DETERMINING
OPTIMAL TRAILER DUTY AS A
FUNCTION
OF USE AND AGE
Project MBTC 2017
Final Report
By
Dr. Richard
Cassady
Dr. Darin
Nutter
Chet-Tuck Wong
January 2002
University of Arkansas
EXECUTIVE SUMMARY
The distribution of fresh and frozen foods requires the use of refrigerated trailers. In addition, Reliability and Maintainability (RAM) is an important issue in the operation of refrigerated trailer fleets. Often, as trailers age, their reliability decreases. This study explores the optimization of refrigerated trailer retirement and job assignment under consideration of container aging and usage. By achieving this objective, Tyson and other organizations that operate similar refrigerated transportation systems know when to retire the trailers and how to assign trailer duty. Also, a better understanding of RAM performance of refrigerated trailer fleets is obtained.
We began by collecting maintenance history for 195 trailers. The data covers the period January 1, 1994 to March 2, 2001. We categorized the trailers as a series system comprised of five major subsystems: refrigeration, engine, tire, wheel assembly, and structure. Next, from the maintenance history data, time between failure data for each subsystem for each trailer was collected.
Finally, a discrete-event simulation model was developed and used to evaluate Tyson’s trailer retirement policy and trailer duty. The trailer retirement policy analysis was based on total maintenance costs, salvage value, and purchase costs for a trailer. Results show that the total annual cost is minimized if the trailer is retired after 7 years of service. Retirement policies 8 years and beyond were not considered in this research because the probability distributions used to model trailer reliability was limited to the 7-year data collection period. In the trailer duty analysis, analysis tables were created to be used as a guideline for the fleet manager to compare trailers of any age based on total maintenance costs and the total number of failures. Also, using the raw data, the actual number of trailers in each percentile was created. The two analysis tables and the actual number of trailer in each percentile table are provided as shown below.
Expected
Life-to-Date Total Number of Failures for Given Percentile
1. INTRODUCTION
The transportation of fresh and frozen foods requires timely delivery and maintained product integrity at a minimized cost. Certainly, Reliability and Maintainability (RAM) is an important issue in the operation of many types of equipment, including refrigerated trailer fleets. Often, equipment is subject to deterioration with usage and age. System deterioration is often reflected in higher operations costs and lower fleet performance. To keep operation costs down while maintaining good fleet performance, RAM analysis can be used to assist in managing the fleet. For example, the decision about when to replace a unit of equipment (system) or when to change its duty is a classic problem facing a fleet manager.
Vehicle fleet retirement policies have been extensively discussed in the literature. Simms et al (1984) discuss a bus replacement problem for an urban transit authority that operates about two thousand old and new buses. The newer buses are used to supply the base demand, and older buses are used to match peak demands. The main objective of this study is to determine the optimal operating and disposing policy for the mix of old and new buses. Another aim of the analysis is to select buying, selling, and operating policies to minimize the total discounted cost over a finite planning horizon. The authors develop a non-linear optimization model and dynamic programming is the solution technique.
Love et al (1982) investigate two economic replacement policies for a Postal Canada vehicle fleet. The first policy is a simple group replacement policy - vehicles are replaced based on pre-set age or mileage. All repair and replacement costs are determined for each value of the aging parameter (years or mileage). From this research, they use average discounted costs to determine an optimal replacement cycle time. The second policy is a repair limit policy - vehicles are replaced whenever they require a repair for which the cost exceeds a set limit. They model the repair limit problem as a Markov decision process. According to the authors, the steady-state repair limits can be determined by using modified Howard’s policy improvement routine (qtd. in Howard, 1960), which allows a search procedure to determine the optimal limits. The authors have shown that the repair limit policy is sensitive to the discounted rate - the lower the discounted rate, the faster vehicles are replaced from the fleet. Finally, they conclude that the repair limit policy is better than the simple group replacement policy because the simple group replacement policy does not take into account the possibility that a vehicle, though not yet having arrived at the prescribed replacement age, suffers an irreparable breakdown.
