Estimation Of Stress-strength Reliability Research Articles

Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times

The estimation of stress-strength reliability in a time-dependent context deals with either the stress or strength or both dynamic. The repeated occurrence of stress in random intervals of time induces a change in the distribution of strength over time. In this paper, we study the stress-strength reliability of a system whose strength reduces by a constant over each run and the stress is considered as either fixed over time or as increasing by a constant over each run. The number of runs in any interval of time is assumed to be random. The stress-strength reliability of the system is obtained, assuming continuous phase-type distribution for the duration of time taken for completion of each run in any interval of time and Weibull or gamma distribution for initial stress and strength. We obtain matrix-based expressions for the stress-strength reliability and numerical illustrations are also discussed.

Stress–strength reliability estimation involving paired observation with ties using bivariate exponentiated half-logistic model

ABSTRACT This paper deals with the problem of maximum likelihood and Bayesian estimation of stress–strength reliability involving paired observation with ties using bivariate exponentiated half-logistic distribution. This problem is of importance because in some real applications the strength of the component is highly dependent on the stress experienced by it. A bivariate extension of exponentiated half-logistic is discussed and an expression for the stress–strength reliability is obtained. This model is also useful to analyse data having the unusual feature of having a number of pairs with tied scores, even when the scores are continuous. The maximum likelihood estimate and interval estimate of the stress–strength reliability has been developed. The Bayes estimates of the stress–strength reliability under squared error loss function are obtained using importance sampling technique. Simulation studies are conducted to evaluate the performance of maximum likelihood and Bayes estimates. Two real-life data sets are analysed to numerically illustrate the usefulness of the developed method.

Comparison of two sampling schemes in estimating the stress-strength reliability under the proportional reversed hazard rate model

In this paper, point and interval estimation of stress-strength reliability based on lower record ranked set sampling scheme under the proportional reversed hazard rate model are considered. Maximum likelihood, uniformly minimum variance unbiased, and Bayesian estimators of $\mathcal{R}$ are derived and their performances are compared. Various confidence intervals for the parameter $\mathcal{R}$ are constructed, and compared based on the simulation study. Moreover, the record ranked set sampling scheme is compared with ordinary records in case of interval estimations. Finally, a data set has been analyzed for illustrative purposes.

Classical and Bayesian estimation of stress-strength reliability of a component having multiple states

PurposeThis article presents the multi-state stress-strength reliability computation of a component having three states namely, working, deteriorating and failed state.Design/methodology/approachThe probabilistic approach is used to obtain the reliability expression by considering the difference between the values of stress and strength of a component, say, for example, the stress (load) and strength of a power generating unit is in terms of megawatt. The range of values taken by the difference variable determines the various states of the component. The method of maximum likelihood and Bayesian estimation is used to obtain the estimators of the parameters and system reliability.FindingsThe maximum likelihood and Bayesian estimates of the reliability approach the actual reliability for increasing sample size.Originality/valueObtained a new expression for the multi-state stress-strength reliability of a component and the findings are positively supported by presenting the general trend of estimated values of reliability approaching the actual value of reliability.

Estimation of stress-strength reliability using discrete phase type distribution

In this paper, the stress-strength reliability of single and multi-component systems are estimated assuming discrete phase type distribution for stress and strength components. The systems with strength following mixture of discrete phase type distributions is also considered. Matrix based expressions are obtained for stress-strength reliability and its maximum likelihood estimate is obtained using EM algorithm. The numerical illustration using various special cases of discrete phase type distribution like geometric, negative binomial, generalized negative binomial and different mixtures of discrete distributions are also carried out.

On Estimation of Stress-Strength Reliability Using Lower Record Values from Proportional Reversed Hazard Family

In this article, a study on the stress-strength parameter based on lower record values from one parameter proportional reversed hazard family (PRHF) has been conducted. The classical and Bayesian results of Khan and Arshad (UMVU Estimation of Reliability Function and Stress-Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records. American Journal of Mathematical and Management Sciences, 35(2), 171–181) and Condino et al. (Likelihood and Bayesian estimation of P(Y < X) using lower record values from a general class of distributions. Statistical Papers), when the strength and stress variables belong to different family of distributions from PRHF have been generalized. Uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and Bayes estimator (BE) are obtained for the powers of the parameter and reliability functions and The estimators of three parametric functions, namely, powers of parameter, and are interrelated, whereas, in the literature, researchers have handled the three estimation problems separately. Moreover, it is has been shown that the expressions for and are not required to estimate them. In this article, the technique of obtaining estimators of and is simpler as it does not require Rao-Blackwellization. Simulation studies have been performed for analyzing the behavior of the proposed estimators. An example using real data has also been considered as an illustration.

