasts are coupled with new lamps when they are installed. This 

implies that Prelamp(0) = 1: that is, there is a 100% probability in the model that a ballast has a 

new lamp installed when it is first installed. 

For aB>0, the probability of ballast relamping depends on the probability of lamp failure 

in the hBth hour of the ballast’s operation. The relamping probability also depends on the annual 

hours of lamp use, u, and on the average number of hours, η, that the lamp is operated each time 

it is started, as GSFLs that are switched on and off more frequently have degraded lifetimes. For 

a set of discrete usage patterns across a given sector, the lamp failure probability in each year of 

the ballast life is:

Prelamp(aB) = �

� Prelamp

′ �aBuq�ηq�fq

q

, aB > 0

1, aB = 0

Eq. 9.24 

Where:

Prelamp(aB) = the probability that a ballast is relamped when it is aB years old, 

q = an index specifying a particular lighting application with a particular usage pattern, 

uq = the average annual hours of lamp use for application q (hr), 

ηq= the average hours of use per lamp start for application q (hr), 

fq = the fraction of all lighting demand associated with application q, 

aB = the number of years since the ballast’s installation (yr), and 
9-21 

Prelamp

′ (aBuq|ηq) = the conditional probability that a ballast is relamped in hour 

hB = aBuq of its operation, given an average of ηq hours of use per start. 

 DOE used the distribution of usage hours from the LCC analysis (chapter 8 of this TSD) 

to determine uq and fq. For each application q, DOE also specified an average hours of use per 

start, ηq, based on industry estimates. The values used in this analysis are given in Table 9.3.15, 

Table 9.3.16, and Table 9.3.17. 

 The probability of relamping as a function of the ballast’s operating hours, given its 

usage pattern, can be computed by summing over the probability that the ballast undergoes its 

nth relamping, for all values of n: 

Prelamp

′ (hB|η) = � Prelamp,n(hB|η)

n

Eq. 9.25 

Where:

Prelamp,n(hB|η) = the conditional probability that the ballast has its nth relamping in 

hour hb of its operation, given that it is burned for η hours per start, 

hB = the number of hours that the ballast has been operated (hr), and

 all other parameters are defined as in Eq. 9.24. 

The sum in Eq. 9.25 is formally an infinite sum, but in practice it is sufficient to compute the first 

few terms of the sum over a domain limited to the maximum expected ballast lifetime in hours.

The sum can be truncated; adding extra terms has a negligible impact on the probability 

computed over that domain. 

 The probability of the nth relamping can be defined recursively from the probability of an 

individual lamp’s retirement as a function of each individual lamp’s operating hours and the 

average number of hours per start, PLR(hL|η). The probability of the first relamping on a ballast 

is just equal to this distribution evaluated at hL = hB: 

Prelamp,1(hB|η) = PLR(hB|η)

Eq. 9.26 

Where:

PLR(hB|η) = the probability that a lamp retirement occurs in hour hL = hB of the lamp’s

lifetime (specified below). 

 The probability of the nth relamping can then be computed recursively for n > 1 using 

the following equation: 
9-22 

Prelamp,n(hB|η) = � PLR(hB

′ |η)Prelamp,n−1(hB − hB′ |η)

hB

hB

′ =0

Eq. 9.27 

Where:

all parameters are defined as in the previous equations. 

 DOE modeled the lamp retirement probability in the above equations as a Weibull 

distribution whose characteristic lifetime parameter depends on the usage pattern:

PLR(hL|η) = wR(hL; T(η))

Eq. 9.28 

Where:

PLR(hL|η) = the probability of a lamp’s retirement in year hL of its operation (given that 

its ballast survives that long), 

wR(hL; T(η)) = the Weibull retirement function (Eq. 9.14), where the dependence on the 

characteristic lifetime T has been made explicit,

hL = the number of hours that the lamp has been operated (hr), and

T(η) = the characteristic lifetime parameter of the Weibull distribution, which depends 

on η, as described below. 

DOE determined the parameters of this distribution from the lamp failure curves 

published in chapter 6 of the Lighting Handbook13

Table 9.2.3

, obtaining the values of k and λ given in

. DOE also determined the scaling of lamp lifetime with η from the same published 

curves. The characteristic lifetime T(η) is given by scaling the rated lamp lifetime by a scaling 

factor that depends on η. Assuming that the rated lamp lifetime reported by manufacturers 

corresponds to η=3 hours per start, the scaling of lamp lifetime to different values of η is 

tabulated in Table 9.2.4. Combining the previously defined equations, it is possible to compute 

the relamping schedule Prelamp(lB) from Eq. 9.24. 

Table 9.2.4 Scaling of Lamp Lifetime with Average Hours of Lamps Use per Start

Average burn 

hours per 

lamp start

Lamp mean 

lifetime as a 

percentage of the 

nominal lifetime

0.1 24

0.2 38

0.3 45

0.4 50

0.5 54

0.6 58

0.7 61
9-23 

0.8 64

1 70

2 89

3 101

4 110

5 116

6 121

7 125

8 129

10 134

20 149

30 156

40 159

60 161

100 162

The equations above, with some minor modifications, can also be used to derive the 

average lamp lifetime, measured in years, after accounting for the various usage patterns present 

in the stock and assuming that the ballast survives throughout the lamp’s life: 

LL = � aBP1st relamp(aB)

∞

aB=0

Eq. 9.29 

 

Where:

LL = the average lifetime of a GSFL, in years, given that its ballast does not fail during 

the lamp’s life, and

P1st relamp(aB) = the probability that a ballast undergoes its first relamping in year aB of 

its life, which can be computed from Eq. 9.24, with the substitution of Prelamp,1

(Eq. 9.26) for Prelamp

′ . 

 Fluorescent Lamp and Ballast Joint Survival Probability. The relamping schedule 

depends on the probability PLR that a given lamp is retired, provided that its ballast survives. For 

some applications in this preliminary analysis it will be necessary to know the total probability 

that a lamp survives to a given age, without either being retired on its own or because its ballast 

is being replaced. This probability depends on the ballast lifetime model and on the probability 

that a lamp is installed on a ballast of a particular age. It is derived below. 

The probability that a particular lamp is installed on a ballast that is in year aB of its life 

is: 
9-24 

PLIB(aB) = 1

NLIB

Prelamp(aB)PBS(aB)

Eq. 9.30 

Where:

 

PLIB(aB) = the probability that a lamp is installed on a ballast when the ballast is aB years 

old, 

Prelamp(aB) = the probability that a ballast is relamped in year aB of its life, provided that 

it survives that long, 

PBS(aB) = the probability that the ballast survives to age aB (Eq. 9.20),

aB = the age of the ballast (yr), and 

NLIB = a normalization factor that ensures that this quantity sums to unity. 

The probability that a lamp’s ballast is retired in year aL of the lamp’s life is then:

PBRL(aL) = 1

NBRL

� � PBR(aB)PLIB(aB − aL

′ )

LB,max

aB=aL

′

LB,max

aL

′ =0

Eq. 9.31 

Where:

 

PBRL(aL) = the probability that a lamp’s ballast is retired in year aL of the lamp’s life,

PBR(aL) = the probability that a ballast retires in year aB of its life (Eq. 9.19),

aL = the age of the lamp (yr), 

LB,max = the maximum ballast lifetime (yr), and

NBRL = a normalization factor that ensures that this quantity sums to unity. 

All other variables are as in Eq. 9.30. 

The previous distribution can be combined with the lamp retirement and survival 

probability distributions to give the approximatef

PLBR(aL) = 1

NLBR �PBRL(aL)PLS(aL) + PLR(aL)�1 − � PBRL(aL

′ )

aL

aL

′ =0 ��

 probability that a lamp or its ballast are retired 

in year aL of the lamp’s lifetime:

Eq. 9.32 

Where:

 

PLBR(aL) = the probability that a lamp or its ballast is retired in year aL of the lamp’s 

lifetime,

 

f Eq. 9.32 is only approximately correct, because it does not account for the growth of the ballast stock over the 

summation period. However, as this computation only feeds into the calculation of the stock fractions represented 

by different technologies, this approximation is sufficient, given that these fractions do not change rapidly during the 

analysis period. 
9-25 

PLS(aL) = the probability that a lamp survives to age aL, 

PLR(aL) = the probability that a lamp is retired in year aL of its life,

NLBR = is an appropriate normalization parameter, and

 all other parameters are as in Eq. 9.31. 

The average lamp lifetime and the probability that a lamp and its ballast both survive to lamp age 

aL are then simply given by summing over the retirement probability: 

LLB = � aLPLBR(aL)

∞

aL=0

Eq. 9.33 

PLBS(aL) = 1 − � PLBR(aL

′ )

aL

aL

′ =0

Eq. 9.34 

Where:

LLB = the average lifetime of a GSFL, in years, accounting for the probability 

 that either the lamp or its ballast retires.

PLBS(aL) = the probability that a lamp and its ballast both survive to the end of year aL of 

the lamp’s life, and

all other parameters are as in Eq. 9.32. 

The latter equation is the probability distribution that is used in section 9.2.2.5 in apportioning 

the lamp stock among the various efficiency levels.

9.2.2.3 Incandescent Reflector Lamps: Turnover and Shipments

Because the three different lamp options considered for IRLs have significantly different 

lifetimes, it was necessary to explicitly model the shipments for each IRL lamp option 

separately. Additionally, because of the different usage patterns in each sector, DOE modeled 

lamps separately in the residential and commercial sectors. 

 

 DOE computes the total lighting demand for each lamp option separately within each 

sector, according to Eq. 9.8, Eq. 9.12, and Eq. 9.18. DOE then reallocates this demand among the 

three lamp options using the consumer choice model, yielding a projection for the shipments of 

each lamp option in each year:

sIRL,l(y) = � Dk(y)Λk

−1σkl(y)

k

 Eq. 9.35 

Where:

sIRL,l(y) = projected shipments for IRL option l in year y (number of units), 
9-26 

Dk = the total lighting demand for lamp option k, which is the sum of the demand for 

replacements and new construction (lm), 

Λk = maximum lumen output of lamp option k (lm/unit), and 

σkl (y)= the substitution matrix in year y. 

The substitution matrix, σkl, specifies the fraction of consumers who switch between the lamp

options, according to the consumer choice model: 

σkl(y) =

ΛiCL,l

ΛjCL,k

Pkl(z)Akl(y)

Eq. 9.36 

Where:

Λk = maximum lumen output of lamp being replaced k (lm/unit), 

Λl = maximum lumen output of replacement lamp l (lm/unit),

CL,k = lifetime correction factor for lamp k, 

CL,l = lifetime correction factor for lamp l, 

Pkl = probability of purchasing lamp option l from among the available lamp options, 

given that option k is being replaced, and 

Akl (y) = availability matrix.

The availability matrix Akl(y) specifies the products that are available to a consumer who 

is replacing a failed lamp of lamp option k: it is zero when lamp option l is not a direct substitute 

for k, or when lamp option l has been eliminated by a proposed standard in the standards case; it 

is equal to unity otherwise. In the case of IRLs, all lamp options being considered are directly 

interchangeable, so Akl(y) =1 for all l except those that would be eliminated by a proposed 

standard. The choice probability Pkl(z) is the probability of purchasing lamp option l from among 

the available lamp options, given that lamp k is being replaced, according to the consumer choice 

model described in section 9.3. 

