Quantifying the Impact of Refrigerated Unit Failures

 

 

 

FINAL REPORT

 

for

 

 

Mack-Blackwell Transportation Center

(MBTC)

 

 

 

 

Project #2005

 

 

 

 

 

 

 

Wednesday, March 14, 2001

 

 

Darin Nutter, Ph.D., P.E.1

Richard Cassady, Ph.D.2

John English, Ph.D., P.E 2.

Don Taylor, Ph.D., P.E.3

Chet Tuck Wong2

 

 

 

1 – Department of Industrial Engineering, University of Arkansas

2 – Department of Mechanical Engineering, University of Arkansas

3 – Department of Industrial Engineering, University of Louisville


ABSTRACT

            The shipment of processed meats, like poultry, dictates the necessity of using refrigerated trailer units (commonly call reefers).  Reefer failures occur and have serious and costly effects on the performance of rural and urban transportation systems typical of the poultry industry.  This project explored the measurable impact of reefer failures through identifying potential reefer failure modes (using FMEA, FTA, and Pareto analysis) and the development of a simulation model based on common poultry industry trucking practices.  Reported performance measures include the number of reefer failures and 7-year costs due to both delays in delivery and refrigeration system repairs.

 

INTRODUCTION

The transportation system of the poultry processing industry embeds multi-layered pick-up and delivery points (like hubs): kill facilities, production facilities and distribution facilities.  Live birds are collected from the rural domain of the farmer and delivered to the kill facility.  From the kill facility, cleaned birds are transported to the processing facilities, and once the birds are processed, complex shipping rules are implemented to insure that appropriate inventory levels of various product types are maintained at the national distribution centers.  The hierarchical design is typical of many transportation systems, but the perishable aspect of the shipped material presents unique challenges. 

            The shipment of processed meats, like chicken, dictates the necessity of using refrigerated trailer units (commonly call reefers).  As the case with any mechanical device, reefer failures (of various modes) are observed and have serious and costly impacts on the operation.  At the kill facility, limited warehouse space is available, and the reefer units are used for storage following the killing process and prior to shipment.  The time the product is held in the reefer unit is limited, and the trailer time is spent in the facility grounds where local maintenance is available, yet any reefer failure still costs time and money.  As the product progresses through the operation, reliable reefer performance becomes even more critical.  Important issues include the dispatching rules, fleet size, season of the year, availability of third party reefer repair, time of day, freight/product mixture and geography. 

 

RESEARCH OBJECTIVE AND TASKS

            This project explored the measurable impact of reefer failures on the economical and logistical performance of the rural and urban transportation systems typical of the poultry industry. The work presented in this project was appropriate to any organization having refrigerated transportation systems.  In this project, we explored and documented the impact of refrigerated unit failures on the logistical infrastructure within the poultry processing industry, namely Tyson Foods, Inc.  As a result of these activities, industries having multi-layered pick-up and delivery points will be able to identify opportunities for improved performance and to determine how factors influence total cost.

This project evolved through four successive phases.  In phase one, reefer failure types and associated failure distributions were identified by reviewing the pertinent literature and discussion/validation with Tyson’s personnel.  The second phase of the project incorporated the failure distributions with the known logistical system at Tyson Foods, Inc. to construct a generalized simulation model to measure the potential impact of reefer failures.  The third phase of the project utilized the simulation model to construct a useful set of experimental scenarios and to identify how factors influence total cost.  The fourth phase of the project consists of documenting and distributing the findings of the research.

 

Phase I:  Reefer Failure Description

            Efforts during this phase included many discussions with Tyson Foods personnel (management and maintenance), the inspection of some reefer units under repair, and a thorough review of pertinent Thermo King operation and maintenance literature.  This first step identified the potential failure modes associated with the trailer’s refrigeration system.  There were two methods used to identify or analyze potential system failure modes and their effects on the local and system trucking operations.  One method used was Failure Mode and Effects Analysis (FMEA), and the second was Fault Tree Analysis (FTA).  Results from both are described below.

