Exact inference for a simple step-stress model with competing risks for failure from exponential distribution under Type-II censoring

被引:115
作者
Balakrishnan, N. [1 ]
Han, Donghoon [1 ]
机构
[1] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada
关键词
accelerated life-testing; competing risks; conditional moment generating function; confidence interval; cumulative exposure model; maximum likelihood estimation; order statistics; parametric bootstrap method; step-stress model; tail probability; Type-II censoring;
D O I
10.1016/j.jspi.2008.03.036
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In reliability analysis, accelerated life-testing allows for gradual increment of stress levels on test units during an experiment. In a special class of accelerated life tests known as step-stress tests, the stress levels increase discretely at pre-fixed time points, and this allows the experimenter to obtain information on the parameters of the lifetime distributions more quickly than under normal operating conditions. Moreover, when a test unit fails, there are often more than one fatal cause for the failure, such as mechanical or electrical. In this article, we consider the simple step-stress model under Type-II censoring when the lifetime distributions of the different risk factors are independently exponentially distributed. Under this setup, we derive the maximum likelihood estimators (MLEs) of the unknown mean parameters of the different causes under the assumption of a cumulative exposure model. The exact distributions of the MLEs of the parameters are then derived through the use of conditional moment generating functions. Using these exact distributions as well as the asymptotic distributions and the parametric bootstrap method, we discuss the construction of confidence intervals for the parameters and assess their performance through Monte Carlo simulations. Finally, we illustrate the methods of inference discussed here with an example. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:4172 / 4186
页数:15
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