Predicted Reliability and Optimal Procurement of an Integrated Circuit
ESE 499: Systems Design Project
Fall 2006

Pankaj Chhabra
Student
Washington University
Gary L. Crawford (advisor)
The Boeing Company
Washington University Adjunct Professor

Introduction

    My project has two stages:

  1. Predicting the reliability of an integrated circuit over three environmental conditions using the MIL-HDBK-217F (Military Handbook: Reliability Prediction of Electronic Equipment) standard, and
  2. Managing the procurement of electronic component parts for use in the circuit by balancing reliability concerns with cost concerns.
     The circuit I analyzed is meant for use in an automobile.  It alerts the driver to power supply failure.  This circuit schematic provides only partial information about the electronic components, meaning that only a rough prediction can be made regarding circuit reliability.  These predictions are made using the most common attributes held by these components.  I analyzed the circuit's reliability in the automobile environment (the circuit's intended environment) and in commercial airplanes and space flight (non-intended environments).

     MIL-HDBK-217F contains models for predicting electronic component failure rates.  Specific component failure rates are found my multiplying a base failure rate by a number of factors, called "pi factors."  Base failure rates are obtained depending on component characteristics, while pi factors are dependent upon variables such as temperature, power rating, and environment.  For example, the failure rate of a resistor can be determined from the following formula:

 

where the Greek letter lambda stands for failure rate and pi stands for the aforementioned pi factors.  λp is therefore the part failure rate, while λb is the base failure rate.  πT is the temperature factor, πP is the power factor, πS is the power stress factor, πQ is the quality factor and πE is the environment factor.  The value for each of the pi factors can be looked up in a table after computing relevant parameters, such as part stress and junction temperature, for example.  A great deal of the work for this project came from computing parameters in order to find the pi factors.

    The failure rate is related to another important measure called Mean Time Between Failures (MTBF).  MTBF is related to the failure rate by the following equation:

MTBF = 1/λ.

    When determining the reliability of a circuit, one wishes for a low failure rate, and similarly a high MTBF.  Both MTBF and failure rate allow for a direct determination of circuit reliability.  Reliability fits the exponential model, and depends on failure rate in the following way.

R = e-λt

    Similarly, reliability depends on MTBF in the following way:

R = e- t/MTBF

    Failure rates (or MTBFs) of component parts are simply summed in order to find the failure rate (or MTBF) of the circuit as a whole.  It is important to note that the failure rates, and MTBF values, determined are in terms of operating hours only, and do not included downtime.  As mentioned previously, I analyzed the integrated circuit over three environmental conditions.

Reliability Prediction

    Since the circuit is meant for use in a car, it should first be tested in such an environment.  In MIL-HDBK-217F terms, this environment is called "ground mobile."  I found the failure rates for the circuit at a low-bound temperature (0C) and a high-bound temperature (75C).  The failure rates are given in the following table.

Component

Failure Rate (0C)

Failure Rate (75C)

Average Value

10k resistor

0.0742

0.139

0.1066

220k variable resistor

0.0239

0.0445

0.0342

22 μF, 16V capacitor

0.2212

3.24

1.7306

10k variable resistor

0.0596

0.1113

0.08545

2N3055 transistor

0.0343

0.0343

0.0343

12V lamp

12.8304

12.8304

12.8304

ua741 operational amplifier

0.2

5.6

2.9

pushbutton switch

4.14

4.14

4.14

Total failure rate (failures per 106 hours)

17.5836

26.1395

21.86155

    The average failure rate found is 21.9 failures per 106 hours.  This failure rate is extremely low.  Therefore, the reliability can be seen graphically, using the exponential model of reliability, as an exponential decay curve that looks very much like a straight line.

    The circuit may also be reliable if used in a commercial airplane.  In MIL-HDBK-217F terms, this environment is called "airborne, inhabited, cargo."  The failure rates are found at the same lower-bound and upper-bound temperatures as in the automobile case.  The failure rates for this circuit in the commercial airplane environment are summarized in the following table.

