Proportional Hazard Model Applications in Reliability

This dissertation proposes two main methods as a modification of the semi-parametric Proportional Hazard Model (PHM) with innovative application for reliability testing. The first method developed uses a median of lifetime survival history for subjects with multiple occurrences to be modeled using the non-recurrent PHM method. The second method developed proposes censoring of influential observations, applying recurrent PHM theory. Both methods are validated using small electromechanical appliances with covariates identifying typical user performance as part of accelerated reliability testing.;The Median PHM method is developed to allow the treatment of time-dependent covariates and competing failure types, which is fairly often necessary to properly model reliability studies. The advantages of this method are discussed and verified to provide the statistics or reliability engineer practitioners with the ability to evaluate multiple stresses, multiple covariates in accelerated reliability testing without the need to fit a physical model for the failure type and define a parametric distribution to model the acceleration parameter of interest. The analysis is presented in terms of hazard ratios that have immediate application for categorical covariates test levels and is easily extended for continuous covariates. Immediate plots for reliability and hazard curves are produced to enhance the analysis of the reliability model. Mendes develops the likelihood function with time-dependent covariates and presents a method to lay out the data and correct the input for the time-dependent covariate value derived from multiple measures for the original subject with multiple failure occurrences. Different models per failure type are evaluated.;The second method, Censored PHM method, is proposed to provide help when too many repeated events for a given subject may bias the analysis using the PHM for recurrent events. The method censors the multiple occurrences at a given threshold that might be related to a reliability product requirement or increased dependency between failure measures. The likelihood function for this method is simpler as the retrieval for covariate levels, since the censored subjects are maintained in the modeling analysis as part of the risk set. Fixed Effects and Stratified Cox models are applied to treat the recurrent events.;Data set arrangements for recurrent events are available in the literature; however the author reviews additional techniques to separate failure modes and properly assign categorical and continuous time-dependent covariate values when both methods are used. A complete guide to the modeling steps for the Median and Censored PHM methods proposed for reliability modeling is presented in the conclusion of this study.