Estimation Of Stress-strength Reliability Research Articles

Stress–strength reliability estimation of s-out-of-k multicomponent systems based on copula function for dependent strength elements under progressively censored sample

The main objective of this research is to determine the reliability of multicomponent stress–strength under progressive Type II censoring. The model comprises k independent strength components, and each component has two elements that are statistically dependent and exposed to the same random stress. To assess the correlation between their elements, we are utilizing the Gumbel copula and assuming that its parameter is unknown. The system is deemed operational only if at least certain number of strength variables s ( 1 ≤ s ≤ k ) surpass the random stress. We are using the Chen distribution to model the stress and strength variables, with varying shape parameters. Different methods are employed to estimate the unknown parameters, including maximum likelihood, maximum product of spacings, Cramér–von-Mises, and bootstrap confidence intervals. The effectiveness of these estimation techniques is evaluated through Monte Carlo simulation, and a real data set is analyzed to illustrate our procedures.

Estimation of Stress–Strength Reliability for Power Transformed Perks Distribution with Applications

The power transformation of the Perks distribution, its survival, and hazard functions are computed. The shapes of hazard function are obtained analytically which shows that this model has increasing and decreasing hazard rates. In the stress–strength reliability estimation, point and interval estimates are computed using maximum likelihood and asymptotic confidence interval methods, respectively. The performance of the estimates is evaluated through the Monte Carlo simulation and the applications of the proposed distribution to three real datasets have been demonstrated.

Stress–Strength Reliability Estimation for Gamma Distributions in a Noisy System

When assessing the reliability of a system or the viability of a material, it is necessary to consider the stress conditions of the operating system. Let X be the strength of the system and Y be the stress of the system caused by the environment. In a stress–strength model, the system’s reliability is defined as [Formula: see text], and due to ignoring environmental shocks or human failure, it is usually overestimated. To underestimate reliability, we assume that when X goes to the environmental conditions, the system’s strength reduces to [Formula: see text], where Z is a random variable on [Formula: see text]. We propose a modified reliability model with [Formula: see text] for the gamma distribution. In this model, stress Y and the scale mixture of the strength of the gamma distribution, [Formula: see text], are modeled as independent random variables. The proposed model is compared with the traditional model through a simulation study. Additionally, the asymptotic distribution is used to construct an asymptotic confidence interval for [Formula: see text]. Finally, we use two real datasets to demonstrate the practical applicability of our proposed method.

On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

On Estimation of Stress-Strength Reliability with Zero-Inflated Poisson Distribution

Stress-strength reliability estimation of multicomponent system with non-identical strength components from inverse Pareto distribution

Stress-strength reliability estimation of multicomponent system with non-identical strength components from inverse Pareto distribution

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.