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RELIABILITY MODELLING OF HETEROGENEOUS DATA BY USING DIFFERENT COMPETING WEIBULL MIXTURE MODELS
Keywords:
life data analysis, Weibull mixture distribution (WMD), competing risk Weibull mixture distribution (CRWMD), compound competing risk Weibull mixture distribution CCRWMD, maximum likelihood estimation (MLE) method, expectation- maximization (EM) algorithm, goodness of fit (GOF) tests, Kolmogorov-Smirnov (KS), the negative log-likelihood value $K S,-l(\hat{\theta})$ the squared value for the correlation coefficient $r^2$DOI:
https://doi.org/10.17654/0972361724031Abstract
We introduce different Weibull mixture distribution (WMD) models that are used for modelling life data and how to distinguish between them. A proposed method is introduced for modelling survival data by Weibull mixture models. A case study has been executed on a sample that includes both ordered exact times-to-failure and censoring (suspensions). The methodology was carried out through expectation-maximization (EM) algorithm to obtain maximum likelihood estimation (MLE) of parameters for each model. Also, confidence intervals of the estimates of the parameters at the confidence level 95% are determined. The motivation of this study is to prove that the 3-fold WMD model is more appropriate than other competing WMD models for modelling heterogeneous censored data sets that include exact failures and suspensions. This paper also addresses the behavior of cumulative distribution functions (CDFs) for different WMD models. A comparison of the fitted CDFs with the empirical distribution and the B10 life is obtained for these WMD models. The goodness of fit tests such as $K S,-l(\hat{\theta})$ and $r^2$ are implemented for the WMD models to show the best one can fit survival data. From a mathematical statistics point of view, we found that modelling multimodal lifetime data under consideration with 3-fold WMD is the best choice.
Received: December 12, 2023
Revised: February 21, 2024
Accepted: March 1, 2024
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