Bell and Mioduski (1976) evaluate the life of a fleet of U.S. Army trucks. There are two objectives in this study. The first objective is to determine the age/mileage at which the trucks should be replaced. The second objective is to determine the economics of overhauling the fleet in order to extend its life. The authors conducted two major analyses. The first analysis is a cost analysis to determine how maintenance costs vary as truck mileage increases. From this analysis, the mileage at which the average system cost per mile is at a minimum can be determined. The purpose of the second analysis is to analyze the reliability, availability, and maintainability characteristics of the fleet. In analyzing the unscheduled maintenance actions (the reliability analysis), a Weibull failure rate function is applied. In the availability analysis, the authors study the Inherent Readiness Analysis as truck mileage increases. Finally, in the maintainability analysis, the authors determine the impacts of working hours for maintenance and major component replacements as a function of mileage.
1.1 Project Description and Objectives
The transportation of fresh and frozen products requires the use of refrigerated trailers. Tyson Foods, Inc. uses approximately 7000 refrigerated trailers to distribute fresh and frozen foods throughout the United States. Like many other systems, refrigerated trailers are subject to failure, repaired upon failure, and subjected to preventive maintenance. Tyson’s maintenance department personnel perform most of the maintenance for the refrigerated trailers. Operation and maintenance of the refrigerated trailers is an integral factor in the performance of the distribution system. As the age of refrigerated trailers increases, their reliability performance may decrease. This possibility leads this study to evaluate Tyson’s trailer retirement policy and trailer assignment/duty. There are three objectives of this research. They are:
· To collect maintenance history data from the Tyson refrigerated trailer fleet
· To model the RAM performance of the fleet
· To use this model to evaluate Tyson’s trailer retirement and trailer duty assignment policies.
By achieving these objectives, Tyson and other organizations that operate similar refrigerated transportation systems will have a better knowledge of when to retire the trailers and how to assign trailer duty. Also, a better understanding of RAM performance of refrigerated trailer fleets will be obtained.
2. METHODOLOGY
This research presented evolved through three successive phases. In this chapter, the three phases are presented. Detailed descriptions of the data collection, fleet performance modeling, retirement policy and trailer duty evaluation are provided.
2.1
Data Collection
In order to study the RAM behavior of the Tyson fleet, we first needed to collect the maintenance history from Tyson. The complete maintenance history on trailers put in service in 1994 –1995 was collected. The raw content of the maintenance history data was reviewed. The data needed in this research includes the trailer “put-in-service” date, repair dates, the types of repair, PM dates and types, and the end date for data collection. Next, a system structure for a refrigerated trailer is defined based on the maintenance history data. The goal is to model a refrigerated trailer as a series system. Finally, the time between failure data for each subsystem on each trailer is collected.
Figure 2.1 includes an example of maintenance history data for a hypothetical 2-subsystem trailer. This data includes the date of each failure for each subsystem, as well as the start and end dates for data collection. Figure 2.2 contains the time between failure data for subsystem 1 taken from Figure 2.1. For example, the first time between failures for subsystem 1 in trailer 1 is 51 days (difference between 01/30/94 and 03/22/94), and the second time between failures is 230 days (difference between 11/07/94 and 03/22/94). The third time between failures is censored (the third failure has not occurred), which is indicated with “S”. However, we do know that the third time between failures is at least 559 days. A data set of this type was constructed for each trailer subsystem.
