CHAPTER 9. SHIPMENTS ANALYSIS

TABLE OF CONTENTS

9.1 INTRODUCTION.................................................................................................................... 1

9.2 METHODOLOGY................................................................................................................... 1

9.1.1 Mathematical Formulation of the Shipments Model.................................................2

9.1.2 Historical Shipments....................................................................................................2

9.1.3 Stock Events................................................................................................................. 2

9.1.3.1 Replacement Equipment ...................................................................................3

9.1.3.2 New Equipment ................................................................................................. 3

9.2 MODEL INPUTS..................................................................................................................... 4

9.2.1 New Construction ........................................................................................................ 4

9.2.2 Replacements............................................................................................................... 6

9.3 RESULTS................................................................................................................................. 7

LIST OF TABLES 

Table 9.2.1 Historical and Projected New Construction (million sq ft) for the 

Shipments Model for PTAC and PTHP Equipment*.......................................... 5

Table 9.2.2 Historical PTAC and PTHP Shipments with New Construction Floor 

Space Values Used to Calculate Saturation*....................................................... 6

Table 9.3.1 PTAC and PTHP Equipment Class Shipment Distribution................................ 7

LIST OF FIGURES

Figure 9.2.1 PTAC Survival Function....................................................................................... 7

Figure 9.3.1 Historical and Projected PTAC Shipments by Equipment Class....................... 8

Figure 9.3.2 Projected PTAC and PTHP Shipments................................................................ 8

9-i 
CHAPTER 9. SHIPMENTS ANALYSIS

9.1 INTRODUCTION

The U.S. Department of Energy (DOE) analyzes shipments of affected equipment as part 

of every rulemaking regarding new or amended energy efficiency standards for appliances or 

commercial and industrial equipment. Estimates of equipment shipments are a necessary input 

for calculating national energy savings (NES) and net present value (NPV) of the investment, 

which are required to justify potential new or amended energy efficiency standards. Shipments 

also are a necessary input to the manufacturer impact analysis (MIA). This chapter describes 

DOE’s method and results of projecting annual shipments for packaged terminal air conditioners 

(PTACs) and packaged terminal heat pumps (PTHPs). 

To project shipments of PTAC and PTHP equipment, DOE considered specific factors 

that drive equipment shipments. DOE developed shipments forecasts by accounting for: (1) the 

growth in the building stock of hotel/motel, healthcare, and small office buildings that are the 

primary end users of PTACs and PTHPs; (2) market segments; (3) equipment failure; and (4) 

equipment age. 

The shipments models are prepared as Microsoft Excel spreadsheets that are accessible 

on the Internet (www.eere.energy.gov/buildings/appliance_standards/). The rest of this chapter 

explains the shipments model in more detail. Section 9.2 describes the methodology that 

underlies development of the model; section 9.3 describes the input data used to develop the 

shipments model; and section 9.4 discusses the results in terms of base-case and standards-case 

shipments.

9.2 METHODOLOGY

This section outlines the methodology used to develop the shipments model that provides 

projections of shipments for PTAC and PTHP equipment classes defined in Chapter 5. First, a 

brief summary of the basic framework is provided in the following section.

PTAC and PTHP shipments are driven primarily by two market segments: new 

construction and replacements. For new construction shipments, DOE combined new 

construction floor space forecasts with a constant market saturation of the equipment in new 

construction floor space. DOE estimated replacement shipments using an equipment retirement 

function that it developed based on equipment lifetimes. DOE designed its shipments model by 

developing a single shipments model for all PTACs and PTHPs and then disaggregating the 

shipments into six equipment classes. The shipments model assumes that, in each year, each 

existing PTAC or PTHP either ages by one year or breaks down, and that equipment that breaks 

down is replaced. In addition, new equipment can be shipped into new commercial building floor 

space. 

9-1 
9.1.1 Mathematical Formulation of the Shipments Model 

DOE determines the yearly stock based on replacement and new shipments of PTAC and 

PTHP equipment. The total stock of equipment U of an age a in a given year t is accounted for 

and is modified by the shipments of new stock in a given year, Uship(t, a), as described below. 

U(t + 1, a) = U(t, a) + Uship(t, 0)| for each t and for each a

Eq. 9.1 

Where:

U(t,a) = total stock of equipment of an age a in a given year t, 

Uship(t,0) = total shipments of new stock, 

a = age of stock in years, 

t = year. 

By definition, the age of the equipment is zero in the year that it is shipped, so Uship(t, a) = 

Uship(t, 0). The total stock of equipment is initialized for the year 2013 after the initial stock is 

built up, as described below.

U(2013, a) = U0(2013, a)

Eq. 9.2 

Where: 

U0(2013,a) = total stock of equipment for year after based on the build-up of the initial 

stock. 

