Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints

Luo, Chunling; Shen, Lijuan; Xu, Ancha

doi:10.1016/j.ress.2021.108136

Cited by 92 publications

(53 citation statements)

References 41 publications

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“…For more details, one may refer to [32]. Many authors have used Bayesian estimation for different lifetime models with many real data applications (see, for example, [33][34][35]).…”

Section: Bayesian Estimationmentioning

confidence: 99%

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Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

Ahmad

Almetwally

2022

Symmetry

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This paper studies three discretization methods to formulate discrete analogues of the well-known continuous generalized Pareto distribution. The generalized Pareto distribution provides a wide variety of probability spaces, which support threshold exceedances, and hence, it is suitable for modeling many failure time issues. Bayesian inference is applied to estimate the discrete models with different symmetric and asymmetric loss functions. The symmetric loss function being used is the squared error loss function, while the two asymmetric loss functions are the linear exponential and general entropy loss functions. A detailed simulation analysis was performed to compare the performance of the Bayesian estimation using the proposed loss functions. In addition, the applicability of the optimal discrete generalized Pareto distribution was compared with other discrete distributions. The comparison was based on different goodness-of-fit criteria. The results of the study reveal that the discretized generalized Pareto distribution is quite an attractive alternative to other discrete competitive distributions.

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“…For more details, one may refer to [32]. Many authors have used Bayesian estimation for different lifetime models with many real data applications (see, for example, [33][34][35]).…”

Section: Bayesian Estimationmentioning

confidence: 99%

“…These data comprise daily new deaths. The data are as follows: 52, 26, 36, 63, 52, 37,35,28,17,21,31,30,10,56,40,14,28,42,24,21,28,22,12,31,24,14,13,25,12,7,13,20,23,9,11,13,3,7,10,21,15,17,5,7,22,24,15,19,18,16,5,20,27. The data are available on the Worldometer website at [36].…”

Section: Real Data Examplesmentioning

confidence: 99%

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

Ahmad

Almetwally

2022

Symmetry

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“…For more details about the reliability characteristics estimations, one may refer to [26][27][28][29].…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Complexity Analysis of E-Bayesian Estimation under Type-II Censoring with Application to Organ Transplant Blood Data

2022

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The E-Bayesian estimation approach has been presented for estimating the parameter and/or reliability characteristics of various models. Several investigations in the literature have considered this method under the assumption that just one parameter is unknown. So, based on Type-II censoring, this study proposes for the first time an effort to use the E-Bayesian estimation approach to estimate the full model parameters as well as certain related functions such as the reliability and hazard rate functions. To illustrate this purpose, we apply the proposed technique to the two-parameter generalized inverted exponential distribution which can be considered to be one of the most flexible asymmetrical probability distributions. Moreover, the E-Bayesian method, maximum likelihood, and Bayesian estimation approaches are also considered for comparison purposes. Under the assumption of independent gamma priors, the Bayes and E-Bayes estimators are developed using the symmetrical squared error loss function. Due to the complex form of the joint posterior density, two approximation techniques, namely the Lindley and Markov chain Monte Carlo methods, are considered to carry out the Bayes and E-Bayes estimates and also to construct the associate credible intervals. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To demonstrate the applicability of the proposed methods in real phenomenon, one real data set is analyzed and it shows that the proposed method is effective and easy to operate in a real-life scenario.

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“…In some situations, independent failure might be an optimal design choice to prevent the system from ever shutting down. The competing risks model and its properties were discussed recently by [12][13][14]. Therefore, in this paper, we study an independent latent failure time model [15] assuming the Burr XII distribution.…”

Section: Introductionmentioning

confidence: 99%

Burr XII Distribution for Disease Data Analysis in the Presence of a Partially Observed Failure Mode

et al. 2022

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Modeling competing failure modes is an important problem in engineering and survival analyses. Competing failure modes are partially observed in many applications and often pose a modeling challenge. This study discusses the inference for partially observed failure modes assuming a Burr XII distribution. In particular, we consider two failure modes, and the failure time data are collected under a hybrid type I censoring scheme. The model parameters are estimated using maximum likelihood and Bayesian methods under a symmetric squared error loss function, whereas the intervals estimation is done with three methods: asymptotic and credible confidence intervals. Besides a simulation study, a real-life data set is taken from individuals who live in an environment with several diseases to present the utility of the work. Additionally, a simulation study is constructed to measure and compare different estimation methods.

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Modelling and estimation of system reliability under dynamic operating environments and lifetime ordering constraints

Cited by 92 publications

References 41 publications

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

Complexity Analysis of E-Bayesian Estimation under Type-II Censoring with Application to Organ Transplant Blood Data

Burr XII Distribution for Disease Data Analysis in the Presence of a Partially Observed Failure Mode

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