Abstract
In this paper, the geometric process is introduced as a constant-stress accelerated model to analyze a series of life data that obtained from several increasing stress levels. The geometric process (GP) model is assumed when the lifetime of test units follows an extension of the exponential distribution. Based on progressive censoring, the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are obtained. Moreover, a real dataset is analyzed to illustrate the proposed procedures. In addition, the approximate, bootstrap and credible confidence intervals (CIs) of the estimators are constructed. Finally, simulation studies are carried out to investigate the precision of the MLEs and BEs for the parameters involved.
Highlights
The aim of traditional life testing and reliability experiments is to analyze data of failure time that obtained under normal operating conditions
We consider two groups of assumptions: group A for the constant-stress model and group B for the geometric process model and we prove that two groups are equivalent
We have considered the geometric process (GP) as a constant-stress accelerated life testing (ALT) model for the EE distribution under progressive type-II censored data
Summary
The aim of traditional life testing and reliability experiments is to analyze data of failure time that obtained under normal operating conditions. Mohie El-Din et al (2016a) considered the constant-stress ALT for the extension of the exponential distribution under progressive censoring. Mohie El-Din et al (2015a) applied the simple step-stress ALT under progressive first-failure censoring, considering a tampered random variable model for Weibull distribution. Mohie El-Din et al (2015b) developed Bayes estimation for step-stress ALT to power generalized Weibull distribution under progressive censoring, using a tampered random variable model. Mohie El-Din et al (2016b) considered the step-stress ALT for the extension of the exponential distribution under progressive censoring. From the assumption 1 in group A and equation (2.4), the pdf of the failure time of an item under the stress level k , k = 0,1,2,..., s, is given by ( ) ( ) fTk (t) = ak 0 1+ ak 0t −1 exp 1− 1+ ak 0t (2.5).
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