 

Failures Mode and Effects Analysis (FMEA)   

            Failure Mode and Effect Analysis  (FMEA) is a structured, qualitative analysis of a system, subsystem, or function to identify potential system failure modes, their causes, and the effects on operation associated with each failure mode occurrence (Bowles and Bonnell, 1998).  The FMEA can be extended to include an assessment of the severity of the failure effect and its probability of occurrence, i.e. a Failure Mode, Effects, and Criticality Analysis (FMECA).  A FMEA/FMECA provides a basis for recognizing component failure modes identified in components and system prototype tests and failure modes developed from historical “lessons learned” in design requirements.  It aids in identifying unacceptable failure effects that prevent achieving design requirements.  It is also used to assess the safety of system components and to identify design modifications and corrective action needed to mitigate the effects of a failure on the system.  It is used in planning system maintenance activities, subsystem design, and as a framework for system failure detection and isolation (Bowles and Bonnell, 1998). 

            In this project, the main purpose of using FMEA was to identify potential system failure modes and their effects on the local and system operations.  Before analyzing the system failure modes and their effects, the first step was to learn the system.  Currently, Tyson Foods is using the Thermo King refrigerated unit (reefer), and FMEA is based on Thermo King’s system.  The functional relationships between the different system components were most easily shown as a functional block diagram, such as in Figure 1 (refrigeration cycle) and Figure 2 (defrost/heating cycle).   Those functional block diagrams help analysts to understand the relationships between the system components.

            The next step of the FMEA was to determine all the ways in which each component can fail and the effect that each failure mode will have on the refrigeration system.  Effects were determined at each level of the system hierarchy – the effect on the module containing the failed component (local), the effect on every subsystem of which the component was a part, and the effect on the total system.  Results from the FMEA can be seen in Table 1. For example, a broken compressor crankshaft causes the compressor to fail at the local level, and subsequently causes the refrigeration system to fail at the system level.  The result of a total system failure can be product delivery delays, product damage, and incurred costs.  The process of identifying possible failure modes and determining their effects on the system operation helped develop a better understanding of the relationships between the different system components.


 

Figure 1.  Functional Block Diagram – Refrigeration Cycle (Thermo King).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure 2.  Functional Block Diagram – Defrost and Heating (Thermo King).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Table 1.  FMEA of the trailer refrigeration system.

 

 

Component

Function

Failure Mode

                          Failure Effects

 

 

 

 

Local

System

 

Compressor

Moves refrigerant and increases

1) Bearing loose

Noisy compressor

Reliability of the system

 

 

refrigerant gas temperature

    or burned out

 

decreases

 

 

and pressure

2) Broken valve

Low head pressure

Unable to pump down system

 

 

 

    plate

Noisy compressor

Unable to pull/hold vacuum on

 

 

 

 

 

 low side

 

 

 

3) Too much oil

 

Unit not refrigerating

 

 

 

4) Broken crank     shaft and seals leak

Compressor not functioning

System failure

 

 

 

 

 

 

 

Discharge

Used for isolating and servicing

1) Leaking

Low head pressure

System will not function

 

service

the discharge side of the

 

Unable to pull vacuum

properly

 

valve

compressor

 

on low side

 

 

 

 

 

 

 

 

Discharge

Reduces vibration transfer

1) Leaking/wear

Flexibility decrease

Vibration will increase and

 

vibrasorber

allows for a flexible discharge

    out

 

damage the nearest

 

 

line

 

 

components

 

 

 

 

 

 

 

Three-Way

Directs the flow of refrigerant

1) Does not respond

The spool moves and

Unit cools in heat and defrost

 

valve

to either the evaporator or

    to pilot solenoid

sticks at one side

cycle or heats in refrigeration

 

 

condenser

 

 

cycle

 

 

 

 

 

