Stress-strength Parameter Research Articles

Estimation of the stress–strength reliability for the exponential-Rayleigh distribution

In this current paper, we consider the problem of estimating the stress–strength parameter ψ=P(X<Y). This is done by using Bayesian and non-Bayesian approaches when X and Y are independent random variables from two exponential-Rayleigh distributions with different shape parameters but the same scale parameter. Maximum likelihood and Bayes estimators are used to estimate and construct the asymptotic confidence interval and credible interval of ψ. Finally, an intensive simulation study is performed to compare the proposed methods and analyze a real data set for illustrative purposes.

Inference for the stress-strength parameter of multi-state systems based on records

. Stress-strength models are used to analyze the reliability of the two-state systems. In this article, the stress-strength model for a multi-state system is discussed. It is assumed that the stress-strength reliability depends on the ratio of strength and stress values. When the stress and the strength random variables follow two independent Weibull distributions, the estimation of the multi-state stress-strength reliability function by various methods is investigated. Particularly, the problem of parameter estimation on the basis of the records is studied in detail. Furthermore, simulation studies are conducted for comparative purposes. Finally, two illustrative examples are presented.

Family of Kumaraswamy generalized distribution in estimation of multi-component reliability under the adaptive hybrid progressive censoring schemes

ABSTRACT In this paper, the statistical inference on multi-component stress-strength parameter with non-identical-component strengths, based on Kumaraswamy generalized distribution under adaptive hybrid progressive censoring samples, is considered. The problem is solved in three cases. First, when one parameter is unknown, the maximum likelihood estimation (MLE), Bayes approximations, asymptotic and highest posterior density intervals are obtained. Second, when the common parameter is known, MLE, approximation Bayes estimations, uniformly minimum variance unbiased estimator and different confidence intervals are provided. Third, when all parameters are different and unknown, MLE and Bayesian estimation are studied. The Monte Carlo simulation is employed to compare the estimations. Based on the simulation results, it is observed that the Bayesian estimates perform better than MLEs. Also, the highest posterior density intervals have better performance than asymptotic intervals. Moreover, it is observed that the performance of uniformly minimum variance unbiased estimators is worse than MLEs. To implement the theoretical method, two real data sets are analyzed.

Exponentiated half‐logistic Weibull distribution with reliability inference

AbstractThis paper presents an in‐depth analysis of the exponentiated half‐logistic Weibull (EHLW) distribution, investigating its fundamental statistical properties and exploring parameters estimation using both maximum likelihood and Bayesian approaches. Specifically, our focus centers on the analysis of stress–strength reliability, denoted as , where the strength variable follows EHLW distribution, and the stress variable follows either Weibull distribution or the EHLW distribution. The estimation of the parameter is discussed in both scenarios, employing both Maximum Likelihood and Bayesian approaches. Furthermore, we calculate that the asymptotic confidence interval, percentile bootstrap interval, and the highest probability density credible interval are obtained for the stress–strength parameter . In order to assess the efficiency of these estimation techniques, simulation studies are conducted, providing valuable insights into the performance of each estimation approach. Finally, the proposed reliability model is applied to real datasets, highlighting its practical significance.

Engineering Applications with Stress-Strength for a New Flexible Extension of Inverse Lomax Model: Bayesian and Non-Bayesian Inference

In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp–Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical to notice that the skewness, kurtosis, and tail weights of the distribution are strongly influenced by these additional characteristics of the extra parameters. The TTLILo model is capable of producing right-skewed, J-shaped, uni-modal, and reversed-J-shaped densities. The proposed model’s statistical characteristics, including the moments, entropy values, stochastic ordering, stress-strength model, incomplete moments, and quantile function, are examined. Moreover, characterization based on two truncated moments is offered. Using Bayesian and non-Bayesian estimating techniques, we estimate the distribution parameters of the suggested distribution. The bootstrap procedure, approximation, and Bayesian credibility are the three forms of confidence intervals that have been created. A simulation study is used to assess the efficiency of the estimated parameters. The TTLILo model is then put to the test by being applied to actual engineering datasets, demonstrating that it offers a good match when compared to alternative models. Two applications based on real engineering datasets are taken into consideration: one on the failure times of airplane air conditioning systems and the other on the active repair times of airborne communication transceivers. Also, we consider the problem of estimating the stress-strength parameter R=P(Z2&lt;Z1) with engineering application.