As also described in section 9.3, the logit z depends linearly on the first costs and the 

annual O&M costs of the available lamps. It is thus an implicit function of time, because the 

product price varies in each year according to the learning model, starting from the prices 

determined for the year 2011 in the engineering analysis. The lamp first costs FCl are given by

the learning-corrected lamp price, computed from Eq. 9.4 and Eq. 9.5, plus sales tax and the 

labor cost for installation determined in the LCC analysis. The O&M costs for IRLs have two 

components: energy costs and the relative relamping costs, averaged annually, for lamps with 

different lifetimes:

OMl(y) = pE(y) × Wl × u� + �

1

Ll

− 1

max({Lk})� FCl

Eq. 9.37 

Where:

 

OMl = the O&M costs of lamp option l ($/yr), 
9-27 

FCl = the first cost of lamp option l ($), 

pE(y) = the sector-specific price of electricity, in year y, as forecast in the AEO2012

reference scenariog

Wl = the national-average wattage of lamp option l (W), 

 ($/kWh), 

u� = average annual hours of use in the sector being considered (hr), 

Ll = the average lifetime of lamp option l (yr), and 

max ({Lk}) = the maximum lifetime of all lamp options (yr).

 For years beyond the end of the AEO projection, which was in 2035, DOE extrapolated 

pE(y) from the trend in the period from 2025 to 2035, through 2060, and held prices constant 

thereafter. While for the shipments analysis electricity prices are relevant only through the end of 

the shipments analysis period in 2046, a longer analysis period is required for the NIA, as 

described in chapter 10 of this TSD. As discussed in section 9.2.2.3, DOE considers that some 

fraction of IRLs is installed on dimmers. Since the use of dimmers will affect operating wattages

of IRLs, DOE adjusts the rated wattage of each IRL option downward by a factor of 6% and 1% 

in the residential and commercial sectors, respectively, to account for typical dimming rates and 

the fractions of lamps that are installed on dimmers in each sector. 

DOE uses the model above to project the shipments of each IRL option in each year of 

the analysis. The input parameters, and their calibration, are discussed in section 9.3.4. Given the 

projections of failures, renovations, and new shipments in each year, and a calculation of the 

total operating stock in the initial year of the analysis period, Eq. 9.9 then yields the total 

operating stock of IRLs in the United States in each subsequent year. DOE also uses that 

equation to compute the OSSDAP (as described in the text following Eq. 9.9) as an input for 

computing the NES in the NIA (chapter 10 of this TSD). 

9.2.2.4 General Service Fluorescent Lamps: Turnover, Consumer Choice, and 

Shipments

As discussed previously, DOE takes a two-stage approach to projecting GSFL shipments, 

first by projecting the shipments and stock of fluorescent ballasts, then using this projection as a 

basis to project lamp shipments. This approach introduces a few complications to the consumer 

choice model used to compute lamp turnover. For example, if the consumer is purchasing a new 

lamp-and-ballast system, for a lighting renovation or new construction, the choice will depend on 

the first cost and O&M cost of the lamp-and-ballast system, with the O&M cost also including 

the price of replacement lamps; but, if the consumer is purchasing only a replacement lamp, the 

lamp price will be included in the first cost. An additional complication also arises because the 

 

g Some model scenarios for the NIA in chapter 10 of this TSD use the High- or Low-Economic-Growth AEO 

forecasts for electricity price. In principle, the shipments analysis should also use these forecasts in such cases, 

because the different electricity prices will impact the consumer choice model. However, DOE performed a 

sensitivity analysis using the different AEO forecasts in the shipments model and found negligible impact on the 

projected shipments. DOE, therefore, chose to use only the reference AEO scenario in the shipments analysis, 

regardless of the electricity price forecast selected for the NIA. 
9-28 

GSFL category includes multiple product class groupings, so the consumer choice model must 

apportion lighting demand among these product class groupings in addition to the different 

efficiency levels (i.e., lamp options) within each product class grouping. To address these issues, 

DOE treats the choice of lamp and lamp-and-ballast system as independent choice events in the 

consumer choice model. As the different GSFL product class groupings are not interoperable on 

the same ballast, DOE assumes in the shipments analysis that a consumer’s choice of a product 

class grouping occurs when choosing a ballast, while the choice of an efficiency level occurs 

when choosing a lamp to couple to a new or existing ballast. 

 Each product class grouping in the model is then represented by one or a few notional 

ballast types that have properties consistent with the national average for each type. The 4-foot 

MBP T8 grouping is represented by two commercial ballast types (programmed and instant start) 

and one residential type, and the 4-foot MBP T12 grouping is represented by one commercial 

and one residential ballast. All other groupings are represented by a single ballast type. The 

ballast types are listed in the first column of Table 9.2.5. 

Ballast Shipments. DOE uses a ballast turnover model that is broadly similar in its 

operation to the turnover model for IRLs developed in section 9.2.2.3, but there are differences 

in the details. DOE determined the total demand for new ballast shipments according to Eq. 9.8, 

Eq. 9.12, and Eq. 9.22. DOE then apportions this demand among the available product class 

groupings in two ways. DOE assumes that, when ballasts are replaced due to equipment failure, 

they are replaced with a ballast of the same type. In the case of new construction and 

renovations, however, DOE allocates the shipments to different ballast types, using the consumer 

choice module. The total shipments of ballasts in ballast type j are then given by: 

sB,j(y) = DF,j(y)

ΛB,j(y)

+ �DNCR,i(y)σij(y)

ΛB,i(y) i

Eq. 9.38 

Where:

sB,j(y) = the shipments of ballasts of type j, in year y (number of units), 

DF,j(y) = the lighting capacity demand for replacements of failed ballasts of type j in 

year y (lm), 

DNCR,i(y) = the lighting capacity demand for ballasts of type i in new construction and 

renovations in year y (lm), 

ΛB,i(y) = the average light output of a ballast of type i in year y (lm/unit), and

σij(y) = the substitution matrix for ballasts of types i and j.

The substitution matrix for ballasts, σij, is similar to the one defined for IRLs in Eq. 9.36, but no 

lifetime correction factors are required:

σij(y) =

ΛB,i

ΛB,j

Pij(z)Aij(y) 

Eq. 9.39 
9-29 

Where:

Pij = the probability of purchasing a ballast of type j given that ballast type i is being 

replaced, 

z = the logit variable, defined in section 9.2.1, and 

Aij (y) = the availability matrix of ballast types. 

The availability matrix in the ballast turnover model defines whether or not ballast type j

can be considered a substitute for ballast type i. This matrix is fixed throughout the analysis 

period, and, unlike in the case of lamps, it does not change between the base case and the 

standards cases, as the candidate standard levels analyzed here will not eliminate any product 

classes. Table 9.2.5 summarizes the substitutions that are available in the ballast choice model.

 Notably, as shown in Table 9.2.5, the consumer choice model does not allow for 

consumer switching between instant start and programmed start ballasts for the 4-foot MBP 

lamps. DOE believes that these different ballast types are generally used in different 

applications; therefore, these ballast types are not considered interchangeable in the consumer 

choice model. To model any switching between instant and programmed start ballast, DOE notes 

that the latter category is typically used in conjunction with automatic lighting controls. 

Therefore, in each year of the shipments projection, DOE exogenously reallocates a fraction of 

the instant start ballast shipments to the programmed-start category, so that the market share of

programmed start ballasts within the 4-foot MBP product class is equal to the fraction of 

commercial floor space implementing controls in that year (see appendix 9A). 

Table 9.2.5 Ballast Substitution Matrix

Description of retiring ballast type Available substitute ballast types

4-foot MBP T12 (Commercial Sector) 4-foot MBP T8 Instant Start (Commercial Sector); 

T5 SO

4-foot MBP T8 Instant Start 

(Commercial Sector)

4-foot MBP T8 Instant Start (Commercial Sector)*; 

T5 SO

4-foot MBP T8 Programmed Start 

(Commercial Sector)

4-foot MBP T8 Programmed Start (Commercial 

Sector); T5 SO

4-foot MBP T12 (Residential Sector) 4-foot MBP T8 Instant Start (Residential Sector)

4-foot MBP T8 Instant Start (Residential 

Sector)

4-foot MBP T8 Instant Start (Residential Sector)

8-foot SP slimline T12 8-foot SP slimline T8; 4-foot MBP T8 Instant Start 

(Commercial Sector); T5 SO; T5 HO

8-foot SP slimline T8 8-foot SP slimline T8; 4-foot MBP T8 Instant Start 

(Commercial Sector); T5 SO; T5 HO

8-foot T12 HO 8-foot RDC T8 HO; T5 HO

8-foot T8 HO 8-foot RDC T8 HO; T5 HO

T5 SO T5 SO

T5 HO T5 HO

* A fraction of these instant start ballasts are later reallocated to the programmed start category to account for the 

incursion of lighting controls, as discussed in this section.
9-30 

 The purchase probability Pij in Eq. 9.39 is determined by the consumer choice model 

from the logit z, defined in section 9.2.1, which depends on the first cost and O&M costs of each 

lamp-and-ballast system. The first cost for a lamp-and-ballast system of ballast type j, for a 

consumer who is replacing a system of ballast type i, is given by a combination of ballast price, 

the average lamp price in the previous year, and any costs associated with substitution: 

FCij(y) = pB,j(y) + n�lamp,j� MSl,j(y − 1)pL,l(y − 1)

l

Eq. 9.40 

 

Where:

FCij(y) = the total first cost for a consumer switching from product class grouping i to 

product class grouping j in year y (2011$),

pB,j(y) = the purchase price of a ballast in product class grouping j in year y (2011$), 

including corrections for learning, as computed using Eq. 9.4 and Eq. 9.5, 

n�lamp,j = the average number of lamps installed on a ballast in product class grouping j, 

l = an index specifying a particular lamp option within product class grouping j, 

MSl,j(y-1) = the market share of lamp option l in product class grouping j in year y -1, 

determined by the consumer choice model as described in section 9.3, and 

pL,l(y − 1) = the purchase price of lamp option l in year y -1 (2011$), including 

corrections for learning and any rare-earth price scenario corrections, as defined 

in appendix 9B. 

 The market share from the prior year, y-1, is assumed to define the average lamp price 

that consumers encounter when choosing between product classes. 

 

The O&M costs associated with a ballast of type j in the choice model are given by the 

mean fuel costs associated with powering the lamp-and-ballast system, as well as the first costs 

of the new lamps required to relamp the ballast over its lifetime:

OMj(y) = pE(y)u�

1000 � MSl,j(y − 1)SIPl,j

l

+ n�lamp,jn�relamp,j� MSl,j(y − 1)

l

pL,l(y − 1)

Eq. 9.41 

Where:

OMj(y) = the operation and maintenance costs in product class grouping j perceived by a 

consumer in year y (2011$/yr),

pE(y) = the price of electricity in year y (2011$/kWh), 

SIPl, j = the average system input power of lamp-and-ballast systems in product class

grouping j that have lamp option l installed (defined in Eq. 9.52) (W), 

u� = the average annual hours of use in the sector being considered (hrs), 
9-31 

n�relamp,j= the average number of relampings that occur over a ballast lifetime in product 

class grouping j, and 

all other variables are as defined in Eq. 9.40. 

 As discussed following Eq. 9.35, DOE used the sector-specific AEO 2012 forecasts for 

electricity prices, extrapolated to years beyond 2035. For ballast types that were analyzed in the 

commercial and industrial sectors jointly, DOE used a weighted average of those sectors’ price 

forecasts, based on the fraction of each ballast type found in the stock estimates from DOE’s 

2010 Lighting Market Characterization (LMC).

12 These fractions are summarized in Table 

9.3.13. 