Classical and Bayesian Estimation of Stress-Strength Reliability from Generalized Inverted Exponential Distribution based on Upper Records

This paper deals with the problem of classical and Bayesian estimation of stress-strength reliability (R=P(X&lt;Y)) based on upper record values from generalized inverted exponential distribution (GIED). Hassan {et al.} (2018) discussed the maximum likelihood estimator (MLE) and Bayes estimator of $R$ by considering that the scale parameter to be known for defined distribution while we consider the case when all the parameters of GIED are unknown. In the classical approach, we have discussed MLE and uniformly minimum variance estimator (UMVUE). In Bayesian approach, we have considered the Bays estimator of R by considering the squared error loss function. Further, based on upper records, we have considered the Asymptotic confidence interval based on MLE, Bayesian credible interval and bootstrap confidence interval for $R$. Finally, Monte Carlo simulations and real data applications are being carried out for comparing the performances of the estimators of R.

Bayesian Estimation of Stress Strength Reliability using Upper Record Values from Generalised Inverted Exponential Distribution

The paper develops Bayesian estimators and HPD intervals for the stress strength reliability of generalised inverted exponential distribution using upper record values. For prior distribution, informative prior as well as non-informative prior both are considered. The Bayes estimators are obtained under both symmetric and asymmetric loss functions. A simulation study is conducted to obtain the Bayes estimates of stress strength reliability. Simulated data sets are also considered here for illustration purpose.

Stress-strength reliability estimation for exponentially distributed system with common minimum guarantee time

In this article, we study the problem of estimating the stress-strength reliability, where the stress and strength variables follow independent exponential distributions with a common location parameter but different scale parameters. All parameters are assumed to be unknown. We derive the MLE, the UMVUE of the reliability parameter. We also derive the Bayes estimators considering conjugate prior distributions for the scale parameters and a dependent prior for the common location parameter. Monte Carlo simulations have been carried out to compare among the proposed estimators with respect to different loss functions.

Estimation of Stress-Strength Reliability for the Pareto Distribution Based on Upper Record Values

In this paper, the estimation of stress-strength reliability based on upper record values is considered when X and Y are independent random variables having a Pareto distribution with the same scale parameter and with different shape parameters. The maximum likelihood estimator (MLE), the approximate Bayes estimators and the exact confidence interval of the stress-strength reliability are obtained. A Monte Carlo simulation study is conducted to investigate the merits of the proposed methods. A real data analysis is presented for illustrative purpose.

Estimation of Stress-Strength Reliability For Weibull Distribution Based on Type-II Right Censored Ranked Set Sampling Data

In this paper, we consider the estimation of stress-strength reliability  under the type-II right censored data when the distributions of both the stress and the strength are Weibull. First, we discuss the estimation of  based on simple random sampling (SRS). Then, we use the effective and the efficient alternative of SRS which is known to be the ranked set sampling (RSS) to estimate . In the estimation procedure of , we use two different approaches they are i) maximum likelihood (ML) which requires an iterative method and ii) modified maximum likelihood (MML) which has an explicit form. Monte-Carlo simulation study is performed to identify the efficient sampling method (i.e., SRS or RSS) and the efficient estimation method (i.e., ML or MML). Finally, strength and wind speed data sets are analyzed to illustrate the proposed methods in practice.

Estimation of Stress Strength Reliability of Inverse Weibull Distribution under Progressive First Failure Censoring

In this article, estimation of stress-strength reliability $\delta=P\left(Y&lt;X\right)$ based on progressively first failure censored data from two independent inverse Weibull distributions with different shape and scale parameters is studied. Maximum likelihood estimator and asymptotic confidence interval of $\delta$ are obtained. Bayes estimator of $\delta$ under generalized entropy loss function using non-informative and gamma informative priors is derived. Also, highest posterior density credible interval of $\delta$ is constructed. Markov Chain Monte Carlo (MCMC) technique is used for Bayes computation. The performance of various estimation methods are compared by a Monte Carlo simulation study. Finally, a pair of real life data is analyzed to illustrate the proposed methods of estimation.

