Classical and Bayesian Estimation of the Inverse Weibull Distribution: Using Progressive Type-I Censoring Scheme

Ali Algarni,Aisha Fayomi,Mohammed Elgarhy,Abdullah M Almarashi,Ahmed R El-Saeed,Afaq Ahmad

doi:10.1155/2021/5701529

Ali Algarni, Aisha Fayomi + Show 4 more

Open Access

https://doi.org/10.1155/2021/5701529

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Abstract

The challenge of estimating the parameters for the inverse Weibull (IW) distribution employing progressive censoring Type-I (PCTI) will be addressed in this study using Bayesian and non-Bayesian procedures. To address the issue of censoring time selection, qauntiles from the IW lifetime distribution will be implemented as censoring time points for PCTI. Focusing on the censoring schemes, maximum likelihood estimators (MLEs) and asymptotic confidence intervals (ACI) for unknown parameters are constructed. Under the squared error (SEr) loss function, Bayes estimates (BEs) and concomitant maximum posterior density credible interval estimations are also produced. The BEs are assessed using two methods: Lindley’s approximation (LiA) technique and the Metropolis-Hasting (MH) algorithm utilizing Markov Chain Monte Carlo (MCMC). The theoretical implications of MLEs and BEs for specified schemes of PCTI samples are shown via a simulation study to compare the performance of the different suggested estimators. Finally, application of two real data sets will be employed.

Highlights

Keller and Kamath [1] were the ones to propose the inverse Weibull (IW) model as a sustainable idea for describing the deterioration of structural devices in diesel engines. e IW distribution gives an excellent match to various real data sets, according to [2]
In the perspective of a mechanical system’s load-strength relationship, Calabria and Pulcini [3] gave an essential explanation of this distribution. e IW distribution, which was created to explain failures of structural devices influenced by degradation phenomena, plays a critical part in reliability engineering and lifetime testing
To assess the quality of fit, we provide the maximum likelihood estimators (MLEs) of the parameters as well as the value of the Kolmogorov–Smirnov (KS) test statistic. e estimated KS and p-value for the IW distribution are 0.116 1 and 0.749 6, respectively, where c􏽢 0.8431 and λ􏽢 0.7121, which indicate that this distribution can be considered as an adequate model for the given data set

Summary

Introduction

Keller and Kamath [1] were the ones to propose the IW model as a sustainable idea for describing the deterioration of structural devices in diesel engines. e IW distribution gives an excellent match to various real data sets, according to [2]. E IW distribution, which was created to explain failures of structural devices influenced by degradation phenomena, plays a critical part in reliability engineering and lifetime testing. It has been looked into from a variety of angles. Censored data arises in real-life testing trials when the experiments, which include the lifetime of test units, must be stopped before acquiring complete observation. E first one was the MLEs and ACI estimates for the unknown parameters of the generalized IE model under the idea that there are two types of failures [16]. E purpose of this paper is to look at the PCTI scheme when the lifetimes have their own IW model.

Estimation Using Method of Maximum Likelihood

Bayesian Estimation

Simulation Study and Real Data Application

Summary and Conclusion