Estimation Of Stress-strength Reliability Research Articles

Estimation of stress-strength reliability in s-out-of-k system for new flexible exponential distribution under progressive type-II censoring

This article addresses stress-strength reliability estimation in s-out-of-k systems under progressive type-II censoring. The system consists of components facing common stress, where stress and strength variable follows independent new flexible exponential (NFE) distributions, sharing a common parameter. The estimation procedure is carried out using MLE, Bayesian estimation and uniformly minimum variance unbiased estimation (UMVUE) techniques. MLE is derived for known and unknown common parameters. Bayesian estimates are obtained using Lindley’s approximation and Markov chain Monte Carlo techniques due to the complexity of obtaining the exact Bayesian estimates, when the common parameter is unknown. Moreover, UMVUE is derived when the common parameter is known. The 95% asymptotic confidence interval, highest posterior density credible intervals, and Bayesian credible intervals, are constructed. An extensive simulation study is carried out to compare the performance of various censoring schemes and estimation methods. Finally, two progressively censored real datasets are analyzed for illustration.

Phase-type stress-strength reliability models under progressive type-II right censoring

. The study of stress-strength reliability estimation based on phase-type distribution helps to gather results on estimation of stress-strength reliability with any probability distribution that is defined on the non negative real numbers as any discrete or continuous probability distributions on the positive real line can be represented as phase-type. The matrix representation of the parameters of phase-type distributions helps in their flexible evaluation and easy manipulation. Also in many of the experimental studies, it is very convenient and useful to apply progressive type-II right censoring mechanism in the process of data collection. In this article, we consider the estimation of stress-strength reliability (R) based on phase-type distribution under progressive type-II right censoring mechanism. Both stress and strength random variables are assumed to follow either continuous phase-type or discrete phase-type distribution. We have developed the algorithm for computing Maximum likelihood estimate (MLE) of R based on the expectation maximization (EM) method and the Bayes estimate of R using Markov Chain Monte Carlo technique. A detailed numerical illustration using simulated data/ real data sets are carried out.

On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data.

The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed.

Estimation of the stress-strength parameter under two-sample balanced progressive censoring scheme

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples.

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

In this study, the stress-strength reliability, $R=P(Y

Stress-Strength Reliability Estimation of a Series System with Cold Standby Redundancy Based on Kumaraswamy Half-Logistic Distribution

This paper deals with study and estimation of stress-strength reliability for a system where strength and stress components are connected in series with cold standby redundancy at system level. It is supposed that the random stress and strength both follow Kumaraswamy half-logistic distribution. In this redundant system, we consider that there N subsystems and in each subsystem, there are M statistically independent strength components under the impact of M statistically independent stress components The problem of estimation is solved in two cases. First under the assumption that random stress and strength have common first shape parameter and different second shape parameter and second with the assumption that common shape parameter is known. The stress-strength reliability is estimated using maximum likelihood and Bayesian estimation methods. Also asymptotic and Bayesian intervals for the stress-strength reliability under both the cases are constructed. Monte Carlo simulations will be performed to compare the performance of various methods. Finally a real life data set is analyzed to demonstrate the findings.

Estimation of $Pr(X&lt;Y)$ for exponential power records

In this study, we tackle the problem of estimation of stress-strength reliability $R = P r(X &amp;lt; Y )$ based on upper record values for exponential power distribution. We use the maximum likelihood and Bayes methods to estimate R. The Tierney-Kadane approximation is used to compute the Bayes estimation of R since the Bayes estimator can not be obtained analytically. We also derive asymptotic confidence interval based on the asymptotic distribution of the maximum likelihood estimator of R. We consider a Monte Carlo simulation study in order to compare the performances of the maximum likelihood estimators and Bayes estimators according to mean square error criteria. Finally, a real data application is presented.

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

AbstractIn 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.

Stress-strength reliability estimation for bivariate copula function with rayleigh marginals

Stress-strength reliability estimation for bivariate copula function with rayleigh marginals

Shrinkage estimation of stress strength reliability P (Y❮X❮Z) for lomax distribution based on records

The present paper deals with the Shrinkage Estimation of stress strength reliability model R=P[Y❮X❮Z] Where X is the random strength and Y and Z are independent random stress variables follows Lomax Distribution based on record values. In this paper we obtain the shrinkage estimation of R based on record values using Classical and Bayesian Estimation method when the scale parameter ݜ† which is common for all the distribution is known. We illustrated the performance of the estimators using simulation study.

Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data.

This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are constructed respectively, and then the generalized point and interval estimates for SSR are proposed in consequence, where the associated Monte-Carlo sampling approach is provided for computation. In addition, when strength and stress variables feature unequal model parameters, different generalized point and confidence interval estimates are also established in this regard. Extensive simulation studies are conducted to examine the behavior of proposed methods. Finally, a real-life data example is presented for illustration.

Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample

&lt;abstract&gt;&lt;p&gt;In this paper, we investigate classical and Bayesian estimation of stress-strength reliability $\delta = P(X &amp;gt; Y)$ under an adaptive progressive type-Ⅱ censored sample. Assume that $X$ and $Y$ are independent random variables that follow inverse Weibull distribution with the same shape but different scale parameters. In classical estimation, the maximum likelihood estimator and asymptotic confidence interval are deduced. An approximate maximum likelihood estimator approach is used to obtain the explicit form. In Bayesian estimation, the Bayesian estimators are derived based on symmetric entropy loss function and LINEX loss function. Due to the complexity of integrals, we proposed Lindley's approximation to get the approximate Bayesian estimates. To compare the different estimators, we performed Monte Carlo simulations. Under gamma prior, the approximate maximum likelihood estimator performs better than Bayesian estimators. Under non-informative prior, the approximate maximum likelihood estimator has the same behavior as Bayesian estimators. In the end, two data sets are used to prove the effectiveness of the proposed methods.&lt;/p&gt;&lt;/abstract&gt;

Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

&lt;abstract&gt; &lt;p&gt;In this paper, we studied the estimation of a stress-strength reliability model ($R = P(X&amp;gt;Y)$) based on inverted exponentiated Rayleigh distribution under the unified progressive hybrid censoring scheme (unified PHCS). The maximum likelihood estimates of the unknown parameters were obtained using the stochastic expectation-maximization algorithm (stochastic EMA). The asymptotic confidence intervals were also created. Under squared error and Linex and generalized entropy loss functions, the Gibbs sampler together with Metropolis-Hastings algorithm was provided to compute the Bayes estimates and the credible intervals. Extensive simulations were performed to see the effectiveness of the proposed estimation methods. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, droplet splashing data under two nozzle pressures were proposed to exemplify the theoretical outcomes.&lt;/p&gt; &lt;/abstract&gt;

Estimation of stress-strength reliability for multicomponent system with a generalized inverted exponential distribution

Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results.

Non-Bayesian and Bayesian estimation of stress-strength reliability from Topp-Leone distribution under progressive first-failure censoring

ABSTRACT In this paper, the Bayesian and non-Bayesian estimation of based on the progressively first-failure censored data is considered. The and are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley’s approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes.

Estimating reliability parameters for inverse Gaussian distributions under complete and progressively type-II censored samples

ABSTRACT In this paper, we study estimation of stress-strength reliability, assuming the stress and strength variables are inverse Gaussian distributed with unknown parameters. When the coefficient of variations of the distributions is unknown but equal, we develop MLE, Bayes estimator, bootstrap interval of the reliability. The profile likelihood Bayes estimator of the coefficient of variation is also derived. When all parameters are different, we derive the MLE, UMVUE, Bayes estimator, bootstrap interval, and highest posterior density credible interval of the stress-strength reliability. The predictive Bayes estimators of the reliability functions are derived. Under progressive type-II censoring, we derive the MLE, Bayes estimator and bootstrap confidence interval. Monte-Carlo simulation results and real data-based examples are also presented. We analyze lung cancer and air pollution data sets as applications of the stress-strength model.

Multicomponent Stress-Strength Reliability estimation based on Unit Generalized Exponential Distribution

Estimation of stress-strength reliability is considered based on frequentist and Bayesian methods of estimation when both stress and strength variables follow unit generalized exponential distributions. In frequentist method we consider maximum likelihood, least squares, weighted least squares and maximum product spacing methods to estimate system reliability when a common scale parameter is unknown. Further asymptotic and bootstrap intervals of system reliability are obtained. Next, we discuss Bayesian procedure under different loss functions using gamma and weighted Lindley priors for model parameters to estimate system reliability. Subsequently, highest posterior density credible intervals are also obtained. Besides, uniformly minimum variance unbiased estimator of system reliability is obtained when the common scale parameter is known. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of proposed estimates with respect to various criteria. Finally, to show the applicability of the proposed methodologies in a real-life scenario, an engineering data set is analyzed.

Estimation of stress-strength reliability for poisson-exponential distribution under progressive type II censoring

Estimation of stress-strength reliability for poisson-exponential distribution under progressive type II censoring

A Copula Based Stress-Strength Reliability Estimation with Lindley Marginals

The stress-strength model is a basic tool used in evaluating the reliability (R). It shows that a component or system with stress (Y) and strength (X) will fail if the stress exceeds the strength, and its counterpart allows it to function. Usually, the statistical independence between X and Y are assumed and reliability models are extensively developed in the literature. However, in real life, there are many situations in which the dependence stress-strength is taken into account. So it is important to consider and model the association between them. In this paper, we estimated R when the stress and strength parameters are linked by a Fralie-Gumble-Morgenstern copula with Lindley marginals. The estimates of reliability and dependence parameter are obtained by using maximum likelihood estimation (MLE), inference function margins (IFM), and semi parametric (SP) methods. In addition, the length of the asymptotic confidence interval and the coverage probability of the dependence parameter are also computed. A simulation study is performed to evaluate the effectiveness of the various estimates, and a real data set is also used for illustrative purposes.

Estimation of stress-strength reliability for Dagum distribution based on progressive type-II censored sample

In this paper, classical as well as Bayesian estimation of stress strength reliability (η) of Dagum distribution under progressive type-II censored sample is done. Maximum likelihood estimators (MLEs) of η are also obtained along with asymptotic, bootstrap-p (boot-p) and bootstrap-t (boot-t) confidence intervals. Bayes estimators of η along with highest posterior density (HPD) credible intervals based on informative and non-informative priors are also obtained. Symmetric as well as asymmetric loss functions are considered for the Bayesian estimation. Monte Carlo simulation study is carried out to check the performance of estimators. Real life data sets are considered for illustration purpose.