The average number of ballast relampings is given by combining the relamping schedule 

(discussed in section 9.2.2.2) with the ballast survival probability:

n�relamp,j = � Prelamp(aB)PBS(aB)

aB,max

aB=0

Eq. 9.42 

Where:

n�relamp,j = the average number of relampings that occur on a given ballast of type j, 

aB = the ballast age (yr), 

aB,max = the maximum expected ballast age (yr), 

Prelamp(aB) = the relamping schedule, or probability of ballast relamping in year aB of 

the ballast’s life, as defined in Eq. 9.24, and 

PBS(aB) = the ballast survival probability, defined in Eq. 9.20.

DOE uses this model to project the shipments of fluorescent ballasts in each year of the 

analysis via Eq. 9.38. The input parameters, and their calibration, are discussed in section 9.3.4. 

Given the projections of failures, renovations, and new shipments in each year, and a calculation 

of the total operating stock in the initial year of the analysis period, Eq. 9.9 yields the total 

operating stock of ballasts in the United States in each subsequent year. The steps in the ballast 

shipments turnover model are summarized as a schematic diagram in Figure 9.2.1, which shows 

failed ballasts and ballasts removed for renovation leaving the stock, the allocation of demand 

for new construction and renovation in the consumer choice module, the compilation of the 

annual shipments projection, and the reallocation of some shipments to LEDs. DOE also uses 

that equation to compute the OSSDAP (as described in the text following Eq. 9.9) as an input for 

computing the NES in the NIA (chapter 10 of this TSD).
9-32 

Figure 9.2.2 Schematic diagram of the annual ballast turnover in the shipments 

model, including the effect of the consumer choice model and LED 

incursion.

 General Service Fluorescent Lamp Shipments. After computing the shipments and stock 

of fluorescent ballasts, DOE projects the shipments and stock of GSFLs by combining the ballast 

projection with the relamping schedule defined in Eq. 9.24. The total operating stock of GSFLs 

in the United States is simple to compute from the total operating stock of ballasts:

SGSFL,j(y) = SB,j(y)n�lamp,j

Eq. 9.43 

 

Where:

SGSFL,j = the total operating stock of GSFLs coupled to ballasts of type j in year y 

(number of units), 

SB,j = the total operating stock of ballasts of type j in year y (number of units), and 

n�lamp,j = the average number of lamps coupled to a ballast of type j. 

 In the context of computing the NES, however, the relevant quantity is not the total stock 

but the OSSDAP (described in the text following Eq. 9.9). This can be computed by adding the 
9-33 

stock of lamps installed on new ballasts since the rulemaking compliance year yrule to the stock 

of lamps shipped during or after yrule installed on old ballasts that were installed prior to yrule: 

SGSFL,j ′ (y) = SLONB,j ′ (y) + SLOOB,j ′ (y)

Eq. 9.44 

 

Where:

SGSFL,j ′ (y) = the OSSDAP of all GSFLs installed on ballast type j (number of units), 

SLONB,j ′ (y) = the OSSDAP of lamps on new ballasts—i.e., ballasts installed in yrule or 

later—of type j (number of units), and 

SLOOB,j ′ (y) = the OSSDAP of lamps on old ballasts—i.e., ballasts installed prior to yrule

that have had their lamps replaced since yrule—of type j (number of units). 

The two terms on the right hand side of Eq. 9.44 can be computed from the projection of 

ballast shipments, the probability distribution of ballast retirement over the ballast lifetime, and 

the probability distribution of lamp replacement on an existing ballast over the ballast lifetime.

For ballasts installed during or after the compliance year, the operating stock of lamps is: 

SLONB,j ′ (y) = � sB,j(v)PBS(y − v)

y

v=yrule

 Eq. 9.45 

 

Where:

SLONB,j ′ (y) = the OSSDAP of lamps on new ballasts (LONB) of type j (number of units), 

v = the vintage, or year, of ballast shipment,

y = the model year,

yrule = the compliance year of the proposed new standards, 

sB,j(v) = the shipments of ballasts of type j in vintage year v (number of units), defined 

in Eq. 9.38, and

PBS(y − v) = the probability of ballast survival to year y - v of the ballast lifetime, 

defined in Eq. 9.20.
9-34 

 For lamps shipped in or after yrule that are coupled to ballasts installed prior to yrule, the 

OSSDAP is:

SLOOB,j ′ (y) = � sB,j(v)Psurv(y − v)Crelamp(y|yrule, v)

yrule−1

v=y0

 Eq. 9.46 

Where:

SLOOB,j ′ (y) = the OSSDAP of lamps on old ballasts (LOOB)—i.e., ballasts installed prior 

to yrule that have had their lamps replaced since yrule—of type j (number of units), 

Crelamp(y|yrule, v) = the cumulative probability that a ballast has been relamped at least 

once since the year yrule, given that it was initially installed in the vintage year v, 

and 

all other variables are as defined in Eq. 9.45. 

The cumulative relamping probability is computed by integrating over the differential relamping 

probability: 

Crelamp(y|yrule, v) = max�1, � Prelamp(y′ − v)

y

y′=yrule �

 Eq. 9.47 

Where:

Prelamp(y′ − v) = the relamping schedule, i.e., the probability that a ballast shipped in 

vintage year v is relamped in year y′ (Eq. 9.24), and 

all other variables are defined as in Eq. 9.46. 

 

 The projected annual shipments of GSFLs, necessary to compute the equipment costs 

portion of the NPV, can also be computed from the relamping probability, when combined with 

the ballast shipments projection: 

sGSFL,j(y) = � sB,j(v)Prelamp(y − v)

v

Eq. 9.48 

Where:

sGSFL,j(y) = the shipments of GSFLs installed on ballasts of type j in year y (number of 

units), 

sB,j(y) = the shipments of ballasts of type j in year y, defined in Eq. 9.38 (number of 

units), and 

 all other variables are defined as in Eq. 9.43, Eq. 9.44, and Eq. 9.45. 
9-35 

9.2.2.5 General Service Fluorescent Lamps: Market Shares and Stock Shares

 To compute the projected equipment costs and energy consumption for GSFLs, it is 

necessary to apportion the projected shipments among the various lamp options available for 

each product class grouping. DOE computes the market share using the consumer choice model 

developed in section 9.2.1.2. Consumers are assumed to be choosing from among the various 

lamp options that can be coupled to their installed ballasts, as given in Table 9.3.12. 

 The market share of shipments allocated to lamp option l of lamps installed on ballast 

type j is given by: 

MSl,j(y) = Pl,j(z(y))

 Eq. 9.49 

Where: 

MSl,j(y) = the market share of lamp option l among lamps installed on ballast type j 

during year y, 

y = the model year,

Pl,j(z) = the consumer choice probability of selecting lamp option l, as defined in 

 section 9.2.1.2, and

z = the logit variable of the consumer choice model. 

The logit z depends on the first cost and the average annual O&M cost of each lamp 

option. For a GSFL, the first cost is simply the sum of the purchase price (including sales tax) 

and the lamp installation cost. The average annual O&M cost for each lamp option is simply the 

electricity cost associated with operating the lamp on a ballast with the average ballast factor for 

the product class for the sector-specific average annual operating hours. The average annual 

operating-hour values in each sector are computed as a weighted average of the annual hours of 

use in each of the building applications documented in section 9.3.6.2. 

 The market share projection for each lamp option can be converted to shares of the 

OSSDAP by summing over the market shares in prior years: 

φl,j(y) = ∑ MSl,j(y′

)sGSFL,j(y′)PLBS(y − y′) y′

y′=yrule

∑ sGSFL,j(y′)PLBS(y − y′) y

y′=yrule

Eq. 9.50 

Where:

φl,j(y) = the fraction of the OSSDAP of GSFLs installed on ballasts of type j that is 

represented by lamp option l, 

sGSFL,j(y) = the shipments of GSFLs installed on ballasts of type j in year y (number of 

units), 
9-36 

PLBS(y − y′

) = the probability that a lamp and its ballast both survive for y − y′ years 

after the lamp’s installation, as defined in Eq. 9.34, and all other variables are as 

in Eq. 9.49. 

9.3 MODEL CALIBRATION AND INPUTS 

9.3.1 Estimation of Historical Shipments and Initial Market Shares 

 Because the lamp shipments modeled in any given year depend on sums of shipments of 

IRLs and GSFL ballasts in prior years (see Eq. 9.28, Eq. 9.14, and Eq. 9.12 for IRLs and Eq. 

9.31, Eq. 9.18, and Eq. 9.17 for ballasts), DOE needed historical data to initiate the shipments 

model. Although the GSFL shipments model does not require a sum of GSFL shipments 

(because it is derived from the ballast shipments), DOE used historical GSFL shipments data as a 

calibration tool by ensuring that the projected GSFL shipments were qualitatively consistent with 

historical data.

To accurately compute the initial shipments and stock projections from historical data, it 

is necessary to have data spanning a sufficiently long time period such that products shipped at 

the beginning of the historical period have a negligible surviving fraction in today’s stock. DOE 

estimates that, for IRLs, 10 years is a sufficiently long historical period to meet this criterion; for 

fluorescent ballasts a historical period of at least 30 years is required. This section describes the 

sources of the historical shipments data; their disaggregation into different sectors, product 

classes, and technology options; and their use in initializing the shipments and stock model. 

9.3.2 Sources of Historical Shipments Data

 DOE obtained historical data on GSFL and IRL shipments from NEMA for the years 

2006-2011. When combined with NEMA data provided for the 2009 lamps rulemaking, these 

data yield a continuous time series of shipments of GSFLs and IRLs by NEMA members over 

the period from 2000 to 2011. As mentioned previously, a historical period of at least ten years’ 

duration is required for an accurate initialization of the IRL shipments model, so this data set is 

sufficient for that purpose. Where possible, the provided data were subdivided by NEMA into 

product categories that are very similar to the product classes considered in this rulemaking 

analysis. The details of any further disaggregation or rearrangement of these data by DOE are 

given in section 9.3.1.2. To account for shipments to the U.S. market by non-NEMA members, 

DOE assumed that NEMA shipments accounted for a fixed fraction of the total U.S. shipments 

over the historical period, using the same fractions that were utilized in the 2009 lamps 

rulemaking. These fractions are summarized in Table 9.3.1. 

Table 9.3.1 Fraction of Lamp Shipments Assumed to be from NEMA Members

Lamp Type Fraction of shipments from NEMA members

GSFL 90

IRL – Halogen 85

IRL – Traditional Incandescent 70
9-37 

 DOE also obtained data from NEMA on shipments of fluorescent ballasts for the years 

2006-2011, divided into subcategories that are very similar to the product classes considered in 

this rulemaking, with an additional subdivision into T12 and T8 ballasts where appropriate. (As 

discussed in section 9.1.1, DOE analyzed T8 and T12 lamps and ballasts separately in the 

shipments analysis and the NIA.) To estimate fluorescent ballast shipments from earlier years, 

DOE made use of data from the U.S. Census Bureau’s Current Industrial Reports14

Table 9.3.2

 (CIR), which 

also were originally obtained from NEMA, spanning the years 1995 (the first year in which T8 

shipments were reported separately from T12) to 2005 (the final year in which data were 

reported). To account for shipments to the U.S. market by non-NEMA members, DOE again 

assumed that NEMA shipments accounted for a fixed fraction of the total U.S. shipments over 

this period, using the same fractions that were utilized in the 2011 fluorescent ballasts 

rulemaking. These fractions are summarized in . 