Figure 2.1:
Example Maintenance History Data
Trailer 1
Date Subsystem Event Failure
03/22/94 1 Recap
09/23/94 2 Brake
11/07/94 1 New Tire
01/10/95 2 Brake
05/19/96 n/a Data collection end date n/a
Trailer 2
Date Subsystem Event Failure
01/30/94 n/a Trailer put in service n/a
07/02/94 1 New tire
10/03/94 1 Recap
11/17/94 1 New tire
01/10/95 2 Brake shoes
05/19/96 n/a Data collection end date n/a
Figure 2.2: Example Time Between Failure Data for Subsystem 1
Trailer Subsystem 1st Failure 2nd Failure 3rd Failure 4th Failure
1 1 51 230 559 S
2 1 153 93 45 549 S
2.2
Fleet Performance Modeling
For each subsystem data set, the Weibull ++ software package is used to fit a probability distribution to the actual 1st failure data, 2nd failure data, 3rd failure data, and so on. Maximum likelihood estimation is used to fit a Weibull distribution to each failure number. Ninety five percent confidence intervals on the shape parameter (b) are used to determine if the hazard functions increase (b > 1), decrease (b < 1), or remain constant over time (b = 1). Where appropriate, consecutive failure numbers are combined into a single probability distribution model. Finally, the individual subsystem models are combined into a trailer-level model.
2.3
Retirement Policy and Trailer Duty
Evaluation
Currently, Tyson’s trailer retirement policy is to retire a trailer after 7 years of service. In order to evaluate Tyson’s trailer retirement policy, the modeling methodologies developed in the previous sections were used in conjunction with a discrete-event simulation model and costs analysis.
3. RESULTS AND DISCUSSION
In this chapter, the results of the research are presented. Detailed results of the data collection, fleet performance modeling, and retirement policy and trailer duty evaluation efforts are provided.
3.1 Data Collection
To model the reliability performance of refrigerated trailers, maintenance history for 195 trailers in Tyson’s fleet trailers was collected. The data covers the period January 1, 1994 to March 2, 2001. Of the 195 trailers analyzed, eight trailers were put into service in 1995, and 187 trailers were put into service in 1994. An example of Tyson’s reefer trailer maintenance history can be found in Figure 3.1.
The maintenance history for a given trailer can be divided into three major sections that contain important information. The first section contains the trailer number, the start date for data collection and the end date for data collection. The second section contains the year, model, type, and serial number of the trailer. The third section is the detail of the trailer’s maintenance history. In this third section, the first column contains the dates associated with the trailer’s preventive maintenance (PM) and repair activities. The second column contains the work order number for each maintenance action. The third column denotes the type of maintenance action - 1 denotes the type 1 preventive maintenance (PM 1), 2 denotes type 2 preventive maintenance (PM 2), and a blank indicates a repair action. The fourth and the fifth columns contain the class and the part number.
Figure 3.1: Example Maintenance History
End Date for Data
Collection Start Date for Data
Collection
Trailer Number Description of the
Maintenance Activity
TYSON FOODS,
INC.
End
Date
VEHICLE: 50794 FROM: 01/ 01/ 94 TO: 03 / 02 / 01
YR:1994
MAKE:DORSY MODEL:LITE BODY-TYPE:RT REEFER TRAILER SERIAL: 1DTV61Z26RA224452
Maintenance Shop Location
DATE WRK-ORD PM-TYPE
CLASS PART DESCRIPTION SHOP-LOCATION
01/30/94 709859
1 46 PUT IN SERVICE 00810 SPRINGDALE
03/22/94 733142
2 008105
ALABAMA
09/23/94
752541 1 008107
NEW H.GARAGE
11/07/94
1024469 2 201100
WILKESBORO
01/10/95
1011691 1 73 NS-000002 LUBE 173101 SEGUIN GA
01/18/95
1011717 1 33
NS-000001 S/C-ANNUAL 173101
SEGUIN GA
02/10/95
1040838 2 201100
WILKESBORO
05/31/95 912347 33
NS-000002 ADJ BRAKES/RPR LIGHTS 203100
MONROE
07/07/95 935754
1 46
NS-000006
BRAKES 008100
SPRINGDALE
11/30/95 056548 46
NS-000006 RPL FAN BELT 008106
POTTSVILLE
01/21/97 156601
2 45 VP-016854
FILTER-AIR 008106
POTTSVILLE
Based on the class and part number, Tyson personnel can track which facility or service center recorded the maintenance activity. The sixth column contains a description of the maintenance activity. The last column contains the shop location where the maintenance activity took place.
