Inference and Optimal Design Based on Step—Partially Accelerated Life Tests for the Generalized Pareto Distribution under Progressive Type-I Censoring

Abstract

Various types of failure, censored and accelerated life tests, are commonly employed for life testing in some manufacturing industries and products that are highly reliable. In this article, we consider the tampered failure rate model as one of such types that relate the distribution under use condition to the distribution under accelerated condition. It is assumed that the lifetimes of products under use condition have generalized Pareto distribution as a lifetime model. Some estimation methods such as graphical, moments, probability weighted moments, and maximum likelihood estimation methods for the parameters are discussed based on progressively type-I censored data. The determination of optimal stress change time is discussed under two different criteria of optimality. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria.

Keywords:

• Generalized Pareto distribution
• Graphical and maximum likelihood estimations
• Moments and probability weighted moments estimations
• Optimality criteria
• Progressive type-I censoring
• Simulation
• Tampered failure rate model

Mathematics Subject Classification:

• 62F10
• 62F12
• 62N05