Models for Data Analysis in Accelerated Reliability Growth

This work develops new methodologies for analyzing accelerated testing data in the context of a reliability growth program for a complex multi-component system. Each component has multiple failure modes and the growth program consists of multiple test-fix stages with corrective actions applied at the end of each stage. The first group of methods considers time-to-failure data and test covariates for predicting the final reliability of the system. The time-to-failure of each failure mode is assumed to follow a Weibull distribution with rate parameter proportional to an acceleration factor. Acceleration factors are specific to each failure mode and test covariates. We develop a Bayesian methodology to analyze the data by assigning a prior distribution to each model parameter, developing a sequential Metropolis-Hastings procedure to sample the posterior distribution of the model parameters, and deriving closed form expressions to aggregate component reliability information to assess the reliability of the system. The second group of methods considers degradation data for predicting the final reliability of a system. First, we provide a non-parametric methodology for a single degradation process. The methodology utilizes functional data analysis to predict the mean time-to-degradation function and Gaussian processes to capture unit-specific deviations from the mean function. Second, we develop parametric model for a component with multiple dependent monotone degradation processes. The model considers random effects on the degradation parameters and a parametric life-stress relationship. The assumptions are that degradation increments follow an Inverse Gaussian process and a Copula function captures the dependency between them. We develop a Bayesian and a maximum likelihood procedure for estimating the model parameters using a two-stage process: (1) estimate the parameters of the degradation processes as if they were independent and (2) estimate the parameters of the Copula function using the estimated cumulative distribution function of the observed degradation increments as observed data. Simulation studies show the efficacy of the proposed methodologies for analyzing multi-stage reliability growth data