A comparative inference on reliability estimation for a multi-component stress-strength model under power Lomax distribution with applications

Abstract

<abstract><p>In this article, reliability estimation for a system of multi-component stress-strength model is considered. Working under progressively censored samples is of great advantage over complete and usual censoring samples, therefore Type-II right progressive censored sample is selected. The lifetime of the components and the stress and strength components are following the power Lomax distribution. Consequently, the problem of point and interval estimation has been studied from different points of view. The maximum likelihood estimate and the maximum product spacing of reliability are evaluated. Also approximate confidence intervals are constructed using the Fisher information matrix. For the traditional methods, bootstrap confidence intervals are calculated. Bayesian estimation is obtained under the squared error and linear-exponential loss functions, where the numerical techniques such as Newton-Raphson and the Markov Chain Monte Carlo algorithm are implemented. For dependability, the largest posterior density credible intervals are generated. Simulations are used to compare the results of the proposed estimation methods, where it shows that the Bayesian estimation method of the reliability function is significantly better than the other methods. Finally, a real data of the water capacity of the Shasta reservoir is examined for illustration.</p></abstract>

Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling

“…Using the prior (17) and the likelihood function (11), the joint posterior density can be expressed as…”

“…For more examples, see [11][12][13][14][15]. Different papers discussed inference on reliability estimation for a multi-component stress-strength model as [16,17] and Almetwally et al [18] discussed P(X < Y < Z) for the alpha power exponential model using progressive first failure. For a comprehensive review of studies of the stress-strength modeling, see Kotz et al [19].…”

Statistical inference for multi stress–strength reliability based on progressive first failure with lifetime inverse Lomax distribution and analysis of transformer insulation data

“…Despite the fact that Bhattacharyya and Johnson 16 developed the multicomponent stress-strength model, it has garnered a lot of attention in recent years and has been explored by numerous researchers for both complete and censored data. Some of the recently appeared articles include Tolba et al, 17 Ramadan et al, 18 Kotb and Raqab, 19 Maurya and Tripathi, 20 Mahto et al, 21 Wang et al, 22 Jha et al, 23 El-Sagheer et al, 24 Rasekhi et al, 25 Alotaibi et al, 26 Maurya et al, 27 Sarhan et al, 28 Sarhan et al, 29 Kohansal and Shoaee, 30 Muse et al, 31 Jana and Bera, 32 Ahmad et al, 33 Ahmad et al 34 , Ramadan 35 and Wu and Kuş. 36 Well-known censoring techniques include the type-II censoring scheme, progressive type-II censoring scheme, and progressive first failure censoring system.…”

X-Gamma Lomax Distribution with Different Applications

“…Rayleigh Lomax distribution was first introduced by Fatima et al (2018). The chances exponential-Pareto IV distribution was first presented by Baharith et al (2020), power Lomax distribution with applications has been discussed by Ahmad et al (2022), Maxwell-Lomax distribution has been introduced by Abiodun and Ishaq (2022), and extended odd Weibull Lomax has been obtained by Alsuhabi et al (2022. The Lomax (Lo) distribution has received some attention in more literature it can be used in the (1.2)…”