Bayesian approach for the reliability parameter of power Lindley distribution

Makhdoom, Iman; Nasiri, Parviz; Pak, Abbas

doi:10.1007/s13198-016-0476-5

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…Abd Elfattah and Marwa (2011) considered Bayesian estimation of stress-strength exponential model by using different loss functions. Makhdoom et al (2016) derived Bayesian estimates of the reliability in stress-strength models with power Lindley components. Akgul and Senoglu (2017) have used ranked set sampling to derive Weibull sress-strength parameter.…”

Section: Bshmentioning

confidence: 99%

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Pak

Khoolenjani

Rastogi

2019

Pak.j.stat.oper.res.

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In the literature, there are a well-developed estimation techniques for the reliability assessment in multicomponent stress-strength models when the information about all the experimental units are available. However, in real applications, only observations that exceed (or fall below) the current value may be recorded. In this paper, assuming that the components of the system follow bathtub-shaped distribution, we investigate Bayesian estimation of the reliability of a multicomponent stress-strength system when the available data are reported in terms of record values. Considering squared error, linex and entropy loss functions, various Bayes estimates of the reliability are derived. Because there are not closed forms for the Bayes estimates, we will use Lindleyâ€™s method to calculate the approximate Bayes estimates. Further, for comparison purposes, the maximum likelihood estimate of the reliability parameter is obtained. Finally, simulation studies are conducted in order to evaluate the performances of the proposed procedures and analysis of real data sets is provided.

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Section: Bshmentioning

confidence: 99%

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Pak

Khoolenjani

Rastogi

2019

Pak.j.stat.oper.res.

Self Cite

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“…[ 8 ] derived a point and interval estimation of θ using maximum likelihood, parametric and nonparametric bootstrap methods when X and Y are independent power Lindley random variables. [ 9 ] extended the work of [ 8 ] and developed a Bayesian inference on θ . In addition, [ 10 ] derived asymptotic confidence intervals for θ when X and Y are two independent generalized Pareto random variables with the same scale parameter.…”

Section: Introductionmentioning

confidence: 99%

Inference on P(X < Y) in Bivariate Lomax model based on progressive type II censoring

Helu

Samawi

2022

PLoS ONE

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This article considers the estimation of the stress-strength reliability parameter, θ = P(X < Y), when both the stress (X) and the strength (Y) are dependent random variables from a Bivariate Lomax distribution based on a progressive type II censored sample. The maximum likelihood, the method of moments and the Bayes estimators are all derived. Bayesian estimators are obtained for both symmetric and asymmetric loss functions, via squared error and Linex loss functions, respectively. Since there is no closed form for the Bayes estimators, Lindley’s approximation is utilized to derive the Bayes estimators under these loss functions. An extensive simulation study is conducted to gauge the performance of the proposed estimators based on three criteria, namely, relative bias, mean squared error, and Pitman nearness probability. A real data application is provided to illustrate the performance of our proposed estimators through bootstrap analysis.

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“…In Ref. [2], a Bayesian estimation method for stress-strength models with power Lindley components was derived, and the Markov Chain Monte-Carlo method was used for the implementation of the posterior mean method. Akgul and Senoglu [3] used a Weibull distribution to represent the stress and strength under three types of ranked set sampling.…”

Section: Introductionmentioning

confidence: 99%

A Parameter Estimation Method for Stress- Strength Model Based on Extending Markov State-Space With Variable Transition Rates

Wang

Zhang

et al. 2020

IEEE Access

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A stress-strength model usually has more than one failure mode since the component suffers at least two types of stresses, complicating the expression of the likelihood function and increasing the computational complexity of the parameter estimation for general distributions (non-exponential distributions). A phase-type distribution (also known as a PH distribution) is dense and has closure properties, which makes it suitable to reduce the computational complexity of the stress-strength model. The traditional expectation-maximization (EM) method for estimating the parameters of the PH distribution cannot be used directly when the strength changes over time since the PH distribution is a continuous-time Markov process that must satisfy the relevant properties of the infinitesimal generator in the Markov statespace. Therefore, a parameter estimation method based on extending the Markov state-space with variable transition rates for the stress-strength model is proposed. Both failure and censored samples are considered. First, the stress-strength model based on the PH distribution is briefly introduced, and the likelihood functions for different failure modes are derived. Subsequently, the principle of the method is described in detail, the derivation process of the relevant equations is provided, and the limitations of the method are discussed. The performance of the method is evaluated using two simulation cases.

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Bayesian approach for the reliability parameter of power Lindley distribution

Cited by 6 publications

References 14 publications

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Bayesian inference on reliability in a multicomponent stress-strength bathtub-shaped model based on record values

Inference on P(X < Y) in Bivariate Lomax model based on progressive type II censoring

A Parameter Estimation Method for Stress- Strength Model Based on Extending Markov State-Space With Variable Transition Rates

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