Semiparametric constant stress accelerated lifetime test with Bayesian Laplace P-spline models under type-II progressive censoring | ||
| AUT Journal of Mathematics and Computing | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از 10 تیر 1404 | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2025.23623.1276 | ||
| نویسندگان | ||
| Bahareh Sedighi1؛ Esmaile Khorram* 1؛ Ali Aghamohammadi2 | ||
| 1Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran | ||
| 2Department of Statistics, University of Zanjan, Zanjan, Iran | ||
| چکیده | ||
| Bayesian semiparametric modeling for constant stress accelerated life test (CSALT) under type-II progressive censoring scheme (T-II PCS) is provided. In this model, lifetimes follow generalized exponential and Weibull distributions, relationships between lifetime characteristics and accelerated stresses are described by nonparametric functions, and P-spline approach is used to approximate the functions. The calculation of full conditional distributions for the parameters within the Bayesian framework is challenging due to the complex structure of the likelihood functions arising from the nonparametric relationships. Consequently, the application of Markov chain Monte Carlo (MCMC) methods demonstrates inefficiency. This paper resolves the issue by employing Laplace P-splines (LPS) in the analysis of the CSALT data based on the T-II PCS. The integration of the P-spline smoothers with a Laplace approximation within the LPS framework provides a unified approach for quick and flexible inference. This approach offers a highly precise approximation of the posterior distribution of penalized parameters. Conversely, the accuracy of the Laplace approximation for nonpenalized parameters’ posterior distributions can be affected by sparse information derived from likelihood and their priors. Therefore, the parameter space is partitioned into two subsets. Compared to the Laplace method that uniformly manages posterior values, dichotomizing the parameter space improves estimation accuracy by creating a unique treatment of the parameters. This version of LPS operates without the need for sampling, which allows it to execute calculations more rapidly than MCMC methods. The simulation study and analysis of a real data set serve to show the performance of the suggested model. | ||
| کلیدواژهها | ||
| Accelerated life test؛ Progressive censoring scheme؛ Laplace approximation؛ Bayesian P-splines؛ Skewness | ||
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