Optimal Design for a Bivariate Simple Step-Stress Accelerated Life Testing Model with Type-II Censoring and Gompertz Distribution

Nooshin Hakamipour () and Sadegh Rezaei ()
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Nooshin Hakamipour: Faculty of Mathematics and Computer Science, Department of Statistics, Amirkabir University of Technology, Tehran, Iran
Sadegh Rezaei: Faculty of Mathematics and Computer Science, Department of Statistics, Amirkabir University of Technology, Tehran, Iran

International Journal of Information Technology & Decision Making (IJITDM), 2015, vol. 14, issue 06, 1243-1262

Abstract: This paper deals with the optimal designing of step-stress accelerated life test (SSALT) for two stress variables. The lifetime of the items follows the Gompertz distribution and the test is subject to termination at a predetermined number of failures of test items (Type II censoring). Furthermore, we model the effects of changing stress as a cumulative exposure (CE) function. This test is presented to obtain the optimal hold times for each combination of stress levels. The optimal test plan with the minimum asymptotic variance (AV) of the maximum likelihood estimator (MLE) of reliability at time ξ is determined. Due to nonlinearity and complexity of the objective function, the particle swarm optimization (PSO) algorithm is developed to calculate the optimal hold times. In this method, the research speed is very fast and optimization ability is more. Finally, simulation results are discussed to illustrate the proposed criteria. For some selected values of the parameters, the effect of initial estimates on optimal values has been studied.

Keywords: Bivariate step-stress accelerated life test; Gompertz distribution; log-linear relationship; cumulative exposure function; maximum likelihood estimator; optimal design; reliability; type II censored data (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219622015500224

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