Statistical Inferences using different Lifetime data

Abstract

This thesis focuses on statistical inferences for reliability models based on various types of lifetime data. We begin by introducing the progressively hybrid censoring scheme (PHC), which combines Type-I and progressively Type-II censoring schemes. The aim of this method is to save time and cost in data collection. Maximum likelihood and Bayesian estimations are employed using the Sarhan-Tadj-Hamilton (STH) distribution. Real data sets are analyzed to compare parameter estimations between complete and PHC samples. Simulation studies assess the performance of the PHC method with the STH distribution. Additionally, we investigate the expected experimentation time using progressively Type-II censoring under the STH distribution. Overall, this research explores statistical inferences, censoring methods, and estimation techniques to enhance reliability modeling using lifetime data. Next, we examine step stress partially accelerated life testing (SSPALT), a methodology that accelerates time to failure by subjecting experimental units to progressively harsher conditions. We apply maximum likelihood and Bayesian estimations for SSPALT using the Sarhan-Tadj-Hamilton (STH) distribution. Additionally, we explore the optimal change time for SSPALT under the STH distribution across various model parameter values. A real data set is analyzed using the STH distribution and compared to the Power Lindley and Weibull distributions. To assess the method’s performance, we conduct simulation studies. Through these investigations, we contribute to the understanding and application of SSPALT and provide insights into the suitability of the STH distribution compared to alternative distributions. In life testing, a competing risks model (CRM) is applicable when multiple causes contribute to failure. This model allows estimation of specific cause risks among other factors. The third problem of this thesis focuses on independent (ICRM) and dependent competing risks (DCRM) within CRM. Multivariate lifetime data commonly occur in practical scenarios, necessitating consideration of appropriate distributional models. We explore the Bivariate Modified Weibull Extension (BMWE) distribution and its properties. DCRM is discussed, and maximum likelihood estimation is applied to bivariate and DCR data using the BMWE distribution. Data generation and simulations evaluate the method's performance. Two real data sets are analyzed using the BMWE distribution and compared with other approaches.