A Bayesian Approach for Modeling Reliability Growth

Abstract

One challenge in reliability growth modeling is the estimation of initial failure intensities of the new design units under reliability growth testing. In existing literature, the failure intensities are usually estimated based expert knowledge and complexity and similarity analysis between new designs and mature existing product designs. Such estimations are mostly assumed to be fixed even though unknown. Likewise, the final projected reliability is estimated under a fixed growth rate according to the characteristics of the new design. Existing reliability growth models have not well incorporated the uncertainty in initial failure intensity estimation due to limited testing data of new design contents, and the uncertainty of growth rate determined by reliability improvement program effectiveness and manufacturing processes along with other supporting functions. This research proposes to model the initial failure intensity with probabilistic models such as gamma distributions, and the growth rate is modeled as a random effect in the log-log reliability growth model. Under such a modeling framework, both failure intensity and growth rate can be continuously updated as more testing and operations data become available. Such a Bayesian reliability growth modeling approach can deal with both uncertainties in failure rate and growth rate estimations.