Carlos Alvarez College of Business Faculty Research
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12588/251
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Browsing Carlos Alvarez College of Business Faculty Research by Author "Alotaibi, Refah Mohammed"
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Item Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions(2022-05-08) Alotaibi, Refah Mohammed; Alamri, Faten S.; Almetwally, Ehab M.; Wang, Min; Rezk, HodaAccelerated life testing (ALT) is a time-saving technology used in a variety of fields to obtain failure time data for test units in a fraction of the time required to test them under normal operating conditions. This study investigated progressive-stress ALT with progressive type II filtering with the lifetime of test units following a Nadarajah–Haghighi (NH) distribution. It is assumed that the scale parameter of the distribution obeys the inverse power law. The maximum likelihood estimates and estimated confidence intervals for the model parameters were obtained first. The Metropolis–Hastings (MH) algorithm was then used to build Bayes estimators for various squared error loss functions. We also computed the highest posterior density (HPD) credible ranges for the model parameters. Monte Carlo simulations were used to compare the outcomes of the various estimation methods proposed. Finally, one data set was analyzed for validation purposes.Item Load-Sharing Model under Lindley Distribution and Its Parameter Estimation Using the Expectation-Maximization Algorithm(2020-11-22) Park, Chanseok; Wang, Min; Alotaibi, Refah Mohammed; Rezk, HodaA load-sharing system is defined as a parallel system whose load will be redistributed to its surviving components as each of the components fails in the system. Our focus is on making statistical inference of the parameters associated with the lifetime distribution of each component in the system. In this paper, we introduce a methodology which integrates the conventional procedure under the assumption of the load-sharing system being made up of fundamental hypothetical latent random variables. We then develop an expectation maximization algorithm for performing the maximum likelihood estimation of the system with Lindley-distributed component lifetimes. We adopt several standard simulation techniques to compare the performance of the proposed methodology with the Newton–Raphson-type algorithm for the maximum likelihood estimate of the parameter. Numerical results indicate that the proposed method is more effective by consistently reaching a global maximum.