Tyson performs two types of preventive maintenance (PM 1 and PM 2) on the reefer trailers and trucks. Tyson’s maintenance division performs PM 1 every month for the trailers and every 7000 miles for the trucks. They perform PM 2 every three months for the trailers and every 21,000 miles for the trucks. PM 1 and PM 2 are identical except for an oil change included with PM 2. Figure A.1 in Appendix A is Tyson’s PM Inspection and Worksheet for trucks and trailers.
After reviewing the maintenance data for content, we categorized the trailer as a series system comprised of six major subsystems. The six major subsystems are: refrigeration, engine, tire, wheel assembly, electrical, and structure.
Figure 3.2: Six Major Subsystems for Refrigerated Trailer in Series System
Refrigeration Electrical Structure
Figure 3.2 shows the six major subsystems for the refrigerated trailer in series system.
· Refrigeration subsystem consists of the components that need to be used in the
operation of the refrigeration system, such as compressor, evaporator,
condenser, etc.
· Engine subsystem consists of the components that need to operate the
refrigeration system such as battery, motor, water pump, etc.
· Electrical subsystem consists of all the electrical components such as electrical
wires, bulb, lights, etc.
· Tire subsystem consists of the mount and dismount process, valve stem, and
tires.
· Wheel Assembly consists of all the brake components such as brake shoes,
bearing, brake drums, wheel casing, etc.
· Structure consists of inside and outside structures of the trailer, door, air chute,
mud flaps, etc.
All the components associated with the six subsystems can be found in Table A.1 in Appendix A.
Next, we enumerated the failure types for each subsystem. The failure types associated with the six major subsystems can be found in Table A.1 in Appendix A. The maintenance history for all 195 trailers was summarized using the format shown in Table 3.1 (Table 3.1 is a summary of the history for trailer 51072). Only failures were included in this summary. This data includes the start date for data collection, the date of each failure for each subsystem, and the end date for data collection.
Table 3.1: Maintenance History Data for
Trailer 51072
Put in Service date: 8/26/94 Data collection end date: 03/02/01
|
Date of Failure |
Subsystem |
Date of Failure |
Subsystem |
|
10/27/94 10/28/94 08/19/95 08/22/95 11/18/95 11/20/95 02/08/96 03/28/96 05/14/96 07/11/96 12/06/96 12/06/96 02/11/97 04/15/97 06/17/97 08/07/97 10/04/97 11/29/97 12/02/97 12/21/97 12/21/97 01/04/98 02/13/98 02/13/98 06/21/98 02/04/99 05/27/99 06/25/99 |
Tire Tire Tire Electrical Refrigeration Wheel assembly Tire Wheel assembly Structure Wheel assembly Tire Structure Tire Tire Tire Tire Engine Tire Tire Tire Wheel assembly Tire Engine Wheel assembly Tire Tire Tire Refrigeration |
07/07/99 08/02/99 09/17/99 10/18/99 11/02/99 03/31/00 04/02/00 05/11/00 09/19/00 09/28/00 10/15/00 12/17/00 12/28/00 |
Refrigeration Tire Engine Engine Tire Engine Structure Tire Engine Wheel assembly Tire Engine Tire |
From the maintenance history data, time between failure data for each subsystem for each trailer was collected. The time between failures was measured using elapsed calendar time. As an example, Table 3.2 shows the time between failure data for trailer 51072’s tire subsystem. Note that 21 failures occurred, the time of 21st failure is not the end date, and the 22nd failure time is right-censored, in other words, 67 days have passed since the 21st failure occurred, but the 22nd failure has yet to occur.
