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Estimation procedures for partially accelerated life test model based on unified hybrid censored sample from the Gompertz distribution
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Online publication date: 2022-06-01
Publication date: 2022-06-01
Eksploatacja i Niezawodność – Maintenance and Reliability 2022;24(3):427–436
  • Statistical inference methods are developed for constant-stress partially accelerated life testing under unified hybrid censoring scheme.
  • Component lifetimes are assumed to follow Gompertz distributions.
  • Different point estimation methods are discussed using the classical and Bayesian approaches.
  • The existence of the maximum likelihood estimate of the parameters of the proposed model is proved.
  • Asymptotic and Bootstrap confidence intervals are given for model parameters and accelerated factor.
  • Numerical studies show that the MAP estimates perform superior than the MLEs (or MPSs) with respect to the smallest MSE values.
The accelerated life testing is the key methodology of evaluating product reliability rapidly. This paper presents statistical inference of Gompertz distribution based on unified hybrid censored data under constant-stress partially accelerated life test (CSPALT) model. We apply the stochastic expectation-maximization algorithm to estimate the CSPALT parameters and to reduce computational complexity. It is shown that the maximum likelihood estimates exist uniquely. Asymptotic confidence intervals and confidence intervals using bootstrap-p and bootstrap-t methods are constructed. Moreover the maximum product of spacing (MPS) and maximum a posteriori (MAP) estimates of the model parameters and accelerated factor are discussed. The performances of the various estimators of the CSPALT parameters are compared through the simulation study. In summary, the MAP estimates perform superior than MLEs (or MPSs) with respect to the smallest MSE values.
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