Unit not refrigerating and not

 

 

 

 

 

heating or defrosting

 

Condenser

Improves three-way valve

1) Leaks around

High pressure gas leaks

Unit not heating or defrosting

 

pressure

heat-to-cool response time

valve

into the unit

 

 

bypass

 

 

 

 

 

check valve

 

 

 

 

 

 

 

 

 

 

 

Condenser

Allows refrigerant to condense

1) Dirt and foreign

Inefficiency on air flow

Decrease efficiency of the

 

 

by transferring heat to ambient

    objects in the fins

recirculating over

unit

 

 

air flowing across fins and coils

2) Idle pulley condenser fan broken

the coil

 

 

Condenser 

Stops refrigerant flow from

1) Leaks / seat

High or low suction

Unit not refrigerating and not

 

check

the receiver tank during

    damage

pressure

heating or defrosting

 

valve

heat and defrost

 

 

Unable to pump down system

 

 

 

 

 

 

 

High pressure

Relieves extremely high 

1) Leaks

Lost refrigerant

Decrease efficiency of the

 

relief

refrigerant pressure from

 

 

system

 

valve

the system

 

 

 

 

 

 

 

 

 

 

 

Table 1.  FMEA of the trailer refrigeration system (continued).

 

 

Component

Function

Failure Mode

                          Failure Effects

 

 

 

 

Local

System

 

Receiver tank

Allows refrigerant to flow

1) Leaks

Refrigerant flows out

Unable to pump down system

 

outlet

from the receiver tank and

 

 

 

 

valve

is used for servicing the low

 

 

 

 

 

side

 

 

 

 

 

 

 

 

 

 

Expansion

Meters the liquid refrigerant 

1) Opened too much

High suction pressure

Suction line frosting back

 

valve

to the evaporator in the

2) Closed too much

Low suction pressure

Unit not refrigerating

 

 

cool mode

3) Needle eroded or

High suction pressure

Suction line frosting back

 

 

 

    leaking

 

 

 

 

 

4) Partially closed by

Low suction pressure

Unit not refrigerating

 

 

 

    ice, dirt or wax

 

Unit operating in a vacuum

 

Expansion

Senses temperature at the 

1) Improperly mounted

High suction pressure

Suction line frosting back

 

valve feeler

evaporator outlet and assists

2) Making pure

High suction pressure

Suction line frosting back

 

bulb

in controlling refrigerant flow

     contact

 

Unit not refrigerating

 

 

 

 

 

 

 

Evaporator

Transfers heat between 

1) Dirty or plugged

 

Gradual reduction in capacity

 

 

refrigerated compartment air

    coils

 

 

 

 

and refrigerant moving through its coils

2) Plugged passes in the coils distribution

 

Gradual reduction in capacity

 

 

 

3) Tubes damaged

 

Gradual reduction in capacity

 

 

 

4) Insufficient

 

Rapid cycling between cool

 

 

 

    circulation

 

and heat

 

Suction

Reduces vibration transfer 

1) Leaking/wear

Flexibility decrease

Vibration will increase and

 

vibrasorber

and allows for a flexible

    out

 

damage the nearest

 

 

suction line

 

 

components

 

 

 

 

 

 

 

 

 

 

 

 

 


Table 1.  FMEA of the trailer refrigeration system (continued).

 

 

Component

Function

Failure Mode

                          Failure Effects

 

 

 

 

Local

System

 

Suction

Used for isolating and

1) Leaks

High suction pressure

Unable to pump down system

 

service

servicing the suction side

 

 

 

 

valve

of the compressor

 

 

 

 

 

 

 

 

 

 

Throttling

Regulates refrigerant vapor

1) Leaks

Refrigerant flows out

Overload the motor or engine

 

valve

pressure entering the

 

 

Decrease efficiency of the

 

 

compressor

 

 

unit

 

 

 

 

 

Unit not refrigerating and not

 

 

 

 

