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

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.  λ_p is therefore the part failure rate, while λ_b is the base failure rate.  π_T is the temperature factor, π_P is the power factor, π_S is the power stress factor, π_Q is the quality factor and π_E 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

•     Automobile

    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 (0°C) and a high-bound temperature (75°C).  The failure rates are given in the following table.

Component	Failure Rate (0°C)	Failure Rate (75°C)	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.

• Commercial Airplane

    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.

    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.

• Space Flight

    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 0°C, but its high bound is now 150°C.  The failure rates for this circuit can be seen in the following table.

    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.

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.