Progressive Censoring and Stage Life Testing

• Progressive Zensierung und gestufte Lebensdauerprüfung

Laumen, Benjamin Christopher; Cramer, Erhard (Thesis advisor); Kamps, Udo (Thesis advisor)

Aachen (2017)
Dissertation / PhD Thesis

Dissertation, RWTH Aachen University, 2017

Abstract

In this thesis, we introduce a new progressive censoring model called modified progressive Type-II censoring with fixed censoring times. This model results from a modification of progressive Type-I censoring. We consider the new model in order to approach the drawback of potentially not observing any failures at all. Furthermore, we propose the notion of stage life testing. Hereby, we extend the model of modified progressive Type-II censoring with fixed censoring times to generalized stage life testing. This model addresses the idea that the testing of withdrawn objects from a modified progressively Type-II censored life test with fixed censoring times is continued after the withdrawal. This means that the exposed items are used for further testing under possibly different conditions. These are referred to as "stages". In Chapter 1, we provide preliminary results for progressive Type-I and progressive Type-II censoring. The model of modified progressive Type-II censoring with fixed censoring times is introduced in Chapter 2. After presenting a generation procedure of modified progressively Type-II censored order statistics with fixed censoring times, we establish respective distributional results. Following, we address likelihood inference for modified progressive Type-II censoring with fixed censoring times based on different underlying lifetime distributions. The main focus is on the one-parameter exponential distribution. Additionally, an underlying Weibull and gamma distribution is considered. We present several simulation studies in order to illustrate the obtained results. For the modeling of generalized stage life testing, we utilize the cumulative exposure model. In Chapters 3 and 4, we introduce the basic stage life testing model and the generalized stage life testing model, respectively. Finally, in Chapter 5, we consider the model of stage life testing for failure-based censoring. This model is an extension of progressive Type-II censoring by using the new stage life testing approach. For each stage life testing model proposed in Chapters 3-5, we establish fundamental distributional results for the respective ordered data. Moreover, we discuss likelihood inference for these models based on different lifetime distributions. In particular, we consider the combination of different distributions on the stages. This likelihood inference is based on complete information. Furthermore, we deal with the problem of losing the crucial information on which stage the observed failures have occurred. We address this problem by applying an EM-algorithm in order to get estimates based on incomplete data. In Chapters 3-5, we conduct several simulation studies that illustrate the respective results.