Mathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 3, May 2015, Pages: 163-169
Received: Apr. 17, 2015; Accepted: Apr. 28, 2015; Published: May 11, 2015
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Authors
Sadia Anwar, Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, U.P, India
Sana Shahab, Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, U.P, India
Arif Ul Islam, Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, U.P, India
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Abstract
This article contains the optimum 3 step stress accelerated life test under cumulative exposure model. The lifetimes of test units are assumed to follow a generalized Pareto distribution. The scale parameter of the used failure time distribution at the constant stress level is assumed to have a log-linear and quadratic relationship with the stress. A comparison between linear plan and quadratic plan by maximum likelihood estimators for the different sample sizes is shown in the table. The optimum test plans is obtained by minimizing the asymptotic variance of the maximum likelihood estimator of the percentile of the lifetime distribution at normal stress condition for the model parameters. Tables of optimum times of changing stress level for both plans are also obtained.
Keywords
Accelerated Life Testing, Generalized Pareto Distribution, Asymptotic Variance, Maximum Likelihood Estimate, Life Stress Relationship (Linear and Quadratic), Cumulative Exposure Model
To cite this article
Sadia Anwar, Sana Shahab, Arif Ul Islam, Mathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 3, 2015, pp. 163-169. doi: 10.11648/j.ajtas.20150403.22
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