 

heating or defrosting

 

Pilot solenoid

When energized, this

1) Coil, needle, and

 

Unit not refrigerating

 

 

electrically-controlled valve

seat failures or

 

Unit not heating or defrosting

 

 

permits the three-way valve

malfunction

 

Unable to pump down system

 

 

to shift from cool to heat

 

 

Unit cools in heat and defrost

 

 

 

 

 

cycle

 

 

 

 

 

Unit heats in refrigerating

 

 

 

 

 

cycle

 

Bypass check

Prevents refrigerant from

1) Leaks or

Refrigerant flows into

Unable to pump down system

 

valve

flowing into the bypass line

malfunction

bypass line when the

 

 

 

when the unit is in the cool

 

unit is in the cool cycle

 

 

 

cycle

 

 

 

 

Bypass

Provides for checking and   

1) Leakage around

Refrigerant flows into

Unable to pump down system

 

service

servicing of the bypass line

the stem

bypass line when the

 

 

valve

and bypass check valve

 

unit is in the cool cycle

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Fault Tree Analysis (FTA)

The second method used to identify failure modes was Fault Tree Analysis (FTA).  A Fault Tree Analysis is a graphical representation of logical relationships between events (usually failure events).  This method has long been used for the qualitative and quantitative analysis of the failure modes of critical systems (Koren and Childs, 1995).  A fault tree provides a mathematical and graphical representation of the combination of events, which can lead to system failure.  The construction of a fault tree model can provide insight into the system by illuminating potential weaknesses with respect to reliability or safety.  A fault tree can help with the diagnosis of failure symptoms (modes) by illustrating which combinations of events could lead to the observed failure symptoms.  The quantitative analysis of a fault tree is used to determine the probability of system failure, given the probability of occurrence for failure events (Koren and Childs, 1995). 

            If performed manually, the construction of a fault tree provides a systematic method for analyzing and documenting the potential causes of system failure.  The analyst begins with the failure scenario being considered and decomposes the failure system into its possible causes.  Each possible cause is then investigated and further refined until the basic causes of the failure are understood.  In other words, FTA provides a logical framework for understanding the way in which a system can fail, which is often as important as understanding how a system operates.

            A fault tree consists of the undesired top events (system or subsystem failures), linked to more basic events by logic gates.  The top events are resolved into their constituent causes, connected by “AND” or “OR” logic gates, which are then further resolved until basic events are identified.  The basic events represent basic causes for the failures, and represent the limit of resolution of the fault tree (Koren and Childs, 1995).  

            In this project, FTA was used to identify the potential causes of reefer failures.  Figures 3 and 4 show the refrigeration cycle FTA and defrost/heating cycle FTA for the Thermo King reefer units, respectively.  The FTA process began with the scenario where the reefer system failed to operate followed by the decomposition of the failed system into its possible causes.  Each possible cause was then investigated and further refined until the basic causes of the failure were understood.

The FMEA and FTA identified the following possible reefer component failures:

  1. Compressor
  2. Discharge Vibrasorber
  3. Suction Vibrasorber
  4. Three-Way Valve
  5. Pilot Solenoid
  6. Throttling Valve
  7. Bypass Check Valve
  8. Evaporator
  9. Expansion Valve
  10. Condenser
  11. Sub-cooler Heat Exchanger
  12. Receiver Tank
  13. Accumulator

 

After identifying the reefer failures types, failure data was collected for appoximately 30 trailers from each of six fleet years (1990-1995).  These data are shown in Tables 2-7.

 

Pareto Analysis

Pareto Analysis was used to determine the percentage of failures for each failure type.  The Pareto Analysis for each fleet year can be seen in Figures 5-10.  It was found that compressor failures caused 56% of all system failures, followed by the malfunction of the discharge vibrasorber (18%) and suction vibrasorber (11%).


Figure 3.  Fault Tree Analysis – Refrigeration Cycle (Thermo King).

