Reliability analysis using the least squares method in nonlinear mixed-effect degradation models

We develop statistical inference procedures in assessing product reliability based on a nonlinear mixed-effect degradation model and the least squares method. With today's high technology, some life tests result in no or very few failures by the end of test. Thus, it is hard to use the traditional reliability analysis to analyze lifetime data. Since product performance degrades over time, we analyze the degradation data and use the analytical results to estimate percentiles of the failure time distribution. The nonlinear mixed-effect degradation model provides us a way to build the relationship between degradation measurements and time. We establish asymptotic properties of the ordinary and weighted least squares estimators under the nonlinear mixed-effect model. We use these asymptotic results to obtain point estimates and approximate confidence intervals for percentiles of the failure time distribution. Two real data sets are analyzed. Performances of the proposed method are studied by simulation.