Table 3.2: Time Between
Failure Data for Trailer 51072’s Tire Subsystem
|
Failure |
Time of Failure (days) |
Time Between Failure (days) |
|
1 |
62 |
62 |
|
2 |
63 |
1 |
|
3 |
358 |
295 |
|
4 |
531 |
173 |
|
5 |
833 |
302 |
|
6 |
900 |
67 |
|
7 |
963 |
63 |
|
8 |
1026 |
63 |
|
9 |
1077 |
51 |
|
10 |
1191 |
114 |
|
11 |
1194 |
3 |
|
12 |
1213 |
19 |
|
13 |
1227 |
14 |
|
14 |
1395 |
168 |
|
15 |
1623 |
228 |
|
16 |
1735 |
112 |
|
17 |
1802 |
67 |
|
18 |
1894 |
92 |
|
19 |
2085 |
191 |
|
20 |
2242 |
157 |
|
21 |
2361 |
74 |
|
22 |
2383 * |
67 (S) |
* - End of Data Collection
S - Right-censored (suspended)
For each subsystem, time between failure data sets were created. Table 3.3 shows a portion of the time between failure data the refrigeration subsystem. For each data value, F denotes an actual time between failure and S denotes a right-censored time between failure. For example, trailer number 50794 has experienced 4 failures. However, trailer number 50812 has experienced only one refrigeration subsystem failure. Table A.2 in Appendix A includes the complete time between failure data for the refrigeration subsystem. Note that similar data sets were constructed for the other subsystems.
Table 3.3: Example Time Between Failure Data for Refrigeration Subsystem
|
Trailer Number |
1st Failure |
|
2nd Failure |
|
3rd Failure |
|
4th Failure |
|
5th Failure |
|
6th Failure |
|
|
50794 |
524 |
F |
11 |
F |
1230 |
F |
227 |
F |
596 |
S |
|
|
|
50796 |
365 |
F |
365 |
F |
872 |
F |
26 |
F |
787 |
F |
148 |
S |
|
50798 |
2596 |
S |
|
|
|
|
|
|
|
|
|
|
|
50800 |
637 |
F |
82 |
F |
1699 |
F |
158 |
S |
|
|
|
|
|
50802 |
2612 |
S |
|
|
|
|
|
|
|
|
|
|
|
50804 |
954 |
F |
716 |
F |
571 |
F |
261 |
F |
104 |
S |
|
|
|
50806 |
627 |
F |
72 |
F |
199 |
F |
25 |
F |
1536 |
F |
25 |
S |
|
50808 |
274 |
F |
2073 |
F |
221 |
F |
18 |
S |
|
|
|
|
|
50812 |
608 |
F |
1998 |
S |
|
|
|
|
|
|
|
|
|
50814 |
1809 |
F |
751 |
S |
|
|
|
|
|
|
|
|
|
50816 |
654 |
F |
1941 |
S |
|
|
|
|
|
|
|
|
|
50818 |
212 |
F |
222 |
F |
126 |
F |
2004 |
S |
|
|
|
|
|
50820 |
1018 |
F |
911 |
F |
677 |
S |
|
|
|
|
|
|
|
50822 |
333 |
F |
1793 |
F |
480 |
S |
|
|
|
|
|
|
|
50824 |
2588 |
S |
|
|
|
|
|
|
|
|
|
|
|
50826 |
2591 |
S |
|
|
|
|
|
|
|
|
|
|
|
50828 |
811 |
F |
805 |
F |
990 |
S |
|
|
|
|
|
|
At this point, the electrical subsystem was eliminated from consideration because only one electrical subsystem failure occurred during the 7-years data collection period. Thus, the electrical subsystem is assumed to be perfectly reliable (reliability equal to one). So, the revised trailer model is a series system comprised five subsystems.
3.2
Fleet Performance Modeling
The purpose of the next phase of this research was to model the reliability performance of a refrigerated trailer. The first step in this phase was to construct probability models corresponding to each set of time between failure data. Initially, we attempted to use the Weibull distribution to model the performance of each subsystem. The Weibull distribution was chosen because it is the most widely used lifetime distribution due to its flexibility in modeling components with increasing, decreasing, or constant hazard functions. Also, many mechanical components exhibit increasing failure rates during their lifetimes (Elsayed, 1996).