 

Moon:   ,Moon:   ,Moon:   ,Moon:   ,Moon:   ,Moon:   ,Moon:   ,Moon:   ,Moon:   ,Moon:    

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 


Figure 4.  Fault Tree Analysis – Heating/Defrost Cycle (Thermo King).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Table 2. 1990 Trailers Failure Data.

Year = 90

 

 

Total Trailers =  27

 

 

 

 

 

Failure Type

Number of Failures

% of Trailer Failures

 

 

 

Compressor

43

68%

Discharge Vibrasorber

5

8%

Suction Vibrasorber

9

14%

3-Way-Valve

2

3%

Pilot Solenoid

0

0%

Throttling Valve

1

2%

By-pass Check Valve

3

5%

Evaporator

0

0%

Expansion Valve

0

0%

Condenser

0

0%

Heat Exchanger

0

0%

Receiver Tank

0

0%

Accumulator

0

0%

Total Failures

63

100%

 

 

Figure 5.  1990 Trailers Pareto Analysis.
Table 3. 1991 Trailers Failure Data.

Year = 91

 

 

Total Trailers = 30

 

 

 

 

 

Failure Type

Number of Failure

% of Total Failures

 

 

 

Compressor

55

75%

Discharge Vibrasorber

7

10%

Suction Vibrasorber

3

4%

3-Way-Valve

2

3%

Pilot Solenoid

2

3%

Throttling Valve

0

0%

By-pass Check Valve

0

0%

Evaporator

0

0%

Expansion Valve

1

1%

Condenser

2

3%

Heat Exchanger

0

0%

Receiver Tank

1

1%

Accumulator

0

0%

Total Failures

73

100%

 

Figure 6.  1991 Trailers Pareto Analysis.

 


Table 4. 1992 Trailers Failure Data.

Year = 92

 

 

Total Trailers = 90

 

 

 

 

 

Failure Type

Number of Failure

% of Total Failures

 

 

 

Compressor

25

48%

Discharge Vibrasorber

10

19%

Suction Vibrasorber

4

8%

3-Way-Valve

1

2%

Pilot Solenoid

4

8%

Throttling Valve

2

4%

By-pass Check Valve

1

2%

Evaporator

1

2%

Expansion Valve

1

2%

Condenser

1

2%

Heat Exchanger

1

2%

Receiver Tank

0

0%

Accumulator

1

2%

Total Failures

52

100%

 

Figure 7.  1992 Trailers Pareto Analysis.


Table 5. 1993 Trailers Failure Data.

Year = 93

 

 

Total Trailers = 26

 

 

 

 

 

Failure Type

Number of Failure

% of Total Failures

 

 

 

Compressor

19

48%

Discharge Vibrasorber

11

28%

Suction Vibrasorber

2

5%

3-Way-Valve

3

8%

Pilot Solenoid

1

3%

Throttling Valve

0

0%

By-pass Check Valve

0

0%

Evaporator

0

0%

Expansion Valve

1

3%

Condenser

3

8%

Heat Exchanger

0

0%

Receiver Tank

0

0%

Accumulator

0

0%

Total Failures

40

100%

 

Figure 8.  1993 Trailers Pareto Analysis.


Table 6. 1994 Trailers Failure Data.

Year = 94

 

 

Total Trailers = 30

 

 

 

 

 

Failure Type

Number of Failure

% of Total Failures

 

 

 

Compressor

26

44%

Discharge Vibrasorber

19

32%

Suction Vibrasorber

9

15%

3-Way-Valve

0

0%

Pilot Solenoid

1

2%

Throttling Valve

2

3%

By-pass Check Valve

2

3%

Evaporator

0

0%

Expansion Valve

0

0%

Condenser

0

0%

Heat Exchanger

0

0%

Receiver Tank

0

0%

Accumulator

0

0%

Total Failures

59

100%

 

Figure 9.  1994 Trailers Pareto Analysis.