Table 9.3.2 Fraction of Ballast Shipments Assumed to be from NEMA Members

Ballast Type Fraction of shipments from 

NEMA members

4-foot MBP T12 – Commercial 70

4-foot MBP T8 – Commercial 90

4-foot MBP T12 and T8 – Residential 50

8-foot SP slimline T12 70

8-foot SP slimline T8 90

8-foot RDC HO T12 60

8-foot RDC HO T8 90

4-foot Mini BPT5 SO 90

4-foot MiniBP T5 HO 90

4-foot MBP T8 – Commercial 90

 As mentioned previously, a historical time series spanning 30 years is required for an 

accurate initialization of the fluorescent ballast shipments model. To obtain historical shipments 

of T12 ballasts for years prior to 1995, DOE made use of data from the Lighting Market 

Sourcebook for the U.S.

15 and the Census Bureau’s CIR,11 which span the period from 1977 to 

2005 for 4-foot and 8-foot T12 ballasts. To estimate the shipments of T8 ballasts prior to 1995, 

DOE noted that T8s were a very small fraction of the market at that time, having only been 

introduced to the market in 1990. Therefore, DOE assumed a linear increase in historical T8 

shipments from zero in 1989 to the CIR values in 1995. Because T5 lamps were introduced to 

the U.S. market after 1995, no modeling of their shipments in prior years was required. 

 As discussed in section 9.1.1, DOE included T12 lamps and ballasts in its model, even 

though they were largely eliminated by new standards with compliance dates in 2012, because 

T12 products remain a large fraction of the existing stock, making it necessary to model their 

retirement and replacement. As historical shipments data were only available through 2011, 

however, and as explicitly modeling T12 shipments in 2012 would require a significantly more 

complicated model, DOE simply extrapolated the disaggregated historical shipments data to 

2012 for GSFLs and fluorescent ballasts, based on 2009-2011 trends. Modeling of GSFL and 
9-38 

fluorescent ballast shipments was performed beginning in 2013. For IRLs no such extrapolation 

was necessary, and modeling began in 2012. 

9.3.3 Subdivision of Historical Shipments by Sector, Product Class, and Technology 

 As mentioned previously, the historical shipments data from NEMA and the CIR are 

subdivided into categories that closely resemble the product class groupings considered in this 

analysis. In a few cases, however, it was necessary to combine or further subdivide some of these 

categories to more accurately match the product class groupings or technology options being 

modeled. It was also necessary to subdivide the shipments in some cases into estimated 

shipments to the residential and the commercial and industrial sectors. 

 As mentioned in section 9.1.1, DOE models shipments of IRLs and 4-foot MBP GSFLs

separately in the residential sector and the commercial (for IRL) or combined commercial and 

industrial (for GSFL) sectors. To subdivide the historical shipments data for these products 

appropriately, DOE estimated the residential fraction of each product’s shipments from the 

estimates of lamp stocks in the 2010 LMC and from the mean lamp lifetimes in each sector:

fRes =

SRes

LRes

SRes

LRes

+ SCI

LCI

Eq. 9.51 

Where:

fRes = the fraction of lamp shipments in the residential sector, 

SRes = the stock of lamps in the residential sector, as reported in Table 4.1 of the LMC 

(number of units), 

SCI = the stock of lamps in the commercial (IRL) or commercial and industrial (GSFL) 

sectors, from the same table (number of units), 

LRes = the average lamp lifetime in the residential sector (yr), i.e., the average failure age 

derived from the lamp failure distribution in Eq. 9.15 or Eq. 9.32 using the 

appropriate hours-of-use distribution and ballast lifetime for the residential sector, 

and

LCI = the lamp lifetime in the commercial (IRL) or commercial and industrial (GSFL) 

sectors (yr), computed as above, except with the use of the appropriate hours-ofuse distribution and ballast lifetimes for the commercial and industrial sectors. 

 

 The data on GSFL and fluorescent ballast shipments from NEMA and the CIR were 

nearly all subdivided into categories corresponding directly to the analyzed product class 

groupings, with additional subdivisions into T12 and T8 technologies, where appropriate. The 

exceptions were 8-foot recessed double contact (RDC) high output (HO) lamps and ballasts, for 

which no subdivision into T12 and T8 technologies was available, and 4-foot MiniBP T5 

standard output (SO) ballasts, for which no shipments were available from the CIR. To 
9-39 

disaggregate the data for 8-foot RDC HO lamps and ballasts into T12 and T8 subcategories, 

DOE assumed that the fractions of T12 and T8 lamps in this product class were the same as the 

fractions in the 8-foot SP slimline product class. Similarly, to infer shipments of 4-foot MiniBP 

T5 SO ballasts prior to 2006, DOE assumed that the ratio of SO to HO T5 ballasts was fixed at 

its 2006 value in the period 2002-2005 and that there were zero shipments of 4-foot MiniBP T5 

ballasts in any year before 2002. 

 As mentioned in section 9.2.2.3, DOE modeled the shipments independently for each of 

the three IRL technology options (the two baseline lamps and the one CSL1 lamp), because their 

lifetimes were significantly different. It was, therefore, necessary to disaggregate the historical 

shipments data for IRLs into estimated shipments for each of the technology options. DOE is 

aware that many shipments prior to 2012 did not correspond to any of these three technology 

options, as compliance with the 2009 GSFL-IRL lamps rulemaking was challenging for some 

significant types of IRL technology. Because these older technologies had lifetimes close to the 

Baseline2 lamp lifetime, however, it sufficed to categorize under Baseline2 all historical 

shipments outside the CSL1 technology. 

 To disaggregate the historical IRL shipments, DOE used the consumer choice model to 

compute the expected market shares of the Baseline1, Baseline2, and CSL1 technology options 

in the commercial and residential sectors in 2011, denoting the CSL1 fraction, MSCSL1(2011). 

By researching historical manufacturer literature, DOE found that the technology options 

corresponding to CSL1 were only introduced to the U.S. market in or around 2007, so DOE 

assumed that the market share of CSL1 lamps, MSCSL1(y), increased linearly in each year from 

zero in 2006 up to the 2012 value. The shipments of CSL1 lamps in each year were then given 

by sCSL1(y) = MSCSL1(y)sTot(y), where sTot(y) represents the total annual shipments in each 

sector. As mentioned previously, the remainder of the historical shipments was allocated to the 

Baseline2 category for the purposes of initializing the shipments model. 

9.3.4 Consumer Choice Model Calibration

 As introduced in section 9.2.1.2, DOE used a logit model, described by Eq. 9.1 and Eq. 

9.2, as the main driver of the consumer choice model used to predict product market share. The 

logit has two parameters, βFC and βOM, which characterize consumer sensitivity to first cost and 

O&M cost, respectively. Because commercial and industrial customers are expected to respond 

similarly to lighting costs but differently from residential customers, DOE calculated two sets of 

logit parameters, one for the commercial and industrial sector and the other for the residential 

sector. The logit parameters for the residential sector were scaled from the results of the 

commercial and industrial sector analysis, as described below. 

 

 Following the procedure adopted by DOE’s Solid State Lighting Program in its report on 

the Energy Savings Potential of Solid-State Lighting in General Illumination Applications,

3 the 

shipments model calculates the logit parameters for the commercial and industrial sector using 

data on fluorescent lamps and ballasts, because GSFL usage is dominantly commercial and 

industrial. The results of the analysis were then used in the consumer choice model to reflect 
9-40 

decision-making in that sector. The following describes how the logit parameters were obtained 

for the commercial and industrial sector. 

Calculation of the logit parameters requires both market share data (shipments) and first 

cost and O&M cost data for products with different costs. DOE used 2011 aggregate data for T8 

and T5 SO lamps and ballasts for this purpose, because they are two product types that can 

provide similar lighting services and are direct competitors in the market for new construction, 

retrofit, and renovation. The cost data included lamp and ballast systems costs and O&M costs to 

reflect the full cost of ownership. Specifically, DOE used data on the baseline 2-lamp 4-foot 

MBP T8 system with a programmed start ballast and the baseline 2-lamp 4-foot T5 SO system 

with a programmed start ballast, documented in the engineering analysis (chapter 5 of this TSD).

Table 9.3.3 lists the cost and market share input data used in the calibration. First costs

include the price of the lamps and ballast, installation, and sales taxh

. As a proxy for the annual 

O&M cost, DOE used the electricity cost for the first year of system operation, which is 

calculated from system wattage, annual run hours, and the cost of electricity in 2011. All costs 

were normalized by dividing by the lumen output of the system. 

Table 9.3.3 Input Data for Logit Parameter Calibration 

Lighting System First Cost 

($/thousand lumens) 

O&M Cost 

($/thousand lumens) 

Market Share

T8 MBP 12.12 5.07 79%

T5 SO 14.07 4.60 21%

 Using the input data from Table 9.3.3 in Eq. 9.1 and Eq. 9.2 results in the system of 

equations below, which can be solved for βFC and βOM.

i

0. 79 = e12.12∗βfc+5.07∗βom

e12.12∗βfc+5.07∗βom + e14.07∗βfc+4.6∗βom

0. 21 = e14.07∗βfc+4.6∗βom

e12.12∗βfc+5.07∗βom + e14.07∗βfc+4.6∗βom

The results of the calibration are listed in Table 9.3.4. 

 

h DOE looked into the effects of utility rebates on first costs seen by consumers by studying a comprehensive dataset 

of nationwide rebate programs compiled by the Consortium for Energy Efficiency for 2011. These data do not 

indicate any substantive difference in rebate amounts between high efficiency T8 lamps or lamp and ballast systems 

and T5 lamps or lamp and ballast systems. Therefore, no adjustments to first costs were made to account for rebates. i

In practice this system of equations is difficult to solve analytically. To solve numerically, DOE used Microsoft 

Excel’s Solver tool to minimize the sum of squared residuals between the probabilities predicted by the logit model 

using the input prices and the market shares listed in Table 9.3.3. 
9-41 

Table 9.3.4 Logit Parameter Results from Calibration 

Sector βFC βOM 

Commercial/Industrial -1.22 -2.13

Residential -0.67 -1.07

For the residential sector, the SSL report used data for medium screw-based lamps to 

calibrate the logit parameters. Given that reliable residential sector price data were unavailable 

for this analysis, DOE scaled the commercial and industrial logit parameters to obtain the 

residential logit parameters shown in Table 9.3.4, consistent with the results of the SSL analysis.j 

 As discussed in section 9.2.1.2 DOE used a diffusion curve published by PNNL16

Table 9.3.5

for its 

shipments model. The adoption curve parameters are shown in and the curve is 

plotted in Figure 9.3.1. 

Table 9.3.5 Bass Adoption Model Parameters

CE 0.005

CI 0.25

Figure 9.3.1 Generic lighting Bass diffusion curve

 

j

The analysis performed for the SSL report made use of proprietary data not available for the analysis presented in 

this TSD. 
9-42 

To calibrate the consumer choice model, DOE used acceptance factors and ballast 

lifetime reduction factors to capture differences among the observed market shares of product 

class groupings and lamp options, as compared to what would be predicted by price factors in the 

logit model alone. Acceptance factors limit the total market share that can be assigned to a 

product and are nominally set to 1 for products with a wide acceptance among consumers. 

