Stress-strength Model Research Articles

Cumulative information generating function and generalized Gini functions

We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of k-out-of-n systems and with stress–strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions.

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.

Employ Stress-Strength Reliability Technique in Case the Inverse Chen Distribution

This paper uses classical and shrinkage estimators to estimate the system reliability (R) in the stress-strength model when the stress and strength follow the Inverse Chen distribution (ICD). The comparisons of the proposed estimators have been presented using a simulation that depends on the mean squared error (MSE) criteria.

Analysis of the Stress–Strength Model Using Uniform Truncated Negative Binomial Distribution under Progressive Type-II Censoring

In this study, we introduce a novel estimation technique for assessing the reliability parameter R=P(Y<X) of the uniform truncated negative binomial distribution (UTNBD) in the context of stress–strength analysis. We base our inferences on the assumption that both the strength (X) and stress (Y) random variables follow a UTNBD with identical first shape and scale parameters. In the presence of a progressive type-II censoring scheme, we employ maximum likelihood, two parametric bootstrap methods, and Bayesian estimation approaches to derive the estimators. Due to the complexity introduced by censoring, the estimators are not available in explicit forms and are instead obtained through numerical approximation techniques. Furthermore, we compute the highest posterior density credible intervals and determine the asymptotic variance-covariance matrix. To assess the performance of our proposed estimators, we conduct a Monte Carlo simulation study and provide a comparative analysis. Finally, we illustrate the practical applicability of our study with an engineering application.

A new bivariate distribution with uniform marginals

Starting from three independent exponential random variables we have generated a bivariate random vector (U, V) having the marginal distributions as standard uniform. The joint distribution function and the survival function have been derived along with the moment generating function. We have also given an expression for the joint moment of order (r, s). The distributions of different functions of U and V have been derived. Different dependence measures between U and V have also been calculated. The reliability of the underlying stress-strength model has been obtained as an application of the distribution. A simulation exercise has been carried out to check for the goodness-of-fit of the model. We have also calculated the relative errors in different reliability measures under the assumption that the variables U and V are independent when actually they are not.

Bayesian and non-Bayesian analysis with MCMC algorithm of stress-strength for a new two parameters lifetime model with applications

A parallel system is one of the special redundant systems that industrial systems frequently use to increase reliability and prevent unexpected failures. In this paper, a new two-parameter model called the Poisson Rayleigh distribution (PRD) is studied. Some of its statistical properties are given. Particularly, we emphasize the study of the stress–strength (SS) reliability parameter, R = p(Y < X), when X and Y have a PRD. Maximum likelihood, maximum product spacing, and Bayesian strategies are utilized to estimate the parameters. Maximum likelihood, maximum product spacing, and Bayesian techniques for R are computed. To assess how each estimation method performs, a simulation study is conducted. In order to demonstrate the adaptability of the suggested model, its goodness of fit for the PRD comparison with other models is demonstrated by application to real datasets. Finally, the SS model for the PRD was applied with two applications of real data depicting the failure times for two types of electrical insulators and pertaining to customer wait times at two banks.

Estimation of $$ P[Y<X] $$ for Dependence of Stress–Strength Models with Weibull Marginals

Estimation of $$ P[Y<X] $$ for Dependence of Stress–Strength Models with Weibull Marginals

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.

Estimation of Reliability in Multicomponent Set-up when Stress and Strength are Non-identical

In the multicomponent stress–strength reliability literary work, though assumption of identical stress and strengths components may not be universally true but have been commonly considered. Herein, we consider a multicomponent stress–strength model having k identical strength components, say X_i,~i=1,2,...,k, which are exposed to a common random stress Y, so that Y, X_i,~i=1,2,...,k are independent. Two different generalized cases of estimation are considered; namely, (i) when the strength components follow the proportional hazard rate model and stress component follows the proportional reversed hazard rate model and (ii) when the strength components follow the proportional reversed hazard rate model and stress component follow the proportional hazard rate model. In each case, maximum likelihood and Bayesian approach using Markov Chain Monte Carlo method has been utilized to estimate the reliability of the system. Asymptotic confidence intervals are also constructed for the reliability functions in both the cases. Monte Carlo simulation study is exercised to compare the performance of the aforementioned estimators. A real data example is also explored to examine the utility of the paper.

