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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Nooshin Hakamipour & Sadegh Rezaei, 2015. "Optimal Design for a Bivariate Simple Step-Stress Accelerated Life Testing Model with Type-II Censoring and Gompertz Distribution," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 1243-1262, November.
    • Handle: RePEc:wsi:ijitdm:v:14:y:2015:i:06:n:s0219622015500224
    DOI: 10.1142/S0219622015500224
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    References listed on IDEAS

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    1. Rafik A. Aliev & Oleg H. Huseynov, 2014. "Fuzzy Geometry-Based Decision Making with Unprecisiated Visual Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 1051-1073.
    2. Khalili-Damghani, Kaveh & Abtahi, Amir-Reza & Tavana, Madjid, 2013. "A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 58-75.
    3. Maxim S. Finkelstein, 2006. "On engineering reliability concepts and biological aging," MPIDR Working Papers WP-2006-021, Max Planck Institute for Demographic Research, Rostock, Germany.
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