Inference on inverted exponentiated Rayleigh data from accelerated life testing with hybrid censoring
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Date
2025
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Abstract
This paper addresses the problem of estimating unknown parameters of
the inverted exponentiated Rayleigh distribution within the context of
accelerated life testing. We consider lifetime data observed through step-
stress and type-I hybrid censoring, and incorporate the cumulative expo
sure model assumptions to establish connections between the distribu
tion at various stress levels. We then write the associated likelihood
function based on the observed data and derive maximum likelihood
estimators for the distribution’s unknown parameters. Furthermore,
employing a Bayesian approach, we initially adopt gamma priors and
compute posterior distributions for the parameters. These posterior dis
tributions are then utilized to calculate Bayesian estimates using the
squared error loss function. To assess the performance of maximum like
lihood and Bayesian estimates, we conduct a simulation study under
various scenarios, considering both non-informative and informative
priors. We also evaluate interval estimates and coverage percentages
under both classical and Bayesian approaches. Finally, for illustrative
purposes, we analyze two real data sets, demonstrating the practical
application of our proposed methodology.