Estimation of stress-strength reliability using discrete phase type distribution

Jose, Joby K.; Drisya, M.; Manoharan, M.

doi:10.1080/03610926.2020.1749663

Cited by 22 publications

(4 citation statements)

References 30 publications

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“…In medical studies, P(Y < X) can be used as a measure of treatment effectiveness when X and Y are the responses for control and treatment groups, respectively. See Joby et al 2 In economics, P(Y < X) is used as a measure of household financial affordability if X and Y are disposable household income and consumption, respectively. More applications of SSR can be found in Domma and Giordano.…”

Section: Introductionmentioning

confidence: 99%

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Shi

2023

Quality & Reliability Eng

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In this paper, we investigate classical and Bayes estimates for stress-strength reliability (SSR) based on two independent progressive first failure censored samples from beta log Weibull distributions with different shape and scale parameters.The maximum likelihood estimation of SSR and its asymptotic confidence interval are obtained. Bayes estimates of SSR are derived under two different loss functions using the Tierney-Kadane's approximation algorithm. In addition, two different bootstrap confidence intervals are provided and the highest posterior density credible interval of SSR is also constructed by applying Monte Carlo Markov chain method. The performances of different point and interval estimates are assessed using the Monte Carlo simulation. Finally, three real data sets are analyzed for illustration purposes.

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Section: Introductionmentioning

confidence: 99%

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Shi

2023

Quality & Reliability Eng

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“…In addition, it has recently been used in discrete distributions, such as geometric-Poison [31], geometric-exponential [21] and phase-type [20] distributions. Generalized Gompertz (GG) distribution, which was put forward by [15], can be used in many areas ranging from the comparison of the mortality rate of different populations to growth models and actuarial studies.…”

Section: Introductionmentioning

confidence: 99%

Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring

ÇİFTCİ

Saraçoğlu

Akdam

et al. 2023

Hacettepe Journal of Mathematics and Statistics

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In this study, the stress-strength reliability, R = P(Y < X) where Y represents the stress of a component and X represents this component’s strength, is obtained when X and Y have two independents generalized Gompertz distribution with different shape parameters under progressive type-II censoring. The Bayes and maximum likelihood estimators of stress-strength reliability can not be acquired in closed forms. The approximate Bayes estimators under squared error loss function by using Lindley’s approximations for stressstrength reliability are derived. A Monte Carlo simulation study is done to check performances of the approximate Bayes against performances of maximum likelihood estimators and observe the coverage probabilities and the intervals’ average width. In addition, the coverage probabilities of the parametric bootstrap estimates are calculated. Two applications based on real datasets are provided.

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“…Most components and systems degrade over time and fail when the degradation level reaches or exceeds the critical level, called a threshold. Many approaches have been widely utilized to assess the reliability of structures or systems, such as the reliability index methods [1,2], stress-strength methods [3][4][5], etc. For high-quality products, failure data are difficult to obtain within a short period of time, even if accelerated lifetime testing is conducted.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis with Wiener-Transmuted Truncated Normal Degradation Model for Linear and Non-Negative Degradation Data

Muhammad

Wang

et al. 2022

Symmetry

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The degradation rates of many engineering systems are always positive in practical applications. In some cases, the degradation process is approximately linear, such as train wheel wear degradation and an increase in the operating current of laser devices. In this paper we introduce a degradation modeling and reliability estimation method based on the Wiener process with a transmuted-truncated normal distribution (TTND). The TTND is employed to characterize unit-to-unit variability due to its flexibility in capturing symmetry and the asymmetrical behavior of the drift variable of the Wiener process. A Wiener process with TTND is applied to model the degradation processes of the deteriorating systems in two cases. In the first case, we assume that the degradation process is unaffected by measurement uncertainties, whereas in the second case, the measurement uncertainties are considered. The exact and explicit expressions of PDFs and the reliability functions are derived based on the concept of first hitting time. The Gibbs sampling technique and the Metropolis–Hastings algorithm are employed to obtain the Bayesian estimates of the model’s parameters. The efficiency and the feasibility of the presented approach are demonstrated through numerical examples, with Monte Carlo simulation and a practical application with laser degradation data. Furthermore, deviance information criteria (DIC) are used to compare the proposed model and some existing models. The result indicated that the proposed approach provided better reliability estimation results.

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Estimation of stress-strength reliability using discrete phase type distribution

Cited by 22 publications

References 30 publications

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Estimation of stress‐strength reliability for beta log Weibull distribution using progressive first failure censored samples

Estimation of stress-strength reliability for generalized Gompertz distribution under progressive type-II censoring

Reliability Analysis with Wiener-Transmuted Truncated Normal Degradation Model for Linear and Non-Negative Degradation Data

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