9.1.2 Historical Shipments

DOE received confidential historical shipments from AHRI for the years 2005-2012. In 

addition, AHRI provided 1998-2004 data that were published in the 2008 PTAC and PTHP 

rulemaking.1

 The average of the historical shipments (1998-2012) was used as the constant value 

for shipments for the years 1993-2012 to build up the initial stock for 2013.

9.1.3 Stock Events 

In the transition from year t to year (t+1), two things could happen to the equipment 

stock: 

• existing equipment could break or be removed during a building renovation and be 

replaced, or 

• the stock could simply age by one year. 

Such stock events as shipments for replacement equipment and shipments for new equipment are 

modeled into the shipments of new stock Uship(t): 

9-2 
Uship(t) = UR(t) + UN(t) 

Eq. 9.3 

Where: 

Uship(t,0) = total shipments of new stock in year t

UR(t) = units replaced in year t

UN(t) = the number of units going into new buildings in year t 

In the model, early replacements (i.e., existing equipment that is replaced before the end of its 

useful life) are not considered, and all broken equipment are assumed to be replaced. The 

following sections present the equations used to represent each possible event.

9.1.3.1 Replacement Equipment

DOE determined the probability that equipment of average age a from the stock of existing units 

U will break, UB(t), and replaced on a one-to-one basis, UR(t) using a function PB(a), based on a 

Weibull statistical distribution of retirements with a 10-year average life and maximum life of 20 

years. The inputs for the Weibull distribution that attains these lifetime characteristics are a scale 

parameter of 11.2 and shape parameter of 3.2. These probabilities do not depend on the model 

year t. DOE defines the quantities of replaced equipment as

UR(t) = UB(t) = � PB(a) ∙ U(t, a)

a=1

all a

Eq. 9.4 

Where: 

UR(t) = units replaced, 

UB(t) = units broken, 

PB(a) = probability that stock of existing units will break, 

U(t, a) = total stock of equipment of an age a in a given year t, 

a = average age of stock in years, 

t = year.

All broken units are assumed to be replaced.

9.1.3.2 New Equipment

New PTAC and PTHP equipment will be purchased to replace the units described above. In 

addition, new equipment will be purchased to install in newly constructed buildings. Available 

information suggests that the purchase of new equipment that would go into new buildings is 

driven by the rate of construction of hotels/motels, health care facilities, and office floor space.

9-3 
The number of PTAC and PTHP units intended for new buildings is:

UN(t) = A0 x NFS(t)

Eq. 9.5 

Where: 

UN(t) = the number of units going into new buildings in year t, 

A0 = the market saturation that accounts for the number of units per new commercial 

floor space, 

NFS(t) = the projected new commercial floor space. 

 

DOE has limited information on the variation in the market saturation of PTAC and PTHP 

equipment by building type or over time. Therefore, in the model, the purchase of new 

equipment is driven by the construction of new floor space, and broken or removed equipment is 

replaced on a one for one basis.

9.2 MODEL INPUTS

As described in Eq. 9.3, the market for PTACs and PTHPs comprises replacement units 

for equipment that has been retired and units for new construction. The following sections 

discuss both the new construction and replacement markets in further detail. 

9.2.1 New Construction

To develop shipments to new construction, DOE combined new construction floor space

forecasts with a constant market saturation of the equipment in new construction. DOE used new 

construction floor space forecasts for the healthcare, lodging, and small office sectors from the 

Energy Information Administration (EIA)’s Annual Energy Outlook 2013 (AEO2013) for 2013–

2040.2 Table 9.2.1 presents these forecasts. The data for 2041 through 2048 are based on an 

extrapolation of the trend from 2030 through 2040. 

9-4 
Table 9.2.1 Historical and Projected New Construction (million sq ft) for the Shipments 

Model for PTAC and PTHP Equipment* 

Year Healthcare Lodging Small Office Year Healthcare Lodging Small Office

2013 66 147 97 2031 71 161 148

2014 66 138 110 2032 71 168 158

2015 67 144 136 2033 72 185 174

2016 67 148 166 2034 72 192 192

2017 68 162 190 2035 73 207 210

2018 67 164 208 2036 74 216 224

2019 66 172 222 2037 74 214 229

2020 65 178 228 2038 75 208 227

2021 63 181 230 2039 76 200 219

2022 62 183 226 2040 76 190 207

2023 61 187 219 2041 77 187 198

2024 61 186 210 2042 78 184 189

2025 63 181 199 2043 78 181 181

2026 65 171 185 2044 79 177 173

2027 67 165 172 2045 80 174 165

2028 69 155 158 2046 81 171 158

2029 71 152 148 2047 81 168 151

2030 71 150 144 2048 82 166 144

*Source: AEO2013; data for 2041-2048 are extrapolated.