Acceptance factors for ballasts that accept 8-foot lamps and reduced wattage 4-foot MBP T8 

lamps were affected by calibration. Ballast lifetime reduction factors, also nominally set to 1, 

reduce a ballast’s lifetime to account for reasons other than failure for ballast replacement, such 

as new standards eliminating some lamp options (e.g., T12s) or a preference of 4-foot lamps over 

8-foot lamps. Ballast lifetime reduction factors for ballast types that accept 8-foot lamps and 

T12s lamps were affected by calibration.

 

Acceptance factors for ballasts affect the outcome of the consumer choice module when 

allocating new lighting demand (i.e., new construction, retrofit, and renovation) among product 

class groupings. Consumers show a preference for 4-foot lamps over 8-foot lamps, as evidenced 

by shipment data. Therefore, during calibration, acceptance factors were reduced for 8-foot 

slimline and 8-foot RDC HO ballast types until the shipments predicted by the consumer choice 

module in the first year of the analysis period were consistent with the 2011 shipment data 

provided by NEMA for these ballasts. After calibration the acceptance factors were assumed to 

apply over the entire analysis period.

Acceptance factors for lamps affect the outcome of the consumer choice module when 

allocating market share among different lamp options (i.e., 32W, 28W, and 25W lamps) when 

choosing a new lamp. During calibration, market shares were decreased for some 4-foot MBP 

T8s until the market shares predicted by the consumer choice module were consistent with 

observed market shares. Because market share data are not available disaggregated down to the 

lamp option level, market shares were estimated based on the share of online listings of each 

lamp option offered by four retailersk

. As for ballasts, the calibration involved adjusting the 

acceptance factors until the predicted market shares agreed with those estimates. After 

calibration the acceptance factors were assumed to apply over the entire analysis period.

 In the final calibration, ballast lifetime reduction factors were reduced for T12 ballasts 

and ballast types that accept 8-foot lamps until shipments in the analysis period were consistent 

with historical shipment trends. Again, after calibration, these parameters were not changed. 

Ballast type acceptance and lifetime reduction factors are listed in Table 9.3.6, and lamp option 

acceptance factors are listed in Table 9.3.7. 

 

k DOE based these market shares on 309 product listings obtained from four lamp retailers.
9-43 

Table 9.3.6 Ballast Acceptance Factors and Lifetime Reduction Factors 

Ballast Type Acceptance 

Factor 

Lifetime 

Reduction 

Factor

4-foot MBP T12 Com/Ind 1 0.7

4-foot MBP T8 IS Com/Ind 1 1

4-foot MBP T8 PS Com/Ind 1 1

4-foot MBP T12 Res 1 0.5

4-foot MBP T8 Res 1 1

8-foot Single Pin T12 1 1

8-foot Single Pin T8 0.5 0.7

8-foot RDC HO T12 1 0.9

8-foot RDC HO T8 0.3 0.7

4-foot T5 SO 1 1

4-foot T5 HO 1 1

Table 9.3.7 Lamp Acceptance Factors 

Product Class

Grouping CSL Wattage Efficacy(lm/W)

Acceptance 

Factor

4-foot MBP (T8)

Baseline 32 89.2 1

CSL1 32 90 1

CSL2

32 95.4 0.7

28 96 0.5

25 93 0.7

8-foot SP slimline 

(T8)

Baseline 59 98.2 1

CSL1

59 99 1

54 105.5 1

50 108 1

8-foot HO T8 (T8) Baseline 86 93 1

CSL1 86 95.3 1

T5 SO

Baseline 28 104.3 1

CSL1

28 109.7 1

26 111.5 1

25 116 1

T5 HO

Baseline 54 92.9 1

CSL1

54 97.3 1

50 100 1

47 102.1 1
9-44 

9.3.5 Price Learning

 As indicated in section 9.2.1.3, DOE uses a price learning model to project future prices

in its shipments analysis. Accordingly, the initial lamp prices determined in the pricing analysis 

(chapter 7 of this TSD) are adjusted for the observed learning rate at later times in the analysis 

period. DOE developed price learning rates for the two categories of lamps and for GSFL 

ballasts based on historical shipments data from the U.S. Census CIRs. DOE extracted the 

historical product data indicated in Table 9.3.8 from the CIRs to calculate price learning rates for 

GSFLs, IRLs, and ballasts. Table 9.3.8 indicates which product categories listed in the CIRs 

were used to represent the two categories of lamps and the ballasts tracked in the shipments 

model. 

 

Table 9.3.8 Data Extracted from Current Industrial Reports (CIRs) for Price 

Learning Analyses 

Dates CIR product category Product addressed in 

rulemaking

1958 to 1994 fluorescent, hot cathode (GSFL) GSFL

1960 to 1994 PAR IRL

1986 to 2005 electronic ballasts ballasts

 

 The CIRs report annual data on shipments (units shipped) and the total nominal dollar 

value of those shipments. DOE interpolated reported shipments to estimate missing year values 

and extrapolated to estimate shipments back to the first unit shipped. Those data were then used 

to calculate the annual cumulative production (Eq. 9.5) used in the price learning analysis. The 

dollar values reported in the CIRs represent the net selling value of units shipped free-on-board 

(FOB) from the factoryl

. These were converted to per-unit sales values and adjusted for inflation 

using the U.S. Office of Budget and Management Gross Domestic Product chained price index17

Eq. 9.4

. 

The data on price and cumulative shipments were then fitted to the learning curve ( ) to 

calculate the learning rates used in the shipments model. The results of these fits are shown in 

Figure 9.3.3, Figure 9.3.4, and Figure 9.3.4 for IRL, GSFL, and ballasts, respectively. The 

equations in the figures indicate the fits to Eq. 9.4 for each of the product groups. The rate 

parameters (exponents) were then used in Eq. 9.6 to determine the product group specific price 

learning factors, which in turn were used by the model, in Eq. 9.7, to calculate the prices in any 

given year. 

 

l

Free-on-board values reflect discounts and allowances, are exclusive of excise taxes, but include freight charges. 

This approximates the cost of production to the manufacturer plus a single mark-up to the first customer, most likely 

a distributor. Ideally, consumer prices would have been used for this analysis, rather than the manufacturer selling 

prices given in the CIR, but the CIR data were considered the best option for two reasons. (1) Given the assumption 

of constant markups, the learning rates deducted from the manufacturer selling prices will be the same as for the 

retailer selling prices. (2) The multi-decade CIR data constituted the most comprehensive and consistent data source 

available that covered the longest time period.
9-45

Figure 9.3.2 IRL Learning Curve

Figure 9.3.3 GSFL Learning Curve

Figure 9.3.4 Ballast Learning Curve 
9-46 

9.3.6 Lamp and Ballast System Assumptions 

 As discussed in chapters 5 and 6 of this TSD, computing the power usage associated with 

a particular GSFL requires assumptions about the ballast to which it is coupled. In the previous 

chapters, DOE analyzed GSFLs coupled to particular representative ballasts to determine 

representative energy consumption values. In those chapters there were several representative 

ballasts in each product class, with different ballast factors and different numbers of lamps per 

ballast. In the case of the NIA (chapter 10), however, the relevant power consumption value is 

not the representative value for individual products, but rather the national-average value. 

Moreover, when implementing the consumer choice module of the shipments model, DOE is 

modeling average consumer behavior, which can be captured by considering GSFLs coupled to a 

single average ballast.

 Thus, in the current chapter and in chapter 10 of this TSD, DOE considers coupling 

lamps to a single composite model ballast in each product class. DOE based these composite 

ballasts on the representative ballasts used in chapters 7 and 8 of this TSD, with some properties, 

such as ballast factor and number of lamps per ballast, replaced with national-average values 

where appropriate. The composite ballast properties were computed from the average of 

available models found in a database of fluorescent ballasts gathered in support of the Federal 

Energy Management Program (FEMP)18

Table 9.3.9

. The average ballast properties, thus, may not 

correspond to the properties of any specific ballast on the market (for example, the national 

average number of lamps per ballast will not necessarily be an integer), but they will allow 

accurate modeling of average consumer behavior and total national energy consumption. The 

composite ballast properties are presented in . 

Table 9.3.9 Properties of Average Ballasts for Product Class Groupings 

Ballast Type Ballast Factor Lamps per 

Ballast

4-foot MBP T12 Com/Ind 0.88 2.6

4-foot MBP T8 IS Com/Ind 0.95 2.4

4-foot MBP T8 PS Com/Ind 0.95 2.1

4-foot MBP T12 Res 0.88 2

4-foot MBP T8 Res 0.88 2

8-foot Single Pin T12 0.87 2

8-foot Single Pin T8 0.87 2

8-foot RDC HO T12 0.81 2

8-foot RDC HO T8 0.81 2

4-foot T5 SO 1 2

4-foot T5 HO 1 2

Source: Ballast factors and number of lamps are averages computed from data in the Federal Energy 

Management Program’s lamp and ballast database.18

 

The average system input power of a lamp-and-ballast system in a particular product 

class grouping using a particular GSFL technology option within that product is then given by 

the following formula:
9-47 

SIPl,i = WlBFin�lamp,i

Eq. 9.52 

Where:

SIPl,i = the average system input power of a lamp-and-ballast system using lamp option l

in product class grouping i (W),

Wl = the rated wattage of lamp option l (W), 

BFi = the ballast factor of the composite ballast used in modeling product class grouping 

i, and 

n�lamp,i = the average number of lamps per ballast in product class grouping i. 

 The following sections document the values used to model properties of IRLs, GSFL 

ballasts, and GSFLs, respectively. 

9.3.6.1 Ballast Substitution Assumptions 

Table 9.3.10 indicates which ballasts the shipments model considers allowable substitutes 

for existing ballasts replaced during retrofits or renovations. An X in an intersecting column and 

row indicate that the ballast in the column header may be replaced by the ballast in the row 

header. In developing this matrix, DOE considered ballast options to be potential substitutes if 

they are used for similar applications. DOE also assumed that consumers do not switch from 

newer back to older technologies (e.g., there is no switching from T5s to T8s). Note that no T12 

ballasts were allowed to substitute for any existing ballasts, even for existing T12 ballasts, 

because DOE assumes that they do not comply with the 2011 fluorescent lamp ballast 

rulemaking10. 
9-48 

Table 9.3.10 Ballast Substitution Matrix: Retrofits and Renovations 

Original Ballast Type

Ballast Type 

4-foot MBP T124-foot MBP T8 Instant Start4-foot MBP T8 Programmed start4-foot MBP T12 (Residential)4-foot MBP T8 (Residential)

8-foot Single Pin SP slimline T128-foot Single Pin SP slimline T88-foot RDC High Output T128-foot RDC High Output T8Two Lamp PS T5 SOTwo Lamp PS T5 HO 

B1.0I B1.I B1.P B1.0R B1.R B2.0 B2.I B3.0 B3.I B4.P B5.P 

B1.0I

B1.I X X X X 

B1.P X 

B1.0R

B1.R X X 

B2.0

B2.I X X

B3.0

B3.I X X 

B4.P X X X X X X 

B5.P X X X X X 
9-49 

9.3.6.2 General Service Fluorescent Lamp Characteristics 

This section documents the model inputs for general service fluorescent lamps in the 

following tables: 

• Table 9.3.11. Properties of Representative GSFL Options: Baseline and All CSLs, 

• Table 9.3.12. GSFL Options for Different Ballast Types (Table 9.3.12), and

• Table 9.3.13. Properties of Representative GSFL Lamp-and-ballast Systems. 

