Practical Bayesian methods for determining device failure rates from zero-failure data

Abstract

This paper presents several practical methods that can be used to supplement classical reliability prediction techniques typically used to calculate electronic system failure rates. These methodologies employ Bayesian data analysis techniques utilizing available field reliability data and accelerated life test (ALT) results. Methodologies include the Clopper-Pearson method which has been shown in the literature to be a special case of the Bayesian method. The Clopper-Pearson lower one-sided confidence bound equation is solved in terms of reliability and allows for the derivation of a failure rate point estimate when no credible prior information is available and zero failures have occurred in the field. When lower level test data such as accelerated life test results (informative prior) are available, a gamma-exponential conjugate model can be used to derive the failure rate from the resulting posterior distribution over a range of credibility intervals using the GAMMAINV Excel function. An example of application in the context of the space industry is presented where the failure rate for a power hybrid device was derived using real accelerated life test results and zero-failure on-orbit data collected from multiple space payloads.