Inference for the Johnson SB distribution

This article develops inferential procedures for the Johnson SB distribution and the associated stress-strength model. The maximum likelihood estimators, uniformly minimum variance unbiased estimators and generalized confidence intervals for the parameters of the Johnson SB distribution are presented. The objective Bayesian inference methods based on the Jeffreys and reference priors are derived. Moreover, the generalized confidence lower limits and Bayesian credible lower limits for the reliability of the stress-strength model are provided. The performance of the proposed methods is evaluated by Monte Carlo simulation. Finally, an example is used to illustrate the proposed procedures.

Simulation Techniques for Strength Component Partially Accelerated to Analyze Stress–Strength Model

Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of δ=P(Y<X) were proposed when the strength variable was subjected to the step–stress partially accelerated life test. The point estimators computed were maximum likelihood and Bayesian under various symmetric and asymmetric loss functions. The interval estimations constructed were approximate, bootstrap-P, and bootstrap-T confidence intervals, and a Bayesian credible interval. A Markov Chain Monte Carlo approach using Gibbs sampling was designed to derive the Bayesian estimate of δ. Based on the mean square error, bias, confidence interval length, and coverage probability, the results of the numerical analysis of the performance of the maximum likelihood and Bayesian estimates using Monte Carlo simulations were quite satisfactory. To support the theoretical component, an empirical investigation based on two actual data sets was carried out.

On the copula-based reliability of stress-strength model under bivariate stress

In this paper, we consider the stress-strength reliability R = P ( X 1 < Y < X 2 ) where the strength Y of a component lies between the dependent stress variables X 1 and X 2 . We propose a copula-based approach for stress-strength reliability having bivariate stress. We obtain R for Farlie-Gumbel-Morgenstern copula with Burr III marginals. Also, we propose a Bernstein copula approximation for evaluating R under the stress-strength setup. We present empirical and maximum likelihood-based estimation procedures and compare their performances by Monte Carlo simulation. We apply the proposed approach to chemical and overt diabetes data for illustration purpose.

On Beta Exponentiated Lomax-Exponential Distribution with applications

This study introduces a new Beta Exponentiated Lomax-Exponential Distribution (BELED) with special reference to its quantile function to enhance closed form solution of its parameters and make its proprietorial effect on data modeling quantifiable with exactness. The obtained BELED which accommodates heavy and light data, either skewed or not, addressed the challenges of intractable parameter estimation in previous related distributions from same family. The BELED properties which includes rth moments, characteristics function, Renyi and Shanon entropy, reliability measures as well as stress-strength model were derived. The estimator (β^) of the exponentiated parameter (β) from an in-built function was obtained in closed form at the modal point in the absence and presence of censoring. Pivot-quantile regression was used to determine the estimate of the scale (σ^) and shape α^ parameters, while the remaining beta generator induced shape parameters (a,b) were derived using maximization techniques via the constrain β^. The quantile function of BELED which averaged out the additive and multiplicative variation in a univariate data set, can be used in modeling the behavioural pattern of both discrete and continuous data.

Doubly Type II Censoring of Two Stress-Strength System Reliability Estimation for Generalized Exponential-Poisson Distribution

In this paper, a Bayesian analysis is made to estimate the Reliability of two stress-strength model systems. First: the reliability of a one component strengths X under stress Y. Second, reliability of one component strength under three stresses. Where X and Y are independent generalized exponential-Poison random variables with parameters (α,λ,θ) and (β,λ,θ) . The analysis is concerned with and based on doubly type II censored samples using gamma prior under four different loss functions, namely quadratic loss function, weighted loss functions, linear and non-linear exponential loss function. The estimators are compared by mean squared error criteria due to a simulation study. We also find that the mean square error is the best performance of the estimator from that found in quadratic, weighted, linear and non-linear exponential loss functions.