Table 9.3.11 Properties of Representative GSFL Options: Baseline and All CSLs

Product Class

Grouping

CSL

Lamp Option 

ID

Lamp Diameter

Nominal 

Wattage 

ANSI Rated 

Wattage 

Efficacy (rated)

Initial Lumens

Mean Lumens

Lamp Price

4-foot MBP Baseline L1.0.1 T8 32 32.5 89.2 2900 2725 $4.85 

CSL1 L1.1.1 T8 32 32.5 90.0 2925 2770 $5.23

CSL2 L1.2.1 T8 32 32.5 95.4 3100 2941 $7.95

L1.2.2 T8 28 28.4 96.0 2725 2560 $6.95

L1.2.3 T8 25 26.6 93.0 2475 2350 $9.30

8-foot SP 

slimline

Baseline L2.0.1 T8 59 60.1 98.2 5900 5430 $13.27

CSL1 L2.2.1 T8 59 60.1 99.0 5950 5650 $15.31

L2.2.2 T8 54 54.0 105.6 5700 5360 $16.78

L2.2.3 T8 50 50.0 108.0 5400 5075 $20.56

8-foot HO Baseline L3.0.1 T8 86 84.0 93.0 8000 7600 $12.58

CSL1 L3.2.1 T8 86 84.0 95.3 8200 7800 $15.15

T5 SO Baseline L4.0.1 T5 28 27.8 104.3 2900 2697 $5.90

CSL1 L4.2.1 T5 28 27.8 109.7 3050 2898 $6.90

L4.2.2 T5 26 26.0 111.5 2900 2660 $7.38

L4.2.3 T5 25 25.0 116.0 2900 2750 $8.12 

T5 HO Baseline L5.0.1 T5 54 53.8 92.9 5000 4850 $7.62

CSL1 L5.2.1 T5 54 53.8 97.3 5237 4871 $9.06

L5.2.2 T5 50 50.0 100.0 5000 4650 $11.69

L5.2.3 T5 47 47.0 102.1 4800 4410 $13.50

Source: Engineering analysis (chapter 5 of this TSD). 

Prices are given in 2011$ for the beginning of the analysis period (2012). 
9-50 

Table 9.3.12 identifies which lamps are assumed to pair to which ballasts. Ballast types

are indicated in the column header. Lamp Options ID are indicted in the row headers. See Table 

9.3.11 for lamp option specifications. 

Table 9.3.12 GSFL Options for Different Ballast Types

Ballast types

4-foot MBP T12 4-foot MBP T8 Instant Start 4-foot MBP T8 Programmed start4-foot MBP T12(Residential)4-foot MBP T8 (Residential)8-foot Single Pin SP slimline T128-foot Single Pin SP slimline T88-foot RDC High Output T128-foot RDC High Output T8Two Lamp PS T5 SO Two Lamp PS T5 HO 

B1.0I B1.I B1.P B1.0R B1.R B2.0 B2.I B3.0 B3.I B4.P B5.P 

L1.0.1 X X X

L1.1.1 X X X

L1.2.1 X X X

L1.2.2 X X X

L1.2.3 X X X

L2.0.1 X

L2.2.1 X

L2.2.2 X

L2.2.3 X

L3.0.1 X

L3.2.1 X

L4.0.1 X

L4.2.1 X

L4.2.2 X

L4.2.3 X

L5.0.1 X

L5.2.1 X

L5.2.2 X

L5.2.3 X

Source: Engineering analysis (chapter 5 of this TSD). 
9-51 

Table 9.3.13 Properties of Representative GSFL Lamp-and-ballast Systems Ballast type 4-foot MBP T12 (Commercial and Industrial) 4-foot MBP T8 Instant Start (Commercial and Industrial) 4-foot MBP T8 Programmed start (Commercial and Industrial) 4-foot MBP T12 (Residential) 4-foot MBP T8 (Residential) 8-foot Single Pin SP 

slimline T12

8-foot Single Pin SP 

slimline T8

8-foot RDC High 

Output T12

8-foot RDC High 

Output T8

Two Lamp PS T5 

SO

Two Lamp PS T5 

HO

Product Class 

Grouping 4ftMBP 4ftMBP 4ftMBP 4ftMBP 4ftMBP 8ftSP 8ftSP 8ftRDC 8ftRDC 4ftT5SO 4ftT5HO

Start Method

IS IS PS IS IS IS IS IS IS PS PS

Lamp Diameter T12 T8 T8 T12 T8 T12 T8 T12 T8 T5 T5

Sector Com Com Com Res Res Com Com Com Com Com Com

Baseline System 

Mean Lumens*

5262 6213 5436 4048 4796 10276 9448 13195 12312 5394 9700

Avg. System 

Mean Lumens, 

2013** 5262 6134 5399 4048 4786 10276 9404 13195 12450 5513 9499

Group relamping 

fraction† 

0.25 0.25 0.25 0.00 0.00 0.37 0.37 0.31 0.31 0.25 0.25

Lamp Life Hours 18938 24000 40000 18938 24000 11108 24000 11070 18000 30000 24000

Lamp Life 

Years†† 5.4 6.7 10.8 17.6 18.1 3.3 6.5 3.3 5.1 6.9 6.7

Ballast Price $0.00 $18.69 $19.28 $0.00 $9.61 $0.00 $21.00 $0.00 $16.75 $28.84 $30.18

Ballast 

Installation Cost $0.00 $27.99 $26.41 $0.00 $32.55 $0.00 $54.96 $0.00 $58.79 $25.88 $25.88

Lamp 

Installation Cost $0.00 $6.73 $6.68 $0.00 $0.00 $0.00 $4.72 $0.00 $6.31 $6.67 $6.67

Fixture 

Disconnect Cost $0.00 $2.71 $2.71 $0.00 $2.71 $0.00 $2.71 $0.00 $2.71 $2.71 $2.71
9-52 

Avg. Lamp Price, 

2013**

$0.00 $6.19 $5.75 $0.00 $5.76 $0.00 $14.90 $0.00 $12.77 $6.60 $9.07 

Lamp disposal 

cost $0.00 $0.24 $0.24 $0.00 $0.00 $0.48 $0.48 $0.48 $0.48 $0.24 $0.24

Avg. First Cost, 

2013** $0.00 $70.98 $67.16 $0.00 $56.38 $0.00 $113.32 $0.00 $110.10 $77.29 $85.38

Avg. Lamp 

Lifetime††† 5.66 4.20 2.27 2.00 2.00 6.97 3.50 6.99 4.56 3.37 3.50

Avg. System 

Wattage, 2013** 

77.8 70.9 62.4 59.8 55.2 130.5 98.5 178.2 136.1 53.4 104.0

Avg. Annual 

Energy Costs, 

2013** $37.76 $34.43 $30.27 $3.92 $3.61 $63.35 $47.81 $86.51 $66.06 $25.90 $50.50

Avg. Annual 

O&M, 2013 $37.76 $35.39 $30.39 $3.92 $3.61 $63.35 $49.83 $86.51 $68.85 $26.69 $51.67 

Bass 

Introduction 

Year‡ 1950 1989 1989 1950 1989 1950 1989 1950 1989 2001 2001

Industrial 

Fraction‡‡

 

0.06 0.08 0.08 0.00 0.00 0.09 0.11 0.09 0.11 0.08 0.08

Source: Engineering analysis (chapter 5 of this TSD) and LCC (chapter 8 of this TSD) unless otherwise noted (with 2 and 4 lamp ballasts aggregated into 

weighted averages based on number of lamps per ballast). Prices are given in 2011$ for the beginning of the analysis period (2012). * System lumens were calculated assuming lamps are installed on a ballast with DOE calculated average ballast factor and average lamps per ballast, see Table 

9.3.9

**These values are computed by the consumer choice model for lamps, based on inputs from the engineering analysis. They are then used as inputs to the 

consumer choice model for ballasts in 2013. New inputs are computed for subsequent years from the output of the previous year, as described in section 9.2.2. † Source: 2011 fluorescent lamp ballast rulemaking TSD.

10 †† Computed from Eq. 9.27

†††Computed from Eq. 9.31

‡ Introduction year for T12s is arbitrary since T12 are not a choice in the consumer choice module. T8 introduction year from Elliot et al. 2004.16 T5 introduction 

year from 2011 fluorescent lamp ballast rulemaking TSD.10 ‡‡ Computed from LMC stock fractions of commercial and industrial stock. 
9-53 

9.3.6.3 Incandescent Reflector Lamp Characteristics

Table 9.3.14 shows the IRL lamp characteristics assumed by the shipments model. 

Table 9.3.14 IRLs: Representative Properties for Baseline and CSL 1 Lamps

Source: Engineering analysis unless otherwise noted. Prices are given in 2011$ for the beginning of the analysis 

period (2012). * Wattage and lamp life hours are adjusted to account for lamps on dimmers (see section 9.2.2.2). ** Average, dimmer-corrected lamp life in years calculated from Eq. 9.15. *** Computed using Eq. 9.37

† Baseline 1 introduction year set to ensure 100% market penetration by 2011, as this is a mature technology. 

Baseline 2 and CSL 1 from gelighting.com.19

†† Extrapolated from the 2012 market shares produced by the consumer choice module, as described in section 9.3.3. Residential Baseline 1 Residential Baseline 2 Residential CSL 1 Commercial Baseline 1 Commercial Baseline 2 Commercial CSL 1

Rated Wattage* 60 60 55 60 60 55

Dimmer Fraction 0.29 0.29 0.29 0.05 0.05 0.05

Dimming Energy 

Reduction 0.2 0.2 0.2 0.2 0.2 0.2 

Dimming Lifetime 

Correction Factor 3.94 3.94 3.94 3.94 3.94 3.94 

Wattage* 56.5 56.5 51.8 59.4 59.4 54.5

Efficacy (lm/w) 17.8 18.3 20 17.8 18.3 20

Rated Lamp Life 

Hours 1500 3000 4400 1500 3000 4400 

Lamp Life Hours* 2779 5558 8151 1721 3441 5047

Lamp Life Years** 3.7 7.3 10.7 0.4 0.8 1.1

Initial Lumens 1070 1100 1100 1070 1100 1100

Lamp Installation 

Cost $ - $ - $ - $1.12 $1.12 $1.12 

Lamp Price $10.25 $10.12 $17.50 $10.25 $10.12 $17.50

Lamp First Cost $10.25 $10.12 $17.50 $11.37 $11.24 $18.62

Annual O&M*** 7.00 5.59 4.72 46.55 31.64 24.72

Bass Introduction 

Year† 1980 1991 2007 1980 1991 2006 

2011 Market 

Share†† 0.94 0.05 0.01 0.94 0.03 0.03 
9-54 

9.3.6.4 Lamp Usage Assumptions 

Table 9.3.15, Table 9.3.16, and Table 9.3.17 document, for the two categories of lamps in 

each of the three sectors, the model assumptions for lamp usage (hours per year), starts per day, 

and the probability that the space in which a lamp is installed is of a given type. 

Table 9.3.15 Commercial Sector Annual Hours of Lamp Use and Starts per Day

Building Use Type

GSFL 

Probability

*

GSFL 

Hrs* 

IRL 

Probability

*

IRL 

Hrs* 

Starts Per 

Day** 

Education 8.3% 4028 8.3% 4526 5

Food Service 6.4% 4064 6.4% 4380 2 

Food Store 4.8% 4138 4.8% 4490 2

Health Care - Inpatient 0.2% 4028 0.2% 4453 5

Health Care - Outpatient 2.6% 4028 2.6% 4490 2

Lodging 3.0% 4028 3.0% 4453 5 

Offices (Non-medical) 17.6% 4028 17.6% 4490 4

Public Assembly 5.9% 4064 5.9% 4417 4 

Public Order and Safety 1.5% 4028 1.5% 4526 2

Religious Worship 7.9% 4028 7.9% 4417 2

Retail - Mall & Non-Mall 14.0% 4174 14.0% 4563 2

Services 13.3% 4028 13.3% 4526 2 

Warehouse and Storage 12.8% 4028 12.8% 4526 4

Other 1.7% 4028 1.7% 4563 4 

Total 100% 100%

Average 4058 4496 3.10 

* Source: Energy use analysis (chapter 6 of this TSD).