Table 7. 1995 Trailers Failure Data.

Year = 95

 

 

Total Trailers = 28

 

 

 

 

 

Failure Type

Number of Failure

% of Total Failures

 

 

 

Compressor

9

31%

Discharge Vibrasorber

5

17%

Suction Vibrasorber

2

7%

3-Way-Valve

5

17%

Pilot Solenoid

5

17%

Throttling Valve

0

0%

By-pass Check Valve

0

0%

Evaporator

0

0%

Expansion Valve

2

7%

Condenser

1

3%

Heat Exchanger

0

0%

Receiver Tank

0

0%

Accumulator

0

0%

Total Failures

29

100%

 

Figure 10.  1995 Trailers Pareto Analysis.

 


Reliability Analysis

            The next step in the project was to characterize the gathered failure data into a useful form.  Reliability Analysis Software (Elsayed, 1996) was used to generate both a best-fit probability distribution and the mean time between failures (MTBF) for each failure type.  Due to the infrequent number of failures for failure types other than compressors, it was determined necessary to group them into two sets, “compressor” failures and the remaining “other” failures.  Also, trailer fleet years 1990-1992 were considered “old” and trailers 1993-1995 considered “new”.  For each combination of old/new and compressor/other, an exponential distribution was used to model the time to failure.  The following MTBFs were computed:

·         Old compressor = 520 hours

·         New compressor = 799 hours

·         Old others = 1083 hours

·         New others = 585 hours

 

Note that all failure data were based on calendar time, not system run time.                

 

Phase II: Generalized simulation model

 

Simulation Model

 

A simulation model of inbound and outbound trailer movement at Tyson’s Berryville facility was constructed using the simulation language SIMNET II.  Trailers were categorized as either old or new.  Failures were classified as either compressor failures or other.  A key assumption in the model is that no trailer shortages occur.  Testing of the simulation model indicated that a simulation run length of 7 years was appropriate for generating accurate results and 20 replications of the model provided adequate precision in performance estimates.  The performance measures estimated from the output included: repair costs, delay costs, total costs (the sum of repair and delay costs), and the number of failures.  A flowchart of the simulation code is shown in Figure 11.

 
Experimental Design

 

Having tested the simulation model, the next phase of the analysis was to determine the effect of certain factors on the performance of the distribution system under consideration.  Five factors were chosen for consideration:

A: frequency of occurrence for delay

This value is a percentage which represents the probability that a failure results in substantial delay of a product shipment.  These delays could result in charges to the trucking division (i.e., cost penalty).  Input values for this factor range between 3-10%.

B: MTBF multiplier

This factor is used to adjust MTBF values.  For example, if the estimated MTBF values are to be used, then this factor would have a value of 1.  A value of less than 1 would correspond to a degradation in the failure rate of trailers.  For example, a value of 0.25 would imply a MTBF 4 times greater than the estimated value.

C: repair time multiplier

This factor is used to adjust the time required to perform trailer repairs.  Note that in this case, slower repair procedures would imply that this factor has a value of greater than 1.  A value of 1.0 utilizes the projected repair times provided by Tyson Foods.

D: old trailer percentage

This factor designates the percentage of trailers in the system fleet that are categorized as old.  Input values for this factor range between 25-75%.

 

E: delay time multiplier

This factor is used to adjust the amount of time consumed by substantial delays.  A value of 1.0 will utilize the delay times provided by Tyson Foods.



Figure 11.  Flowchart showing simulation logic excluding data collection and output.


The objective of the experimental design and analysis was to determine which of these factors and which interactions between factors have a significant effect on the performance of the system.  The experimental design used in this analysis was a 25 factorial design.  Therefore, low and high values for each of the five factors were chosen for experimentation.   These values are summarized in the table below.

Table 8.  Summary of five factors.