The Reliability of Stored Water behind Dams Using the Multi-Component Stress-Strength System

Dams are essential infrastructure for managing water resources and providing entry to clean water for human needs. However, the construction and maintenance of dams require careful consideration of their reliability and safety, specifically in the event of extreme weather conditions such as heavy rainfall or flooding. In this study, the stress-strength model provides a useful framework for evaluating the reliability of dams and their ability to cope with external stresses such as water pressure, earthquake activity, and erosion. The Shasta reservoir in the United States is a prime example of a dam that requires regular assessment of its reliability to guarantee the safety of communities and infrastructure. The Gumbel Type II distribution has been suggested as a suitable model for fitting the collected data on the stress and strength of the reservoir behind the Shasta dam. Both classical and Bayesian approaches have been used to estimate the reliability function under the multi-component stress-strength model, and Monte Carlo simulation has been employed for parameter estimation. In addition, some measures of goodness-of-fit are employed to examine the suitability of the suggested model.

Estimation in a multicomponent stress-strength model for progressive censored lognormal distribution

We consider estimation of multicomponent stress-strength reliability under classical as well as Bayesian approaches when stress-strength components follow lognormal distributions and data are observed under progressive censoring. Various estimates are obtained by sequentially considering one parameter common and unknown. Different expressions for the reliability are evaluated under these cases. For both the cases, we obtain different estimates of considered parametric function using likelihood, Lindley and repeated sampling methods. Asymptotic and credible intervals are also obtained. Extensive simulations are conducted to examine the behavior of all estimates under various censoring schemes. We finally present analysis of a real life example from application purposes.

Inference for reliability in a multicomponent stress–strength model for a unit inverse Weibull distribution under type-II censoring

ABSTRACT In this paper, a unit inverse Weibull distribution as well as its basic structural properties is proposed. Furthermore, classical inferences for multicomponent reliability are discussed under type-II censoring when stress and strength components have a common parameter. The maximum likelihood estimator of the reliability is obtained and in sequel an asymptotic interval is constructed. Pivotal quantities are constructed and then generalized point and interval estimators are obtained for the reliability. Likelihood and pivotal quantities-based estimations are presented when all parameters are unequal as well. The performance of different estimators is investigated using simulation studies and real-life examples are studied from an application viewpoint. Finally, some concluding remarks are given.

On the Estimation of Stress-Strength Model Reliability Parameter of Power Rayleigh Distribution

The aim of this paper is to estimate a single reliability system (R = P, Z &gt; W) with a strength Z subjected to a stress W in a stress-strength model that follows a power Rayleigh distribution. It proposes, generates and examines eight methods and techniques for estimating distribution parameters and reliability functions. These methods are the maximum likelihood estimation(MLE), the exact moment estimation (EMME), the percentile estimation (PE), the least-squares estimation (LSE), the weighted least squares estimation (WLSE) and three shrinkage estimation methods (sh1) (sh2) (sh3). We also use the mean square error (MSE) Bias and the mean absolute percentage error (MAPE) to compare the estimation methods. Both theoretical comparison, simulation and real data are used. The results in light of this distribution show the advantage of the proposed methods.

Statistical Inference for Multicomponent System Stress-Strength Model with Bounded Strengths

Statistical Inference for Multicomponent System Stress-Strength Model with Bounded Strengths

Estimation of a Parallel Stress-strength Model Based on the Inverse Kumaraswamy Distribution

The reliability of the stress-strength model attracted many statisticians for several years owing to its applicability in different and diverse parts such as engineering, quality control, and economics. In this paper, the system reliability estimation in the stress-strength model containing Kth parallel components will be offered by four types of shrinkage methods: constant Shrinkage Estimation Method, Shrinkage Function Estimator, Modified Thompson Type Shrinkage Estimator, Squared Shrinkage Estimator. The Monte Carlo simulation study is compared among proposed estimators using the mean squared error. The result analyses of the shrinkage estimation methods showed that the shrinkage functions estimator was the best since it has a minor mean squared error than the other methods followed by the additional shrinkage estimator. The stress and strength belong to the In verse Kumaraswamy distribution