Product of Spacing Estimation of Stress–Strength Reliability for Alpha Power Exponential Progressively Type-II Censored Data

The present study focuses on estimating the stress–strength parameter when the parent distribution is the alpha power exponential model and the available data are progressively Type-II censored. As a starting point, the usual maximum likelihood approach is applied to obtain point and interval estimates of the model parameters, as well as the stress–strength parameter. Another competing strategy employed in this paper is the maximum product of spacing method, which may be thought of as a rival to the maximum likelihood method. The product of spacing approach is used to obtain point and interval estimates for the various parameters. The asymptotic properties of both methods are used to obtain interval estimates of the model parameter and the stress–strength parameter, and the variance of the stress–strength parameter is approximated using the well-known delta method. Two parametric bootstrap confidence intervals are provided based on the suggested classical estimation procedures. A simulation study is also used to assess the performance of various point and interval estimations. For illustrative purposes, the proposed methods are applied to two real data sets, one for the kidney patients’ recurrence times to infection and the other for breaking the strength of jute fibers.

Powered Inverse Rayleigh Distribution Using DUS Transformation

This article reports an extension of powered inverse Rayleigh distribution via DUS transformation, named DUS-Powered Inverse Rayleigh (DUS-PIR) distribution. Some statistical properties of suggested distribution in particular, moments, mode, quantiles, order statistics, entropy, inequality measures and stress-strength parameter have been investigated extensively. To estimate the parameters, maximum likelihood estimation (MLE) is discussed. The model superiority is verified through two real datasets.

Estimating the Parametric Functions and Reliability Measures for Exponentiated Lifetime Distributions Family

The paper aims are to extend the theory to estimate the parameters of the exponentiated lifetime distribution. For it, in this paper, we derived the probability density function, cumulative density, reliability function and the stress-strength parameter of the distribution. To estimate the parameters of such distribution, we considered the maximum likelihood and uniformly minimum variance unbiased methods. The validity of the proposed work has been conducted over the simulation study of both estimation methods under the special sub model as exponentiated inverse Gompertz distribution. Finally, some real data has been taken to conduct an analysis and to discuss the effectiveness and advantages of the established work by comparing with other methods.

A crucial note on stress-strength models: Wrong asymptotic variance in some published papers

The purpose of this note is to point out a problem related to stress-strength models in some published papers. This difficulty has occurred in the asymptotic variance of the maximum likelihood estimator of the stress-strength parameter. The asymptotic variance will be studied in general and then in the mentioned papers. Finally, the correct version of asymptotic variance is computed.

A Generalized Form of Power Transformation on Exponential Family of Distribution with Properties and Application

In this paper, we proposed a new generalized family of distribution namely new alpha power Exponential (NAPE) distribution based on the new alpha power transformation (NAPT) method by Elbatal et al. (2019). Various statistical properties of the proposed distribution are obtained including moment, incomplete moment, conditional moment, probability weighted moments (PWMs), quantile function, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics. The percentage point of NAPE distribution for some specific values of the parameters is also obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters of NAPE distribution. A simulation study has been performed to evaluate and execute the behavior of the estimated parameters for mean square errors (MSEs) and bias. Finally, the efficiency and flexibility of the new proposed model are illustrated by analyzing three real-life data sets.

Alpha Power Generalized Inverse Rayleigh Distribution: Its Properties and Applications

This manuscript is related with the development of Alpha Power Generalized Inverse Rayleigh (APGIR) Distribution. The suggested model provides fit of life time data more efficiently. Some of the important characteristics of the suggested model are obtained including moments, moment generating function, quantile, mode, order statistics, stress-strength parameter, and entropies. Parameter estimates are obtained by MLE technique. The performance of the suggested model is evaluated using real-world data sets. The findings of the simulation and real data sets suggest that the newly proposed model is superior to other current competitor models.

Marshall olkin extended exponentiated Gamma distribution and its applications

Different methods for obtaining new probability distributions have been introduced in the literature in recent years, for example, (Gupta et al., 1998) proposed an interesting uni-parametric lifetime distribution, Exponentiated Gamma (EG), which hazard function has increasing and bathtub shapes. In this paper, we build a new two-parameters distribution, the Marshall Olkin Extended Exponentiated Gamma (MOEEG) distribution, which is derived from the Marshall-Olkin method and the EG distribution. The hazard function of this new distribution can accommodate monotonic, non-monotonic and unimodal shapes, allowing a better fit to greater data variability. In addition to the great flexibility of fitting the data, it contains only two parameters providing a simple parameter estimation procedure, unlike other distributions proposed in the literature that have three or more parameters. Some properties of the new distribution considered in this paper are presented such as n-th time, r-th moment of residual life, r-thmoment of residual life inverted, stochastic ordering, entropy, mean deviation, Bonferroni and Lorenz curve, skewness, kurtosis, order statistics, and stress-strength parameter. We also apply two different estimation methods, maximum likelihood and Bayesian approach. Real data applications are presented to illustrate the usefulness of this new distribution.

Inference on P(X < Y) in Bivariate Lomax model based on progressive type II censoring.