** Source: Expert opinion.
9-55 

Table 9.3.16 Industrial Sector Annual Hours of Lamp Use and Starts per Day

Building Use Type GSFL 

Probability* 

GSFL 

Hrs*

Starts 

Per 

Day**

Apparel 0.9% 4582 2

Beverage and Tobacco 

Products 1.0% 4582 2 

Chemicals 8.1% 4582 2

Computer and Electronic 

Products 2.3% 4582 2 

Electrical Eq. Appliances & 

Components 1.0% 4618 2 

Fabricated Metal Products 10.2% 4618 2

Food 6.0% 4545 2 

Furniture and Related

Products 2.5% 4545 2 

Leather and Allied Products 0.2% 4582 2

Machinery 5.2% 4545 2

Nonmetallic Mineral 

Products 5.1% 4582 2 

Paper 1.8% 4545 2

Petroleum and Coal Products 1.8% 4545 2

Plastics and Rubber Products 3.0% 4618 2 

Primary Metals 2.8% 4618 2 

Printing and Related Support 3.2% 4618 2

Textile Mills 0.8% 4582 2

Textile Product Mills 0.6% 4508 2

Transportation Equipment 4.9% 4582 2

Wood Products 6.4% 4435 2

Miscellaneous 32.2% 4618 2 

Total 100% 

Average 4585 2

* Source: Energy use analysis (chapter 6 of this TSD).

** Source: Expert opinion. 
9-56 

Table 9.3.17 Residential Sector Annual Hours of Lamp Use and Starts per Day

Building 

Type Room Type GSFL Probability

GSFL 

Hrs

IRL 

Probability

IRL 

Hrs

Starts Per 

Day* 

Single Family Detached

Basement(s) 4.191% 584 0.55% 584 1

Bathroom(s) 3.143% 584 3.88% 584 7

Bedroom(s) 1.936% 584 3.58% 584 3

Closet(s) 2.884% 511 0.63% 511 1 

Dining Room(s) 0.409% 694 1.51% 694 2

Exterior(s) 1.078% 949 21.94% 949 5

Garage(s) 20.357% 548 0.00% 548 2

Hall(s) 1.118% 548 6.20% 548 5

Kitchen(s) 15.807% 840 10.64% 840 7

Laundry/Utility 

Room(s) 3.912% 548 0.52% 548 2 

Living/Family 

Room(s) 2.245% 730 8.31% 730 4 

Office(s) 1.357% 694 2.51% 694 3 

Other/Unknown 4.790% 365 2.95% 365 2

Single Family Attached 

Basement(s) 0.672% 621 0.09% 621 1 

Bathroom(s) 0.344% 584 0.41% 584 7

Bedroom(s) 0.213% 584 0.38% 584 3

Closet(s) 0.249% 511 0.05% 511 1 

Dining Room(s) 0.048% 694 0.17% 694 2

Exterior(s) 0.072% 986 1.41% 986 5

Garage(s) 0.953% 548 0.00% 548 2

Hall(s) 0.125% 548 0.67% 548 5 

Kitchen(s) 1.996% 840 1.29% 840 7

Laundry/Utility 

Room(s) 0.262% 511 0.03% 511 2 

Living/Family 

Room(s) 0.240% 730 0.86% 730 4 

Office(s) 0.096% 657 0.17% 657 3

Other/Unknown 0.640% 365 0.38% 365 2

Multifamily

Basement(s) 0.689% 511 0.08% 511 1

Bathroom(s) 1.881% 584 1.97% 584 7

Bedroom(s) 1.082% 584 1.70% 584 3

Closet(s) 1.463% 475 0.27% 475 1

Dining Room(s) 0.209% 694 0.66% 694 2

Exterior(s) 0.271% 986 4.67% 986 5

Garage(s) 3.136% 548 0.00% 548 2
9-57 

Hall(s) 0.541% 548 2.55% 548 5

Kitchen(s) 11.903% 840 6.80% 840 7

Laundry/Utility 

Room(s) 0.689% 475 0.08% 475 2 

Living/Family 

Room(s) 1.512% 730 4.75% 730 4 

Office(s) 0.492% 657 0.77% 657 3 

Other/Unknown 0.885% 329 0.46% 329 2 

Mobile Home

Basement(s) 0.128% 694 0.01% 694 1

Bathroom(s) 0.485% 584 0.46% 584 7

Bedroom(s) 0.301% 584 0.43% 584 3

Closet(s) 0.271% 511 0.05% 511 1

Dining Room(s) 0.057% 694 0.16% 694 2

Exterior(s) 0.132% 949 2.06% 949 5

Garage(s) 0.697% 584 0.00% 584 2

Hall(s) 0.064% 548 0.27% 548 5

Kitchen(s) 2.206% 840 1.14% 840 7

Laundry/Utility 

Room(s) 0.638% 548 0.06% 548 2 

Living/Family 

Room(s) 0.383% 767 1.08% 767 4 

Office(s) 0.036% 657 0.05% 657 3 

Other/Unknown 0.711% 329 0.34% 329 2 

Total 100% 100% 

Average 648 761 4.03 

Probabilities and hours of use were calculated as part of the life cycle cost analysis (chapter 6 of this TSD).

* Source: Expert opinion.
9-58 

9.3.7 Rare Earth Costs

 As described in section 9.1, DOE considered the impact of possible changes in REO 

prices in its GSFL shipments modeling. REOs are used in fluorescent lamp phosphors at higher 

concentrations in more-efficient models. REOs saw large price increases in the third quarter of 

2010 and into 2011, which have now largely corrected themselves, as shown by the GSFL triband phosphor price index shown in Figure 9.3.5 and described in appendix 9B. This volatility 

has resulted in significant uncertainty about the potential long-term impact on GSFL prices.

Figure 9.3.5 Inflation-Adjusted, Tri-band Phosphor REO Price Index for GSFLs 

Given the large uncertainty caused by such price volatility, DOE modeled GSFL lamp 

prices assuming three different price estimates: a best, a high, and a low estimate, as reflected in 

the model scenarios (section 9.3). Given the lack of any clear consistent price trend, in any given 

scenario, the REO real price was assumed to remain constant over the analysis period. 

 
9-59 

The best-estimate analysis assumes current (October 2012) REO prices, resulting in the 

following manufacturer materials costs for the indicated lamp types: 

• 4-foot T8, cREO,Ref = $ 0.47/GSFL, 

• 4-foot T5, cREO,Ref = $ 0.30/GSFL, and

• 8-foot T8, cREO,Ref = $ 0.95/GSFL. 

9.4 ALTERNATIVE ANALYSES

9.4.1 Overview

In addition to determining best estimates of the impacts of the four candidate standards 

cases described in the introduction to this chapter (section 9.1) , DOE conducted alternative 

analyses to gauge the importance of various assumptions on the shipments and NIA. Alternative 

analyses that affect the NIA only are described in chapter 10 of this TSD. This section describes 

the analyses that affect both shipments, and, therefore, also the NIA. As summarized in Table 

9.4.1, these analyses are (a) an analysis of shipments uncertainty resulting from uncertainties in 

REO prices, (b) a determination of the impacts on GSFL and IRL shipments resulting from the 

incursion of LEDs and lighting controls into the GSFL and IRL markets, and (c) an analysis of 

the impact that could result from manufacturers meeting an IRL CSL 1 standard by using higherwattage, shorter-lamp-life lamps, as described in chapter 5. This section describes these

scenarios. The results of the scenarios are presented in section 9.5. 

Table 9.4.1 summarizes the configuration in the shipments model of the scenario 

variables used to generate the analyses. As shown, an individual scenario tests the effect of 

modifying only one scenario variable. The effect is determined by comparing the results of the 

alternative scenario model runs to the standard best-estimate scenario model runs, which hold all 

variables at their reference values.
9-60 

Table 9.4.1 Definition Alternative Analyses

Scenario Variables

Analysis Type Scenario 

Rare 

Earth 

Price

LED Controls 

Adoption 

Short 

IRL Life

Standard Best Estimate Ref Ref Ref Ref

Uncertainty Analyses REO High High Ref Ref Ref

REO Low Low Ref Ref Ref

Impact Determination Controls Ref Ref Fixed Ref

LED Ref No LED Ref Ref

Alternative 

Technology Effect IRL Short Life Ref Ref Ref Short life

 

Table 9.4.2 summarizes the variable assumptions used in the best estimate and alternative 

standards analyses. As indicated in the table, Appendix 9A describes the analysis used to 

generate DOE’s best estimate of the future penetration of lighting controls. Further information 

on the best-estimate and alternative assumptions about REO prices is contained in appendix 9B. 

The impact of the LED incursion and shortened IRL lamp life assumptions are described in 

section 9.4.2 and section 9.4.3, respectively. 

Table 9.4.2 Summary of Variable Assumptions for Best Estimate and Alternative 

Analyses 

Shipments 

Scenarios 

Variables

Best Estimate Alternative 1 Alternative 2

Rare earth oxide 

prices

(appendix 9B)

Ref: Prices in October 2012 High: 2011 peak price Low: 2006 – 2009 

average price

Lighting controls 

penetration

(appendix 9A)

Ref: Commercial in-growth 

determined by today’s 

building codes (appendix 

9A). Residential constant at 

today’s level.2

Fixed: Constant 

controls penetration at 

today’s level

LED market 

incursion

(section 9.4.2)

Ref: Increasing according to 

Figure 9.4.1

No LED: No additional 

LED incursion

Alternative 

technology 

(chapter 5 and 

section 9.4.3) 

Ref: Lamp life for CSL 1 

IRLs assumed to be 55-watt, 

4400 hour lamp life 

Short life. Two 60-W 

models assumed to 

meet CSL 1, one with a 

lamp life of 1046 

hours, the other with a 

lamp life of 2564 hours 
9-61 

9.4.2 Light Emitting Diode Impact Determination

 As discussed in Section 9.2.2.1, DOE assumes in its reference scenario that LED lighting 

technology will penetrate GSFL/IRL markets. To simplify the shipments model, DOE does not 

include LEDs as a choice in the consumer choice model, but rather models LEDs as an 

exogenous effect on the GSFL and IRL markets. The lumen demand satisfied by LEDs in each 

year is determined by a logistic curve, discussed in this section and in section 9.2.1.1, with the 

remaining lighting demand allocated to covered products by the consumer choice module as 

discussed in section 0. 

The logistic curve that characterizes LED incursion, assumed to be a Bass adoption curve 

(Eq. 9.3), is based on the analysis in the SSL report1

. The SSL report projects the percentage of 

lumen demand (lm-hr/year) fulfilled by LEDs between 2010 and 2030 for a variety of lamp 

categories, including linear fluorescent and reflector lamps, in each sector. DOE used the SSL 

forecasts for LED incursion into the residential and commercial GSFL market in this analysis. 

