1. Integrated circuit failure times in hours during stress test David Swanick DSES-6070 HV5 Statistical Methods for Reliability Engineering Summer 2008 Professor Ernesto Gutierrez-Miravete August 14, 2008

2. Integrated circuit failure times in hours during stress test Failure data on integrated circuits during stress testing; data includes: total number of units tested, number and times of failures, number of units surviving, and length of test time. Objective of the study is to apply fundamental concepts of reliability engineering and produce an appropriate reliability model. This will involve analysis of the provided failure data. Analysis will include: a) Computing descriptive statistics for data b) Constructing histograms c) Selecting best fitting distribution for reliability model. d) Determining distribution parameters and confidence intervals. e) Determine analytical expressions for failure probability distribution function, survival probability function, hazard function, MTTF, and MRL by evaluating with Maple. Data: IC Data (Meeker, 1987) Integrated circuit failure times in hours –stress test Test ended at 1,370 hours –28 failed; 4,128 units were still running at end of test – (right) censored 0.1 0.150.6 0.8 1.22.5 3446 10 12.520 43 48 547484 94168263593

3. 28 failure times of the circuit boards were recorded. The number of failures were put into 31 bins, 20 hour intervals, and the number of survivors was calculated. From that data R was calculated by dividing the number of survivors by the total number tested. F was obtained by subtracting R from 1. z was found by dividing the number failed by the time interval, then dividing by the number of survivors. Z was computed by averaging the number of failures and multiplying it by the time interval.

4. Histogram of failure times

5. Goodness-of-Fit Anderson-Darling Correlation Distribution (adj) Coefficient Weibull 0.720 0.983 Lognormal 0.740 0.986 Exponential 13.158 * Loglogistic 0.825 0.981 3-Parameter Weibull 0.597 0.990 3-Parameter Lognormal 0.702 0.988 2-Parameter Exponential 3.840 * 3-Parameter Loglogistic 0.815 0.982 Smallest Extreme Value 10.065 0.576 Normal 5.625 0.695 Logistic 4.636 0.712 The three parameter Wiebull had the highest correlation coefficient, but was only slightly higher than the Wiebull, so Weibull was used for the calculations going forward.

6. Shape and scale parameters were obtained from the Minitab output and used in the equation for F. Once F was obtained, expressions for f, R, z, MTTF, and MRL could be generated in Maple.

7. Above and below are comparisons of the plots for F and z compared with the charts generated in excel from the failure data.

8. Monte Carlo simulation performed, 1000 runs, the inverse equation used in the function cells ‘=-(1/0.01927)*LN(RAND())

9. Output from the Monte Carlo simulation generated an plotted against the calculated formula.