Multicomponent Stress Strength Research Articles

Reliability inference of a multicomponent stress-strength model for exponentiated Pareto distribution based on progressive first failure censored samples

Multicomponent stress-strength (MC-SS) analysis is crucial for risk management and decision-making in various fields such as engineering, manufacturing, and quality control. It helps in identifying vulnerable components and areas where improvements can enhance overall system reliability. A primary contribution of this research is the implementation of the progressive first-Failure censored (PFIF-C) scheme. This scheme offers a novel and efficient approach to time and cost censoring, surpassing many existing censoring schemes found in the literature. The current study investigates the issue of MC-SS reliability inference under PFIF-C from the exponentiated Pareto distribution. The reliability of the MC-SS system is considered under the condition that both stress and strength follow an exponentiated Pareto distribution with a common second shape parameter. The parameter estimates and reliability estimate of the MC-SS system is produced using the maximum likelihood and Bayesian procedures. The asymptotic confidence intervals and highest posterior density credible intervals for the MC-SS system reliability are produced. Bayesian estimates are yielded using Markov Chain Monte Carlo under both informative and non-informative priors, considering symmetric and asymmetric loss functions. In order to assess the efficacy of the suggested methodology, simulation analyses are conducted. According to the simulation data Bayesian estimates of the MC-SS reliability, employing both symmetric and asymmetric loss functions, consistently outperform maximum likelihood estimates in terms of estimated risks. In general, Bayesian estimates based on asymmetric loss function perform better than the other competing loss function. The procedure is further shown with one real-world data example about failure times of a specific software model to show how the recommended approach may be applied to assess the strength and stress of a multicomponent model.

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.

Classical and Bayesian estimation of multicomponent stress–strength reliability with power Lindley distribution under progressive first-failure censored samples

This research article presents a methodology for estimating the multicomponent reliability based on progressively first-failure censored samples, where the underlying distribution of stress and strength is modelled using the power Lindley distribution. The classical and Bayesian estimation methods are utilized for estimating the multicomponent reliability. In the Bayesian estimation, the Markov Chain Monte Carlo approximation method is employed to obtain the posterior mean under a generalized entropy loss function. Various intervals including asymptotic confidence, bootstrap-p confidence, bootstrap-t confidence, Bayesian credible, and highest posterior density credible intervals are computed. A simulation study is conducted to evaluate the performance of the proposed methodology. Also, two different real data applications are presented to illustrate the practicality of the approach.

Statistical inference on multicomponent stress–strength reliability with non-identical component strengths using progressively censored data from Kumaraswamy distribution

Statistical inference on multicomponent stress–strength reliability with non-identical component strengths using progressively censored data from Kumaraswamy distribution

Reliability estimation of a multicomponent stress-strength model based on copula function under progressive first failure censoring

In reliability analysis of a multicomponent stress-strength model, most studies assumed independence between stress and strength variable. However, this assumption may not be realistic. To account for dependency, copula approach can be used. Although it is important, only few studies considered this case and usually under complete study. Observing the failures for all units may be difficult due to cost and time limitation. Recently, progressive first failure censoring scheme has attracted attention in the literature due to its ability to save time and money. To the best of our knowledge, dependent multicomponent stress-strength model under progressive first failure censoring was not considered yet. In this article, we derived the likelihood function for progressive first failure censored sample under copula and multicomponent stress strength model. A simulation study is performed and a real dataset is analyzed to test the applicability of the model. Maximum likelihood estimates, asymptotic confidence interval and bootstrap confidence intervals are obtained. The results illustrated that the proposed censoring scheme under copula provides a good estimate for the reliability.

Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data

Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data

The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution

The reliability of the multicomponent stress–strength system was investigated under the two-parameter Burr X distribution model. Based on the structure of the system, the type II censored sample of strength and random sample of stress were obtained for the study. The maximum likelihood estimators were established by utilizing the type II censored Burr X distributed strength and complete random stress data sets collected from the multicomponent system. Two related approximate confidence intervals were achieved by utilizing the delta method under the asymptotic normal distribution theory and parametric bootstrap procedure. Meanwhile, point and confidence interval estimators based on alternative generalized pivotal quantities were derived. Furthermore, a likelihood ratio test to infer the equality of both scalar parameters is provided. Finally, a practical example is provided for illustration.

Based Copula Reliability Estimation with Stress-Strength Model for Bivariate Stress under Progressive Type II Censoring

This study investigates the dependence between stress and component strength in a stress–strength model with bivariate stresses by incorporating a specialized Archimedean copula, specifically the 3-dimensional Clayton copula. Diverging from prior research, we consider a scenario where two stresses simultaneously influence the component strength, enhancing the realism of our model. Initially, dependent parameter estimates were obtained through moment estimation. Subsequently, maximum likelihood estimation and Bayesian estimation were employed to acquire point and interval estimates for the model parameters. Finally, numerical simulations and real-world data analysis were conducted to validate the accuracy and practicality of our proposed model. This research establishes a foundation for further exploration of general dependence structures and multi-component stress–strength correlation issues.