Factor

Low Value (-1)

High Value (+1)

 

 

 

A: frequency of occurrence for delay

3%

10%

B: MTBF multiplier

1.0

0.25

C: repair time multiplier

1.0

4.0

D: old trailer percentage

25%

75%

E: delay time multiplier

1.0

4.0

 

Thirty-two (32) experiments were conducted by simulating the distribution system using each combination of the low and high values for the five factors.  Each of the 32 experiments was replicated 20 times.

Results and Analysis

Primary results of the simulation experiments are captured in Tables 9-12.  An analysis of variance (ANOVA) was performed to determine which effects and which interactions between factors have a statistically significant effect on the system performance measures.  There are 31 potential main effects and interactive effects:

·        5 main effects (A, B, C, D and E)

·        10 two-way interactive effects (AB, AC, … , DE)

·        10 three way interactive effects (ABC, ABD, … , CDE)

·        5 four-way interactive effects (ABCD, ABCE, ABDE, ACDE, BCDE)

·        1 five-way interactive effects (ABCDE)

 

Note that to complete the ANOVA, some subset of these factors must be assumed to be insignificant.  Results from each ANOVA and the models derived from each are described below.  ANOVA and models for individual performance measures were also developed.  Experimental results are shown in Tables 9-12 while Tables 13-16 contain the main and interactive effects that were found to be significant for each individual performance measure.

 

Repair Costs ANOVA

 

Factors assumed to be insignificant:

A: frequency of occurrence of delay

E: delay time multiplier

all interactive effects containing A and/or E

 

Factors found to be significant:

B: MTBF multiplier

C: repair time multiplier

D: old trailer percentage

BC, BD, CD, BCD

 

Model of 7-Year Total Repair Cost:

Total Repair Cost = $30521 + $18444 XB + $18327 XC - $902 XD

                                    + $11111 XBXC - $520 XBXD - $648 XCXD

                                    - $384 XBXCXD

 

Note that:

 

 

 

 

The model is only valid for values of XB, XC and XD between -1 and 1.

Delay Costs ANOVA

 

Factors assumed to be insignificant:

C: repair time multiplier

all interactive effects containing C

 

Factors found to be significant:

A: frequency of occurrence of delay

B: MTBF multiplier

AB

 

Model of 7-Year Total Delay Cost:

Total Delay Cost = $6601 + $3488 XA + $4080 XB + $2174 XAXB

 

Note that:

 

 

The model is only valid for values of XA and XB between -1 and 1.

 

 

 

Total Costs ANOVA

 

Factors assumed to be insignificant:

interactive effects not found to be significant during any portion of repair and delay cost analysis

 

Factors found to be significant:

A: frequency of occurrence of delay

B: MTBF multiplier

C: repair time multiplier

D: old trailer percentage

E: delay time multiplier

AB, BC, BD, BE, CD, BCD

 

Model of 7-Year Total Cost:

Total Cost = $37122 + $3385 XA + $22524 XB + $18471 XC - $917 XD - $310 XE

                        + $2226 XAXB + $11201 XBXC - $569 XBXD - $445 XBXE

- $819 XCXD - $617 XBXCXD

 

Note that:

 

 

The model is only valid for values of XA, XB, XC, XD and XE between -1 and 1.

 

 

 

Number of Failures ANOVA

 

Factors assumed to be insignificant:

A: frequency of occurrence of delay

C: repair time multiplier

E: delay time multiplier

all interactive effects including one or more of A, C and E

 

Factors found to be significant:

B: MTBF multiplier

 

Model of 7-Year Total Number of Failures:

Total Number of Failures = 144 + 87 XB

 

Note that the model is only valid for values of XB between -1 and 1.

 

 

 

Analysis Tool

 

A spreadsheet was created which allows the user to input actual values for the five experimental factors.  The spreadsheet then estimates each of the system performance measures using the models derived from the ANOVA.  Figure 12 contains a screen capture of this spreadsheet.


Table 9.  Repair cost simulation results.

 

A

B