This article considers the estimation of the stress-strength reliability parameter, θ = P(X < Y), when both the stress (X) and the strength (Y) are dependent random variables from a Bivariate Lomax distribution based on a progressive type II censored sample. The maximum likelihood, the method of moments and the Bayes estimators are all derived. Bayesian estimators are obtained for both symmetric and asymmetric loss functions, via squared error and Linex loss functions, respectively. Since there is no closed form for the Bayes estimators, Lindley’s approximation is utilized to derive the Bayes estimators under these loss functions. An extensive simulation study is conducted to gauge the performance of the proposed estimators based on three criteria, namely, relative bias, mean squared error, and Pitman nearness probability. A real data application is provided to illustrate the performance of our proposed estimators through bootstrap analysis.

Estimation of P(Y

ABSTRACT The problem of estimating a stress-strength parameter is considered under the assumption that both stress and strength variables follow independent lognormal distributions. The maximum likelihood estimator of this parametric function is obtained and based on its asymptotic distribution, approximate intervals are constructed. Properties of a heuristic estimator are studied as well. Bootstrap intervals are also constructed. Bayes estimator is derived against proper and improper prior distributions. We further compute credible intervals of stress–strength parameter using importance sampling. The empirical Bayes procedure is also discussed. Proposed point and interval estimators are compared numerically using Monte Carlo simulations. Analysis of a real data set is presented for illustration purposes.

Estimation of Stress-Strength Reliability Following Extended Chen Distribution

This paper considers the estimation of the stress-strength parameter [Formula: see text] under progressive type-II censored samples, where [Formula: see text] is the strength and [Formula: see text] is the stress follow extended Chen distribution. It is assumed that [Formula: see text] and [Formula: see text] are independent. Two cases are studied. The uniformly minimum variance unbiased estimator is derived when a common scale parameter and a common shape parameter are known. In both the cases, the maximum likelihood estimates are computed using numerical iteration technique. Sufficient conditions are derived under which the MLEs of [Formula: see text] exist and unique. The Bayes estimates with respect to the squared error loss function are evaluated using Lindley’s and MCMC methods. Interval estimates are also constructed using asymptotic and bootstrap techniques. A simulation study is carried out to compare the proposed methods. Finally, data analysis has been performed on two real-life data sets for the purpose of illustration.

The U Family of Distributions: Properties and Applications

Abstract In this article, we develop a new general family of distributions aimed at unifying some well-established lifetime distributions and offering new work perspectives. A special family member based on the so-called modified Weibull distribution is highlighted and studied. It differs from the competition with a very flexible hazard rate function exhibiting increasing, decreasing, constant, upside-down bathtub and bathtub shapes. This panel of shapes remains rare and particularly desirable for modeling purposes. We provide the main mathematical properties of the special distribution, such as a tractable infinite series expansion of the probability density function, moments of several kinds (raw, incomplete, probability weighted…) with discussions on the skewness and kurtosis. The stochastic ordering structure and stress-strength parameter are also considered, as well as the basics of the order statistics. Then, an emphasis is put on the inferential features of the related model. In particular, the estimation of the model parameters is employed by the maximum likelihood method, with a simulation study to confirm the suitability of the approach. Three practical data sets are then analyzed. It is observed that the proposed model gives better fits than other well-known lifetime models derived from the Weibull model.

Applications of HLMOL-X Family of Distributions to Time Series, Acceptance Sampling and Stress-strength Parameter

In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are investigated with special emphasis to the half logistic-Marshall Olkin Lomax distribution. The specific areas we concentrated are time series modeling, acceptance sampling plan and stress-strength analysis. Different autoregressive minification structures of order one are introduced. The acceptance sampling plan is detailed by considering life time of products following the half logistic-Marshall Olkin Lomax distribution. The stress-strength reliability of the half logistic-Marshall Olkin Lomax distribution is derived and estimated. A simulation study is carried out to examine the bias, mean square error, average confidence length and coverage probability of the maximum likelihood estimator of thestress-strength reliability. Finally a real-life data analysis has also been presented.

On bounded range distribution of a Wiener process

We present an exact distribution for the bounded range of a Wiener process by using the truncation method of the probability distributions. Rather than deriving some statistical properties of this distribution including reliability properties, moments, stress-strength parameter, order statistics, Bonferroni curve, Lorenz curve, and Gini’s index, a dataset is analyzed to clarify the effectiveness of this distribution.

Estimating the stress-strength parameter in multi-component systems based on adaptive hybrid progressive censoring

Estimating the stress-strength parameter in multi-component systems based on adaptive hybrid progressive censoring

Bayesian and Classical Inference for Generalized Stress-Strength Parameter Under Generalized Logistic Distribution

In this paper, we study generalized stress-strength model for generalized logistic distribution. The maximum likelihood estimator of this quantity is obtained and then a confidence interval is presented for it. Bayesian and bootstrap methods are also applied for the recommended model. A Markov Chain Monte Carlo (MCMC) simulation study for assessing the estimation methods is performed via the Metropolis-Hastings algorithm in each step of Gibbs algorithm. An application to real data set is addressed.