| Distribution Free Verification of System Level Reliability
Master's Candidate, Department of Statistics
Colorado State University
Thursday, July 20, 2006
Product reliability verification provides experimental evidence that a product's reliability meets predefined requirements prior to the release of a product design to manufacturing for full production. Reliability requirements usually specify that no more than /F_max /(for example 0.01 to 0.05) percent failure occur prior to time /T_min /. Testing products until failure can be costly both in time and numbers of test units. Therefore it is useful to optimize the numbers of units required for testing and use a method of failure probability estimation that is both realistic and efficient.
This project demonstrates how to minimize the number of units required given a value of /F_max / based on Greenwood's Formula for the estimated variance of a failure distribution. The work includes a comparison of three methods of generating the empirical failure distribution including the standard Kaplan Meier, linear interpolated Kaplan Meier, and kernel smoothed Kaplan Meier methods. The work concludes with a comparison of the Greenwood's Formula method and bootstraps of the three Kaplan Meier methods for calculation of the upper confidence bounds for the empirical failure distribution and lower confidence bounds for the desired failure quantile.
The findings of this work show that the best methods estimation and calculation of confidence bounds depend on the number of units available for testing, the type of censoring mechanism involved, and the general shape of the empirical failure distribution in the region of interest.