New generalized-X family: Modeling the reliability engineering applications

As is already known, statistical models are very important for modeling data in applied fields, particularly in engineering, medicine, and many other disciplines. In this paper, we propose a new family to introduce new distributions suitable for modeling reliability engineering data. We called our proposed family a new generalized-X family of distributions. For the practical illustration, we introduced a new special sub-model, called the new generalized-Weibull distribution, to describe the new family’s significance. For the proposed family, we introduced some mathematical reliability properties. The maximum likelihood estimators for the parameters of the new generalized-X distributions are derived. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. To assess the efficiency of the proposed model, the new generalized-Weibull model is applied to the coating machine failure time data. Finally, Bayesian analysis and performance of Gibbs sampling for the coating machine failure time data are also carried out. Furthermore, the measures such as Gelman-Rubin, Geweke and Raftery-Lewis are used to track algorithm convergence.

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On a New Modification of the Weibull Model with Classical and Bayesian Analysis

Complexity ◽

10.1155/2021/5574112 ◽

2021 ◽

Vol 2021 ◽

pp. 1-19

Author(s):

Yen Liang Tung ◽

Zubair Ahmad ◽

Omid Kharazmi ◽

Clement Boateng Ampadu ◽

E.H. Hafez ◽

...

Keyword(s):

Bayesian Analysis ◽

Real Life ◽

Weibull Model ◽

Vital Role ◽

Model Parameters ◽

Reliability Engineering ◽

Monte Carlo Simulation Study ◽

New Class ◽

Failure Times ◽

And Performance

Modelling data in applied areas particularly in reliability engineering is a prominent research topic. Statistical models play a vital role in modelling reliability data and are useful for further decision-making policies. In this paper, we study a new class of distributions with one additional shape parameter, called a new generalized exponential-X family. Some of its properties are taken into account. The maximum likelihood approach is adopted to obtain the estimates of the model parameters. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. The usefulness of the proposed family is demonstrated by means of a real-life application representing the failure times of electronic components. The fitted results show that the new generalized exponential-X family provides a close fit to data. Finally, considering the failure times data, the Bayesian analysis and performance of Gibbs sampling are discussed. The diagnostics measures such as the Raftery–Lewis, Geweke, and Gelman–Rubin are applied to check the convergence of the algorithm.

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Correlation analysis of software failure time data

Journal of Computer Applications ◽

10.3724/sp.j.1087.2010.00600 ◽

2010 ◽

Vol 30 (3) ◽

pp. 600-602

Author(s):

Jun-gang LOU ◽

Jian-hui JIANG

Keyword(s):

Correlation Analysis ◽

Failure Time ◽

Failure Time Data ◽

Time Data ◽

Software Failure

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A unified approach to variable selection for Cox’s proportional hazards model with interval-censored failure time data

Statistical Methods in Medical Research ◽

10.1177/09622802211009259 ◽

2021 ◽

pp. 096228022110092

Author(s):

Mingyue Du ◽

Hui Zhao ◽

Jianguo Sun

Keyword(s):

Variable Selection ◽

Proportional Hazards ◽

Proportional Hazards Model ◽

Failure Time ◽

Significant Feature ◽

Failure Time Data ◽

Time Data ◽

Hazards Model ◽

Interval Censored ◽

Cox's Proportional Hazards Model

Cox’s proportional hazards model is the most commonly used model for regression analysis of failure time data and some methods have been developed for its variable selection under different situations. In this paper, we consider a general type of failure time data, case K interval-censored data, that include all of other types discussed as special cases, and propose a unified penalized variable selection procedure. In addition to its generality, another significant feature of the proposed approach is that unlike all of the existing variable selection methods for failure time data, the proposed approach allows dependent censoring, which can occur quite often and could lead to biased or misleading conclusions if not taken into account. For the implementation, a coordinate descent algorithm is developed and the oracle property of the proposed method is established. The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Alzheimer’s Disease Neuroimaging Initiative study that motivated this study.

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