Inference for the survival function of the linearly decreasing stress Weibull
Perera, Chamila Dilhani
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The survival function is defined as the probability that a person or an object will survive beyond a specified time point. It is used in many applications including human mortality. It is also known as the survivor function or reliability function. The Weibull distribution has long drawn the attention of statisticians for modeling the reliability of systems. In this thesis, making inferences for the survival function of a Weibull system which is exposed to linearly decreasing stress is of concern. The derivation of the Linearly Decreasing Stress Weibull first appears in Guenther (2014). Parameters will be estimated using maximum likelihood estimation. The approximate normality of the maximum likelihood estimate of the survival function will be studied through a small scale simulation study. Various methods for finding confidence intervals of the survival function of a Linearly Decreasing Stress Weibull system are given. A large-scale simulation study will also be conducted to study the effectiveness of the resulting confidence intervals. The simulation study will also allow for the comparison of the various methods, and the selection of the best method.