To derive the saturation of PTACs and PTHPs (combined) in new construction, DOE 

used data on shipments to new construction and commercial new construction floor space 

provided in the 2008 rulemaking, as shown in Table 9.2.2. DOE divided the new construction 

shipments by the total new construction floor space and used this saturation as the constant 

saturation for the analysis period. 

9-5 
Table 9.2.2 Historical PTAC and PTHP Shipments with New Construction Floor Space 

Values Used to Calculate Saturation* 

Year

Health care 

(million s.f.)

Lodging 

(million s.f.)

Small Office 

(million s.f.)

Total 

(million 

s.f.)

New 

Construction 

Shipments

Saturation 

(units/

million s.f.)

2000 68 172 179 419 66,407 6,315

*Source: DOE 2008 PTAC and PTHP Energy Conservation Standards Rulemaking. 

For new commercial buildings acquiring equipment, shipments are estimated by 

multiplying new construction floor space in each projection year by the saturation value. 

9.2.2 Replacements

To determine shipments to the replacement market, DOE used an accounting method that 

tracks the total stock of units by vintage. DOE estimated a stock of PTACs and PTHPs by using 

the average of the available historical shipments (1998-2012) as the constant value for shipments 

for the years 1993-2012. Over time, some units break and are removed from the stock, triggering 

the one-for-one shipment of a replacement unit. Depending on the vintage, a certain percentage 

of units will fail and need to be replaced. All PTACs and PTHPs are presumed to be replaced by 

a unit of the same equipment class and capacity, but of an age of zero. To estimate how long a 

unit will function before failing, DOE used a survival function based on the distributions of 

equipment lifetime. The survival function that DOE used had an average lifetime of 10 years and

a maximum lifetime of 20 years, consistent with the lifetime used in the previous rulemaking. 

Figure 9.2.1 shows the survival function DOE used to estimate replacement shipments. 

9-6 
Figure 9.2.1 PTAC Survival Function

9.3 RESULTS

 

For each year in the analysis period, DOE distributed total PTAC and PTHP shipments

into the individual equipment classes using the average of the 1998-2004 shipments by 

equipment class provided by AHRI for the previous rulemaking. Since the data did not 

perceptibly indicate an increasing or decreasing trend, DOE assumed the distribution to persist 

throughout projection years. Table 9.3.1 shows the distribution of PTAC and PTHP shipments by 

equipment class. Since shipments are not expected to change with efficiency level, results are 

presented only for the base case. 

Table 9.3.1 PTAC and PTHP Equipment Class Shipment Distribution

PTAC PTHP

<7,000 

Btu/h

≥7,000 -

≤15,000 

Btu/h

>15,000 

Btu/h

<7,000 

Btu/h

≥7,000 -

≤15,000 

Btu/h

>15,000 

Btu/h

1998-

2004 

Average 

Shipments 12,898 205,355 15,407 7,702 168,068 13,534

Percent 3% 48.5% 3.7% 1.8% 39.8% 3.2%

Figure 9.3.1 shows the projected shipments of PTACs and PTHPs by equipment class 

and the historical shipments DOE used to develop the initial stock that drove the replacement 

shipment projection for the base-case scenario. Figure 9.3.2 shows total shipments (aggregated 

from individual equipment classes) broken into new construction and replacement shipments. 

This figure starts in 2013, as historical shipments are not disaggregated into new construction 

and replacements. For the NOPR analysis, DOE assumed that the total number of shipments do 

not change with trial standard levels. The distribution of the efficiencies of shipments may 

change over time, but DOE did not change the total number of PTACs and PTHPs shipped based 

on standard levels. 

9-7 
Figure 9.3.1 Historical and Projected PTAC Shipments by Equipment Class

Figure 9.3.2 Projected PTAC and PTHP Shipments

0

50000

100000

150000

200000

250000

300000

350000

1993199519971999200120032005200720092011201320152017201920212023202520272029203120332035203720392041204320452047

Shipments

Year

PTAC <7 PTAC 7-15 PTAC > 15 PTHP <7 PTHP 7-15 PTHP >15

 -

 100,000

 200,000

 300,000

 400,000

 500,000

 600,000

 700,000

 800,000

Shipmnets

Year

New Construction Replacements

9-8 
REFERENCES

1. U.S. Department of Energy – Office of Energy Efficiency and Renewable Energy, 

Energy Conservation Program for Commercial and Industrial Equipment: Packaged 

Terminal Air Conditioner and Packaged Terminal Heat Pump Energy Conservation 

Standards., 2007. (Last accessed June, 2014.) 

<http://www.regulations.gov/#!docketDetail;D=EERE-2007-BT-STD-0012>

2. U.S. Department of Energy/Energy Information Administration, Annual Energy Outlook 

2013, 2013. Washington, D.C. Report No. DOE/EIA0383. 

9-9