An Application of Bayesian Posterior Analysis for Disc Drive Annual Failure Rate (AFR) Estimate

ABSTRACT As an important reliability metric in disc drive industries, the annual failure rate (AFR), estimated from reliability demonstration tests (RDTs), is often used to make business decisions. Due to limited test sample size and short test duration, estimating the AFR from direct test data using Weibull distribution fit may result in a wide confidence interval, raising concerns regarding the uncertainty of the AFR estimate. To improve the confidence of the estimate, this article presents a Bayesian posterior analysis approach to estimate the AFR. Prior distributions of the Weibull distribution's shape and scale parameters are presented based on historic test data. An analysis of real RDT data demonstrates that the Bayesian posterior estimate of the AFR can produce a significantly narrower confidence interval than direct Weibull fitting, promoting higher confidence to accept the AFR estimate. To evaluate the significance of the prior distribution parameters on the AFR estimate, a sensitivity analysis is presented with respect to each individual parameter. The results indicate that the standard deviation value of either β or η has a more significant impact on the AFR estimate than the mean value.