Optimal Design of Step Stress Partially Accelerated Life Test under Progressive Type-II Censored Data with Random Removal for Gompertz Distribution

Dina H. Abdel Hady^1,

¹Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Tanta University

Cite this paper:
Dina H. Abdel Hady. Optimal Design of Step Stress Partially Accelerated Life Test under Progressive Type-II Censored Data with Random Removal for Gompertz Distribution. American Journal of Applied Mathematics and Statistics. 2019; 7(1):37-42. doi: 10.12691/ajams-7-1-6

Abstract

This paper deals with random removal of progressively type II censored data. The removal of the data is assumed to follow a binomial or a uniform distribution, and the life time testing is assumed to follow a Gompertz distribution. Parameters of these distributions are estimated using the Maximum Likelihood estimation procedure. Fisher information matrix is used to estimate the asymptotic mean squared error and to construct confidence intervals of model parameters. The optimal partially accelerated lifetime testing (PALT) is estimated by minimizing the Generalized Asymptotic Variance (GAV). Simulation study is performed to Clarification the statistical properties of the parameters. A simulation results reveal that for the fixed values of the parameters, the error and optimal time decrease with increasing sample size n; estimates of binomial are more stable with a relatively small error with increasing sample size; and the test design is robust and works well for binomial removal.

Keywords:
partially accelerated life test PALT SS-PALT progressively type II censored data Gompertz distribution optimal design D-optimality

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