The commercial forecast was assumed to cover both the commercial and industrial sectors for 

simplicity, since the forecast for LED incursion into the industrial GSFL market was nearly 

identical to the commercial forecast. The SSL report used a single curve for all sectors for IRLs, 

which DOE used in this analysis. These curves were then extrapolated out to the end of the 

analysis period.

 

Figure 9.4.1 shows the growth in the percentage of the GSFL and IRL markets that DOE 

expects to be serviced by LEDs over the shipments analysis period. Because of the large 

expected impact of LED incursion into the GSFL and IRL markets, DOE is considering 

conducting an analysis that reflects uncertainties in these incursion rates. DOE seeks input on 

these uncertainties. 

Figure 9.4.1 LED Incursion Curve Projections for GSFLs and IRLs, Best Estimate 
9-62 

 DOE used the incursion curves shown in Figure 9.4.1 to project GSFL and IRL lumen 

capacity (teralumens) displaced by LEDs over the analysis period. Figure 9.4.2 shows DOE’s 

best estimate of the IRL and GSFL lumen capacity displaced by LEDs (light blue and dark blue, 

respectively) and the lumen capacity expected to remain as IRL and GSFL (light green and dark 

green, respectively). As revealed by Figure 9.4.1 and 9.4.2 together, while the LED incursion is 

expected to result in a large reduction in the use of both categories of lamps, the total impact on 

GSFLs is expected to be much larger, because of the much larger size of their market. 

Figure 9.4.2 Lumen Capacity of GSFL, IRL, and Combined GSFL and IRL displaced 

by LED (Total LED), Best Estimate 

9.4.3 Alternative Incandescent Reflector Lamp Technology 

 Chapter 5 described the possibility that manufacturers respond to an amended IRL 

standard set at CSL 1 by producing shorter-lifetime lamps. DOE identified two representative 

short-lived lamp options that would meet a CSL 1 standard. Their lifetimes and O&M costs, as 

used in the shipments analysis and the NIA, are documented in Table 9.4.3, along with the 

properties of the longer-lived reference lamp used in DOE’s best-estimate scenario. Because the 

Alternative1 and Alternative2 short-lifetime lamps were very similar to the Baseline1 and 

Baseline2 lamp options, DOE assumed that their prices and wattages were the same, 

respectively, as those baseline lamps. The alternative IRL technology analysis includes all of 
9-63 

these lamp options (listed in Table 9.4.3) in the consumer choice model, with the reference 

models being available only after the 2017 compliance year. 

Table 9.4.3 IRL Lamp Life Assumptions for Best-Estimate and Alternative 

Technologies that Meet a CSL 1 Standard 

Lamp 

Technology 

Assumption

Initial 

Light 

Output 

(lumens)

Efficacy 

(lm/w)

Rated 

Lamp 

Life 

(hours)

Lamp 

Life 

(hours)

Lamp 

Life 

(years)

Annual 

O&M**

Reference 

technology,* 

reference 

lamp life 

1100 20.0 4400 8151 10.7 $3.98 

Alternative 1, 

short lamp 

life

1124 17.8 1046 1938 2.5 $7.41 

Alternative 2, 

short lamp 

life 

1124 18.3 2564 4750 6.2 $5.02 

* The reference technology is the lamp option that DOE determined to be most representative of lamps able to meet 

CSL 1 in the engineering analysis, see Table 9.3.14.

**Calculated using Eq. 9.37. 

9.5 RESULTS

This section presents the results of the analyses of the CSCs and the alternative analyses. 

9.5.1 Results of Analyses of Candidate Standards Cases 

Table 9.5.1 presents DOE’s best estimates of cumulative shipments of GSFLs and IRLs 

over the 30-year shipments analysis period (2017 – 2046) for the four CSCs considered in the 

analysis (see Table 9.1.1, for definitions of the CSCs). As described in section 9.1, DOE initially 

considered two CSCs: one (CSL 1) in which the standards were assumed to be set at CSL 1 for 

product class groupings, and the other (Max CSL) in which the standards were assumed to be set 

at the maximum CSL for each product class grouping (which in practice is CSL 2 for 4-foot 

MBP and CSL 1 for all other product class groupings). DOE also considered a variation on each 

of these—the All CSL 1 Except T5=Baseline CSC and the Max CSL Except T5=Baseline CSC—

in which the standard for T5s is kept at its current level (i.e., at the baseline). 

The T5 = Baseline CSCs were included to test if this might result in a greater overall

energy and cost savings due to more rapid migration to T5s (which generally have higher 
9-64 

efficacy than T8s).

m

Table 9.5.1

 The assumption is that, if a standard increases the price of 4-foot MBP T8 

lamps relative to 4-foot MiniBP T5 lamps, consumers should adopt the more efficacious T5s 

more rapidly, because the marginal cost of switching is reduced. It is not immediately obvious 

whether this will lead to greater savings from the increased migration to T5s or reduced savings 

from the lower efficacy of the T5s in the standards case. While shows that 

maintaining the T5 standard at the baseline level has essentially no impact on the overall 

shipments of GSFLs, the results of the NIA project that NES and NPV are lower than would be 

achieved by setting the T5 standard at CSL 1 (see chapter 10). For this reason, in the subsequent 

discussion of results, only the All CSL 1 and the Max CSL CSCs are included. 

Table 9.5.1 Best Estimate of Cumulative Shipments of GSFLs and IRLs from 2017 – 

2046, for Each of the Candidate Standards Cases 

Cumulative Shipments (Millions of Lamps Shipped)

Analysis 

Type Scenario Base Case All 

CSL 1 

All CSL 1 

Except 

T5=Baseline 

Max 

CSL

Max CSL 

Except 

T5=Baseline 

Standard Best 

Estimate

GSFL 7049 7048 6827 7040 6827

IRL* 564 388 388 388 388 

* All CSCs produce the same result for IRLs because all CSCs reflect an IRL standard set at CSL 1, the only CSL 

considered for this category of lamps. 

Figure 9.5.1 shows DOE’s best estimate of the historical and projected shipments of 

GSFLs, broken down by product class grouping. The modeling projects a systematic migration 

of the market toward the adoption of standard output T5s over the 30-year analysis period, with 

and without new standards. That shift occurs fastest for the Max CSL CSC, because the higher 

standard on 4-foot MBP GSFLs drives the market toward T5s more rapidly. The projections also 

reflect the expected large incursion of LEDs into the GSFL market (see section 9.4.2), which 

causes a marked drop in shipments for all product class groupings except for standard output 

T5s. 

 

m See footnote a.
9-65

Figure 9.5.1 Historical and Projected Shipments of GSFLs by Product Class Grouping, 

Best Estimaten

 

n In some cases, the change in shipments between the candidate standards case and base case is so small it is 

indistinguishable on the figure. In that case, the higher standard level overwrites the lower.
9-66 

Figure 9.5.2 shows DOE’s best estimate of the historical and projected shipments of 

IRLs, broken down into residential, commercial, and total shipments. Again, both the base case 

and the CSC show a sharp decline in shipments due to the expected market incursion of LEDs, 

which is expected to occur faster, earlier, and to a greater extent in the IRL market than the 

GSFL market (see Figure 9.4.1). The noticeable dip in shipments after the 2017 compliance year 

for CSL1 occurs because the CSL1 lamp option has a much longer lifetime than the baseline 

options, so fewer replacement lamps are shipped for a period until the stock turnover regains 

equilibrium.

Figure 9.5.2 Historical and Projected Shipments for IRLs, Best Estimateo

 Table 9.5.2 shows DOE’s best estimates of cumulative shipments for each of the 

modeled product class groupings for the All CSL 1 and Max CSL CSCs. In each case the table 

also shows the percentage change in shipments of the CSC relative to the base case. 

 

o In some cases, the change in shipments between the candidate standards case and base case is so small it is 

indistinguishable on the figure. In that case, the higher standard level overwrites the lower.
9-67 

Table 9.5.2 Effects of Candidate Standards Cases on Cumulative Shipments 

Compared to Base Case for GSFLs and IRLs, Best Estimate

Product Class 

Groupings

Base Case All CSL 1 Max CSL*

Cumulative 

Shipments

millions

Cumulative 

Shipments

millions

Change in 

Shipments 

Relative to 

Base Case 

Cumulative 

Shipments

millions

Change in 

Shipments 

Relative 

to Base 

Case

4-foot MBP 5,082 4,989 -2% 4,814 -6%

8-foot SP slimline 46 46 1% 46 1%

8-foot RDC HO 20 22 12% 22 12%

4-foot T5, MiniBP 

SO 826 925 12% 1,097 33% 

4-foot T5, MiniBP 

HO 867 861 -1% 863 0% 

2-foot U-shaped 208 204 -2% 197 -5% 

Total GSFL** 7,049 7,048 0% 7,040 0%

IRL Residential 498 329 -34% 329 -34% 

IRL Commercial 66 60 -10% 60 -10%

Total IRL** 564 388 -31% 388 -31%

*The maximum CSL is CSL 2 for 4-foot MBP GSFLs and CSL 1 for all other GSFLs.

The maximum CSL for all IRLs is CSL 1.

** May not add due to rounding.

9.5.2 Results of the Alternative Analyses

Table 9.5.3 summarizes the cumulative shipments results for all of the alternative 

analyses for the CSL 1 and Max CSL CSCs. These analyses include scenario comparisons run to 

estimate

• the uncertainty introduced into the GSFL shipments analysis because of the uncertainty in 

REO prices, 

• the impact of LEDs, 

• the impact of controls penetration, and 

• the impact should manufacturers respond to an IRL standard at CSL 1 by making 

compliant, but shorter-lived, lamps. 

Table 9.5.3 summarizes the results of the alternative analyses and compares them to the 

best-estimate analyses. As shown, the uncertainty in the cumulative GSFL shipments introduced 

by volatile REO prices is small given the assumed bounds on the uncertainty in REO prices.p

 

p It is worth noting in this context that the analysis assumes constant lumen capacity demand per square foot, i.e., 

that consumers will not respond to increased lamp prices by using less light, although the analysis does capture 

shifts that can occur because different lamp options have different amounts of triband phosphor per unit lumen 

output.

By 
9-68 

contrast, the assumed LED incursion has a very large impact on the projected shipments for both 

product categories, nearly halving shipments of GSFLs and reducing IRL shipments more than 

fivefold compared to a projection that neglects LED incursion. The reference controlspenetration assumption decreases the estimated GSFL shipments only slightly (about 2%) over a 

projection with fixed controls penetration, because of the controls’ indirect effect on lamp 

lifetime. Because the penetration of dimmers, for all sectors, was assumed to be fixed at the 

current levels, and because the impact of growth in switching-based controls on IRL life was 

assumed to be negligible, there is no detectable effect on IRL shipments. However, the 

introduction of short-lived IRLs into the market in the alternative standards case could increase

IRL shipments by almost 65 percent over a standards case with no such short-lived lamps. 

Table 9.5.3 Cumulative Shipments of GSFLs and IRLs from 2017 – 2046, for All 

CSL 1 and Max CSL, Alternative Analyses 

Standard

Uncertainty 

Analysis

Impact 

Determination

Alternative 

IRL 

Technology 

Best

Estimate

REO 

High

REO 

Low No LED

Fixed

Controls IRL Short Life

GSFL

 

Base Case 7049 7024 7043 12549 7201 NA

CSL 1 7048 7022 7043 12546 7195 NA

Max CSL 7040 7016 7035 12531 7179 NA

IRL

 

Base Case 564 NA NA 3229 564 564

CSL 1 388 NA NA 2375 388 638 
9-69 

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