Reliability In Stress-strength Model Research Articles

Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation

In this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength reliability function is derived with its important reliability characteristics. Estimates of dependence reliability parameters are obtained. We analyse the effects of dependence parameters on the reliability function. We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals. A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β. We propose a two-phase estimation procedure for estimating the reliability parameters. A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators. Finally, the proposed estimators are examined and validated with real data sets.

Classical and Bayesian inferences of stress-strength reliability model based on record data

Classical and Bayesian inferences of stress-strength reliability model based on record data

Inference of reliability model with burr type XII distribution under two sample balanced progressive censored samples

Abstract The balanced joint progressive censoring scheme gives guidelines for researchers in reducing the expense and period of the experiment with modified efficiency. In this paper, the stress-strength reliability model are considered and investigated, in which two independent samples are generated from Burr Type XII distributions under balanced joint progressive censoring scheme. In the classical analysis, the maximum likelihood estimate of the reliability parameter is derived, then the relevant confidence interval is provided based on the Fisher matrix. Under the Bayesian framework, the Lindley’s technique and hybrid Gibbs within Metropolis-Hastings algorithm are applied to acquire the estimates of the parameters, and the corresponding highest posterior density credible interval of the reliability model is also constructed. The reliability inference is realized by numerical simulation, and the validity of the inference method is analyzed based on the splashing data of silicone oil droplets impact (SSODI) under two surfaces wettability conditions.

Estimation of fixed-accuracy confidence interval of the stress–strength reliability for inverse Pareto distribution using two-stage sampling technique

In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (IPD) is an appropriate choice among them. For stress–strength reliability models, estimation of parameters is an interesting area of research. In this article, we estimate the stress–strength reliability parameter R = P ( X > Y ) (where X and Y are strength and stress variables, respectively) of the IPD, whereby we focus on the problem of fixed-accuracy confidence interval estimation of R. It is established that the proposed interval estimation problem cannot be solved with the help of any fixed sample technique. As a result, we propose a two-stage sequential sampling strategy (which reduces the sample size significantly) to solve the given estimation problem. We obtain the expressions of several exact operating characteristics associated with our two-stage sampling technique. We also establish that the proposed two-stage procedure enjoys interesting first-order asymptotic properties. The detailed simulation analyses support our theoretical findings, and two real data sets based on insurance claims reinforce the practical utility of the proposed technique.

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.

Bayesian Estimation of Exponentiated Exponential Strength and Exponentiated Weibull Stress Reliability Model for Real Data

Stress-strength reliability is an important concept in reliability analysis, quantifies the probability that the strength of a system surpasses its applied stress. This paper focuses on the reliability analysis for exponentiated exponential distribution strength variable and the exponentiated Weibull distribution stress variable. The study explores the estimation of the parameters in stress-strength reliability model using maximum likelihood estimation and Bayesian estimation. In particular, the Bayesian estimator of stress-strength reliability is obtained by utilizing Lindley’s approximation by considering both linear exponential loss function and squared error loss function for informative and non-informative priors. A comprehensive simulation study is conducted and the performances of estimators are compared using mean squared errors. The stress-strength reliability for real datasets is also investigated for real-time data sets.

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 Multicomponent Stress-Strength Reliability Model Under the Topp-Leone Distribution: Applications, Bayesian and Non-Bayesian Assessement

The advantages of applying multicomponent stress-strength models lie in their ability to provide a comprehensive and accurate analysis of system reliability under real-world conditions. By accounting for the interactions between different stress components and identifying critical weaknesses, engineers can make informed decisions, leading to safer and more reliable designs. The primary emphasis of this research is placed on the Bayesian and classical estimations of a multicomponent stress-strength reliability model that is derived from the bounded Topp Leone distribution. It is presumable that both stress and strength follow a Topp Leone distribution, but the shape parameters of each variable differ, and the scale parameters (which determine where the variable is bounded) remain the same. Statisticians utilize approaches such as maximum likelihood paired with parametric and non-parametric bootstrap, as well as Bayesian methods, in order to evaluate the dependability of a system. Bayesian methods are also utilized. Simulation studies are carried out with the intention of establishing the degree of precision that may be achieved by employing the various methods of estimating. For the sake of this example, two genuine data sets are dissected and examined in detail.