We used the Weibull ++ software package and maximum likelihood estimation to fit a Weibull distribution to each failure number (1st, 2nd, …) within each subsystem time to failure data set. The shape parameter (b) and scale parameter (h) of the Weibull distribution for each failure number within each subsystem were estimated. In addition, 95% confidence intervals on b were used to determine if the hazard function is increasing (b >1), decreasing (b < 1), or constant (b = 1). Tables 3.4 - 3.8 show the estimated values of b and h as well as the corresponding 95 % confidence intervals for b for each of the five subsystems.
Table 3.4: Weibull Distribution Parameters
for Engine Subsystem
|
Failure Number |
b |
h |
||
|
Lower 95% C.I. |
Estimate |
Upper 95% C.I. |
Estimate |
|
|
1 |
1.6350 |
1.8282 |
2.0443 |
969.0681 |
|
2 |
0.8888 |
0.9983 |
1.1215 |
432.8821 |
|
3 |
1.0782 |
1.2163 |
1.3722 |
449.7208 |
|
4 |
0.9020 |
1.0264 |
1.1680 |
341.8529 |
|
5 |
0.7071 |
0.8195 |
0.9498 |
340.8895 |
|
6 |
0.7015 |
0.8451 |
1.0181 |
415.7143 |
|
7 |
0.6893 |
0.8806 |
1.1250 |
327.5526 |
|
8 |
0.7117 |
0.9561 |
1.2845 |
262.6713 |
|
9 |
0.6967 |
1.1126 |
1.7768 |
319.9364 |
|
10 |
0.4627 |
0.9388 |
1.9049 |
503.2325 |
|
11 |
0.5153 |
1.3438 |
3.5041 |
87.8272 |
|
12 |
0.2019 |
1.1550 |
6.6083 |
417.0540 |
Table 3.5: Weibull Distribution Parameters for Refrigeration Subsystem
|
Failure Number |
b |
h |
||
|
Lower 95% C.I. |
Estimate |
Upper 95% C.I. |
Estimate |
|
|
1 |
1.2035 |
1.3594 |
1.5355 |
1385.1115 |
|
2 |
0.7153 |
0.8313 |
0.9661 |
1096.0116 |
|
3 |
0.7204 |
0.8660 |
1.0409 |
836.6606 |
|
4 |
0.6405 |
0.8213 |
1.0532 |
834.1801 |
|
5 |
0.9280 |
1.2756 |
1.7532 |
607.3153 |
|
6 |
0.6149 |
0.9266 |
1.3962 |
381.2062 |
|
7 |
0.3916 |
0.8163 |
1.7015 |
482.6098 |
|
8 |
0.5854 |
1.8990 |
6.1595 |
559.7014 |
Table 3.6:
Weibull Distribution Parameters for Structure Subsystem
|
Failure Number |
b |
h |
||
|
Lower 95% C.I. |
Estimate |
Upper 95% C.I. |
Estimate |
|
|
1 |
1.1395 |
1.3363 |
1.5671 |
2510.3095 |
|
2 |
0.5562 |
0.7183 |
0.9276 |
3093.1565 |
|
3 |
0.4901 |
0.7656 |
1.1959 |
3004.0838 |
|
4 |
0.1586 |
0.8643 |
4.7105 |
10345.9000 |
Table 3.7: Weibull Distribution Parameters
for Tire Subsystem
|
Failure Number |
b |
h |
||
|
Lower 95% C.I. |
Estimate |
Upper 95% C.I. |
Estimate |
|
|
1 |
1.8309 |
2.0300 |
2.2514 |
494.5900 |
|
2 |
1.1084 |
1.2400 |
1.3780 |
204.6300 |
|
3 |
0.8969 |
1.0000 |
1.1238 |
|