Component

Failure Rate (0C)

Failure Rate (75C)

Average Value

10k resistor

0.0835

0.1748

0.12915

220k variable resistor

0.0268

0.05596

0.04138

22 μF, 16V capacitor

0.1327

3.28

1.70635

10k variable resistor

0.06705

0.13997

0.10351

2N3055 transistor

0.0589

0.0589

0.0589

12V lamp

17.1068

17.1068

17.1068

ua741 operational amplifier

0.2

14

7.1

pushbutton switch

2.3

2.3

2.3

Total failure rate (failures per 106 hours)

19.97575

37.11643

28.54609

    The average failure rate for the commercial airplane condition is 28.5.  failures per 106 hours.  This failure rate is low, as in the case of an automobile, but since airplanes operate for a greater portion of the day than automobiles, the circuit is not reliable enough for use in such an environment.  The reliability can be seen graphically, using the exponential model of reliability.

    The space flight condition is known as the "space flight" environment, simply, in MIL-HDBK-217F terms.  The temperature low-bound in this case is still 0C, but its high bound is now 150C.  The failure rates for this circuit can be seen in the following table.

Component

Failure Rate (0C)

Failure Rate (150C)

Average Value

10k resistor

0.0023

0.00776

0.00503

220k variable resistor

0.0007438

0.00248

0.0016119

22 μF, 16V capacitor

0.00553

1.08

0.542765

10k variable resistor

0.00186

0.00621

0.004035

2N3055 transistor

0.0019

0.0019

0.0019

12V lamp

2.99

2.99

2.99

ua741 operational amplifier

0.2

15120

7560.1

pushbutton switch

0.115

0.115

0.115

Total failure rate (failures per 106 hours)

3.3173338

15124.20335

7563.760342

    Notice that the high temperature failure rate for this circuit is extremely high.  This high value suggests that the circuit would probably not be functional after takeoff of a space mission.  Nevertheless, the reliability curve for this circuit under space flight conditions can be seen to follow the exponential model.

Optimal Procurement

    Using vendor data sheets for specific models of the components needed to build the integrated circuit, I determined the failure rates for all component offerings.  I also found pricing information for these components at Digi-key.  I then ran a binary integer program to determine which specific components I should buy if I wanted to build the circuit.  The objective function for this linear program simply minimizes price-to-MTBF ratio, while the constraints make sure that I only procure one model of each component.  I ran my linear program using the CPLEX 300 solver in MPL.  The following table shows the information used in making the procurement decision, along with whether the specific component is a high-reliability, low-cost part.

Part

Manufacturer

Unit Price

Average MTBF

Price/Average MTBF

Buy?

2n3055 transistor

ON Semiconductor

1.05

28.0112

0.037485

Yes

 

STMicroelectronics

1.68

28.0112

0.059976

No

12V lamp

JKL Components

1.14

0.114548

9.9522

Yes

 

NKK Switches

1.92

0.114548

16.7616

No

10k variable resistor

Bourns

27.34

100.5025

0.272033

No

 

Bourns

2.61

95.34706

0.02737368

No

 

Panasonic

0.73

95.34706

0.00765624

No

 

Panasonic

0.41

100.5025

0.0040795

Yes

220k variable resistor

Panasonic

0.63

9.534706

0.0660744

No

 

Murata

0.2

19.19754

0.010418

Yes

10k resistor

Yageo

0.05

1072.731

0.00004661

Yes

 

Yageo

0.05

28.26456

0.001769

No

pushbutton switch

Judco

1.06

0.241546

4.3884

Yes

 

Lumex

3.21

0.187688

17.10288

No

capacitor

TDK

1.55

3.625159

0.4275675

No

 

Panasonic

0.86

3.625159

0.237231

Yes

operational amplifier

Texas Instruments

0.4

6.904647

0.057932

Yes

 

National Semiconductor

0.84

6.543218

0.1283772

No

 

STMicroelectronics

0.21

6.217745

0.1302723

No

Summary

    This circuit is reliable only in the automobile environment, its intended application.  Also, components may be purchased that balance cost considerations and meet high reliability standards.  This project properly reflects the work of a reliability engineer, one of the subspecialties of systems engineering that is not often covered.

    This project was chosen mainly due to my interest in reliability, which was thanks in great part to my project advisor, Gary L. Crawford.  For those of you interested in reliability, I suggest taking Reliability and Quality Control (ESE 405), taught in the Fall 2006 semester by Mr. Crawford.