Inference on the stress strength reliability with exponentiated generalized Marshall Olkin-G distribution.

In this paper, an inference on stress-strength reliability model is introduced in case of the exponentiated generalized Marshall Olkin G family of distributions. The maximum likelihood estimator of the stress-strength reliability function is deduced. An asymptotic confidence and bootstrap confidence intervals for the stress-strength reliability function are derived. A Bayesian inference is introduced for the stress-strength reliability. A simulation is introduced to obtain the maximum likelihood and Bayesian estimates for the stress strength reliability. Real data applications are provided to show the results for the stress-strength model and compare the exponentiated generalized Marshall Olkin-G distribution with other distributions.

Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application

In this study, we look at how to estimate stress–strength reliability models, R1 = P (Y &lt; X) and R2 = P (Y &lt; X), where the strength X and stress Y have the same distribution in the first model, R1, and strength X and stress Z have different distributions in the second model, R2. Based on the first model, the stress Y and strength X are assumed to have the Lomax distributions, whereas, in the second model, X and Z are assumed to have both the Lomax and inverse Lomax distributions, respectively. With the assumption that the variables in both models are independent, the median-ranked set sampling (MRSS) strategy is used to look at different possibilities. Using the maximum likelihood technique and an MRSS design, we derive the reliability estimators for both models when the strength and stress variables have a similar or dissimilar set size. The simulation study is used to verify the accuracy of various estimates. In most cases, the simulation results show that the reliability estimates for the second model are more efficient than those for the first model in the case of dissimilar set sizes. However, with identical set sizes, the reliability estimates for the first model are more efficient than the equivalent estimates for the second model. Medical data are used for further illustration, allowing the theoretical conclusions to be verified.

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.

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 reliability in multicomponent stress-strength based on exponential Frechet distributions

When strength and stress variables follow the exponential Frechet distribution with different shape parameters and common scale parameters, the multicomponent stress-strength reliability model of an s-out-of-k system is studied in this paper. Based on samples from stress and strength distributions, the maximum likelihood estimation of the model parameters is obtained. The asymptotic confidence interval for the system reliability is also calculated. The comparison of the reliability estimates based on small sample is given by Monte-Carlo simulation.

Stress–strength reliability models on power-Muth distribution

Stress–strength reliability models on power-Muth distribution

Bayesian Inference of the Phase-Type Stress-Strength Reliability Models

Stress-strength modeling has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, psychology, biology, genetics, medicine etc. Phase-type distribution is a generalized class of distributions that is closed under several mathematical operations like maxima, minima, convolution, finite mixture etc and any discrete or continuous probability distributions on the positive real line can be represented as phase-type. Hence stress-strength reliability models based on phase-type distributions give a generalized structure for the stress-strength models. Moreover, matrix representation of the parameters helps in their flexible evaluation and easy manipulation. In Bayesian inference, we combine the prior knowledge with the information provided by the set of current observations to make more reliable inferences. Bayesian approach has the advantage of providing more meaningful inferences by making use of all available information. In this paper, we assume that the strength of the system and the stress imposed on the system are phase-type random variables, and the Bayesian inference of stress-strength reliability is discussed for the single-component systems and multi-component systems. The computation of the Bayes estimate of stress-strength reliability using the Markov Chain Monte Carlo method, based on continuous and discrete phase-type distributions are explained.

Estimation of the stress-strength reliability for the inverse Weibull distribution under adaptive type-II progressive hybrid censoring.

In this article, we compare the maximum likelihood estimate (MLE) and the maximum product of spacing estimate (MPSE) of a stress-strength reliability model, θ = P(Y < X), under adaptive progressive type-II progressive hybrid censoring, when X and Y are independent random variables taken from the inverse Weibull distribution (IWD) with the same shape parameter and different scale parameters. The performance of both estimators is compared, through a comprehensive computer simulation based on two criteria, namely bias and mean squared error (MSE). To demonstrate the effectiveness of our proposed methods, we used two examples of real-life data based on Breakdown Times of an Insulated Fluid by (Nelson, 2003) and Head and Neck Cancer Data by (Efron, 1988). It is concluded that the MPSE method outperformed the MLE method in terms of bias and MSE values.

