Statistical Approaches to Planning of Accelerated Reliability Testing

Abstract

This chapter presents a few statistical methods for designing test plans in which products are tested under harsher environment with more severe stresses than usual operating conditions. Following a short introduction, three different types of testing conditions are dealt with in Sects. 23.2, 23.3, and 23.4; namely, life testing under constant stress, life testing in which stresses are increased in steps, and accelerated testing by monitoring degradation data. Brief literature surveys of the work done in these areas precede presentations of methodologies in each of these sections. In Sect. 23.2, we present the conventional framework for designing accelerated test plans using asymptotic variance of maximum likelihood estimators (MLE) derived from the Fisher information matrix. We then give two possible extensions from the framework for accelerated life testing under three different constant stress levels; one based on a nonlinear programming (NLP) nonlinear programming (NLP) formulation so that experimenters can specify the desired number of failures, and one based on an enlarged solution space so that the design of the test plan can be more flexible in view of the many possible limitations in practice. These ideas are illustrated using numerical examples and followed by a comparison across different test plans. We then present planning of accelerated life testing (ALT) accelerated life test (ALT) in which stresses are increased in steps and held constant for some time before the next increment. The design strategy is based on a target acceleration factor which specifies the desired time compression needed to complete the test compared to testing under use conditions. Using a scheme similar to backward induction in dynamic programming, an algorithm for planning multiple-step step-stress ALT is presented. In Sect. 23.4, we consider planning problems for accelerated degradation test (ADT) accelerated degradation test (ADT) in which degradation data, instead of lifetime data, are used to predict a productʼs reliability. We give a unifying framework for dealing with both constant-stress and step-stress accelerated degradation test (ADT)constant-stressaccelerated degradation test (ADT)step-stress ADT. An NLP model which minimizes cost with precision constraint is formulated so that the tradeoff between getting more data and the cost of conducting the test can be quantified.