Inference for multicomponent stress–strength reliability based on unit generalized Rayleigh distribution

Inference for multicomponent stress–strength reliability based on unit generalized Rayleigh distribution

Fuzzy multicomponent stress-strength reliability in presence of partially accelerated life testing under generalized progressive hybrid censoring scheme subject to inverse Weibull model

It typically takes a lot of time to monitor life-testing experiments on a product or material. Units can be tested under harsher conditions than usual, known as accelerated life tests to shorten the testing period. This study's goal is to investigate the issue of partially accelerated life testing that use generalized progressive hybrid censored samples to estimate the stress-strength reliability in the multicomponent case. Also, the fuzziness of the model is considered that gives more sensitive and accurate analyses about the underlying system. Maximum likelihood estimation method under the inverse Weibull distribution and using the generalized progressively hybrid censoring scheme is introduced to obtain an estimator for the fuzzy multicomponent stress-strength reliability. Also, an asymptotic confidence interval is deduced to examine the reliability of the fuzzy multicomponent stress-strength. Simulation study is conducted using maximum likelihood estimates and confidence intervals for the fuzzy multicomponent stress-strength reliability for different values of the parameters and different schemes. A real data application representing the data for the failure times for a certain software model is introduced to obtain the fuzzy multicomponent stress-strength reliability for different schemes.•The fuzzy multicomponent stress-strength reliability is investigated under partially accelerated life testing and the generalized progressively hybrid censored scheme.•An algorithm is introduced to simulate data for the censoring scheme.•A real data application is presented to obtain the fuzzy multicomponent stress-strength reliability at different schemes.

Estimation of multicomponent stress–strength reliability for exponentiated Gumbel distribution

In this paper, the stress–strength reliability R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration.

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.

Bayesian and likelihood estimation of multicomponent stress–strength reliability from power Lindley distribution based on progressively censored samples

In this article, the problem of estimation of reliability of a ℓ-component system when both the stress and strength components are assumed to have a power Lindley distribution is discussed. The multicomponent stress–strength reliability parameter is obtained using both the Bayesian and the classical approaches when component-wise each unit follows a power Lindley distribution. To estimate the multicomponent stress–strength reliability parameter under the classical approach, the method of maximum likelihood and the asymptotic confidence interval estimation method are used as point and interval estimation methods, respectively. Under the Bayesian paradigm, the reliability parameter is estimated under the linear exponential loss function using the Lindley approximation, the Tierney–Kadane approximation and the Markov chain Monte Carlo (MCMC) techniques and subsequently highest posterior density credible intervals are obtained. To validate the efficacy of the proposed estimation strategies, a simulation study is carried out. Finally, two real-life data sets are re-analysed for illustrative purposes.

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.

Estimation of multicomponent stress–strength reliability based on unit Burr XII distribution: an application to dam occupancy rate of Istanbul, Turkey

ABSTRACT In this paper, we consider the estimation of a multicomponent stress–strength reliability when stress and strength variables follow unit Bur XII distribution. In estimation procedure, the maximum likelihood and Bayesian methods are used. The maximum likelihood estimator is obtained via iterative methods. The asymptotic confidence interval is constructed using asymptotic properties of the corresponding estimator. In addition, two bootstrap confidence intervals are constructed. Bayesian estimator is obtained using three different approximation methods: Lindley’s approximation, Tierney–Kadane approximation and Markov Chain Monte Carlo method. The interval estimation based on Bayesian method is studied. The simulation study is conducted to investigate and compare the performance of the considered methods. Finally, an original data set, general dam occupancy rate of Istanbul, Turkey obtained from Istanbul Statistic Office, is analysed in the concept of multicomponent stress–strength reliability.

Reliability Inference of Multicomponent Stress–Strength System Based on Chen Distribution Using Progressively Censored Data

In this paper, we study the inference of the multicomponent stress–strength reliability (MSSR) based on the Chen distribution using progressively Type-II censored data. Both the stress and strength variables follow the Chen distribution with a common second shape parameter. The maximum likelihood estimates and the asymptotic confidence intervals of the MSSR are developed. The bootstrap confidence interval of the MSSR is also constructed. The Bayesian estimation of the MSSR is obtained under the generalized entropy loss function using the Markov Chain Monte Carlo method. To check the effectiveness of the proposed approach, simulation studies are performed. Finally, a real data set is analyzed.

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.

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.

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.

Bayesian Estimation of Reliability for Multicomponent Stress-Strength Model Based on Topp-Leone Distribution

In this paper, the reliability function of a multicomponent stress-strength model was calculated when each stress and strength variable had a Topp-Leone distribution and an identically independent distribution (i.i.d). By assuming that the primary normal information is related to the Gamma Distribution and the Weibull Distribution on several occasions, the estimation was based on the Bayes using Lindley approximation methods, under the squared error loss function, in order to find the optimal method, the mathematical formulas for these estimators were developed and compared. Using a Monte Carlo simulation method, the estimators were compared based on the mean squares error (MSE)..