Reliability analysis for stress–strength model from inverted exponentiated Rayleigh based on the hybrid censored sample

PurposeThe study based on the estimation of the stress–strength reliability parameter plays a vital role in showing system efficiency. In this paper, considering independent strength and stress random variables distributed as inverted exponentiated Rayleigh model, the author have developed estimation procedures for the stress–strength reliability parameter R = P(X>Y) under Type II hybrid censored samples.Design/methodology/approachThe maximum likelihood and Bayesian estimates of R based on Type II hybrid censored samples are evaluated. Because there is no closed form for the Bayes estimate, the author use the Metropolis–Hastings algorithm to obtain approximate Bayes estimate of the reliability parameter. Furthermore, the author construct the asymptotic confidence interval, bootstrap confidence interval and highest posterior density (HPD) credible interval for R. The Monte Carlo simulation study has been conducted to compare the performance of various proposed point and interval estimators. Finally, the validity of the stress–strength reliability model is demonstrated via a practical case.FindingsThe performance of various point and interval estimators is compared via the simulation study. Among all proposed estimators, Bayes estimators using MHG algorithm show minimum MSE for all considered censoring schemes. Furthermore, the real data analysis indicates that the splashing diameter decreases with the increase of MPa under different hybrid censored samples.Originality/valueThe frequentist and Bayesian methods are developed to estimate the associated parameters of the reliability model under the hybrid censored inverted exponentiated Rayleigh distribution. The application of the proposed stress–strength reliability model will help the reliability engineers and also other scientists to estimate the system reliability.

The stereographic generalized inverse Weibull distribution

When the unit circle is taken as a sample space, the circular data manifest in different aspects of real life. Minh and Farnum (2003) used a stereographic projection to generate new probability distributions on real line [1]. Here, we present an asymmetric distribution called Stereographic generalized inverse Weibull distribution (SGIWD) to represent circular data with focus on the inverse Stereographic Projection. The graph of probability density function is done. We consider here some statistical properties of SGIW distribution, survival and reverse hazard functions, the rth raw moments function, trigonometric moments, stress-strength reliability model, Tsallis, Renyi Shannon entropies and the Kullback–Leibler divergence measure. A simulation study is conducted to evaluate the behavior of the maximum likelihood method to estimate parameters of SGIWD.

Inferences for Stress-Strength Reliability Model in the Presence of Partially Accelerated Life Test to Its Strength Variable.

We focus on estimating the stress-strength reliability model when the strength variable is subjected to the step-stress partially accelerated life test. Based on the assumption that both stress and strength random variables follow Weibull distribution with a common first shape parameter, the inferences for this reliability system are constructed. The maximum likelihood, two parametric bootstraps, and Bayes estimates are obtained. Moreover, approximate confidence intervals, asymptotic variance-covariance matrix, and highest posterior density credible intervals are derived. A simulation study and application to real-life data are conducted to compare the proposed estimation methods developed here and also check the accuracy of the results.

Estimation of stress–strength reliability based on censored data and its evaluation for coating processes

ABSTRACT In this paper, the classical and Bayesian estimation procedures for stress–strength reliability parameter (SSRP) have been considered based on two independent adaptive Type II progressive hybrid censored samples from inverted exponentiated Rayleigh distributions with different shape parameters. The maximum likelihood estimate of SSRP and its asymptotic confidence interval are attained. The Bayes estimate of SSRP is obtained under two loss functions using the Lindley’s approximation and Metropolis–Hastings algorithm. The highest posterior density credible interval is successively constructed. The behavior of suggested estimators is assessed using a simulation study. Finally, the droplet splashing data under two surface wettabilities are considered to illustrate the application of the stress–strength reliability model to the engineering data.