Estimation of Stress Strength Reliability in s-out-of-k System for a Two Parameter Inverse Chen Distribution

Estimation of Stress Strength Reliability in s-out-of-k System for a Two Parameter Inverse Chen Distribution

Stress–strength reliability estimation under the standard two-sided power distribution

• The stress–strength model based on the two-sided power distribution is considered. • An expression for the stress-strength reliability is obtained exactly. • Methods for estimating of the stress–strength reliability are given. • Comparison of estimation methods are made through simulation studies. • A real data application to see the performances of the estimators is given. In this report, the distribution for setting up a system reliability exposed to some stress is studied. The standard two-sided power distribution is assumed to be the underlying distribution. We obtained the exact expressions and estimates for the reliability by applying different methods such as maximum likelihood and Bayesian estimators. Three different scenarios were examined: known and equal reflection parameters, known but unequal reflection parameters, and all parameters are unknown, providing practical guidance and recommendations for the estimator design. For large samples, we recommend use of the parametric bootstrap method with the maximum likelihood estimate . Real data sets were used to illustrate the performances of the estimators.

Dynamic stress–strength reliability estimation of system with survival signature

ABSTRACTIn this paper, we proposed a dynamic stress–strength model for coherent system. It is supposed that the system consists of n components with initial random strength and each component is subjected to random stresses. The stresses, applied repeatedly at random cycle times, will cause the degradation of strength. In addition, the number of cycles in an interval is assumed to follow a Poisson distribution. In the case of the strength and stress random variables following exponential distributions, the expression for the reliability of the proposed dynamic stress–strength model is derived based on survival signature. The reliability is estimated by using the best linear unbiased estimation (BLUE). Considering the Type-II censored failure times, the best linear unbiased predictors (BLUP) for the unobserved coherent system failure times are developed based on the observed failure times. Monte Carlo simulations are performed to compare the BLUE of parameters with different values and compute the BLUP. A real data set is also analysed for an illustration of the findings.

Classical and Bayesian estimation of stress-strength reliability in type II censored Pareto distributions

ABSTRACTIn this paper, the stress-strength reliability, R, is estimated in type II censored samples from Pareto distributions. The classical inference includes obtaining the maximum likelihood estimator, an exact confidence interval, and the confidence intervals based on Wald and signed log-likelihood ratio statistics. Bayesian inference includes obtaining Bayes estimator, equi-tailed credible interval, and highest posterior density (HPD) interval given both informative and non-informative prior distributions. Bayes estimator of R is obtained using four methods: Lindley's approximation, Tierney-Kadane method, Monte Carlo integration, and MCMC. Also, we compare the proposed methods by simulation study and provide a real example to illustrate them.

Stress-Strength Reliability Estimation for Exponentiated Generalized Inverse Weibull Distribution

Stress-Strength Reliability Estimation for Exponentiated Generalized Inverse Weibull Distribution

Bayesian and Classical Estimation of Stress-Strength Reliability for Inverse Weibull Lifetime Models

In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn’t hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidence interval and two bootstrap intervals are obtained. Using the Gibbs sampling technique, Bayesian estimator and the corresponding credible interval are obtained. The Metropolis-Hastings algorithm is used to generate random variates. Monte Carlo simulations are conducted to compare the proposed methods. Analysis of a real dataset is performed.

Estimation of stress-strength reliability of a parallel system with active, warm and cold standby components

In this paper we estimate the stress–strength reliability of a parallel system with l active components, s warm standby components, and k cold standby components. We assume perfect switching among the components from warm standby mode to active mode and from cold standby mode to warm standby mode. A reduced stress for the warm standby components is introduced and the components may fail in the warm standby mode. The reliability of the parallel system is evaluated by assuming the stress and strength of the components to be independent random variables. We derive the expression of reliability of the system by assuming both the stress and strength of the components having Exponential, Weibull, and Lomax distributions, respectively. The method of maximum likelihood estimation is used to obtain the reliability estimators. Illustrations are provided through an example using MATLAB programming.

Estimation of stress-strength reliability for Kumaraswamy exponential distribution based on upper record values

Estimation of stress-strength reliability for Kumaraswamy exponential distribution based on upper record values