Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

In this paper, we studied the estimation of a stress-strength reliability model (R = P(X>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

Reliability analysis of s-out-of-k multicomponent stress-strength system with dependent strength elements based on copula function

This paper considers the reliability analysis of a multicomponent stress-strength system which has $k$ statistically independent and identically distributed strength components, and each component is constructed by a pair of statistically dependent elements. These elements are exposed to a common random stress, and the dependence among lifetimes of elements is generated by Clayton copula with unknown copula parameter. The system is regarded to be operating only if at least $s$($1 \leq s \leq k$) strength variables in the system exceed the random stress. The maximum likelihood estimates (MLE) of unknown parameters and system reliability is established and associated asymptotic confidence interval is constructed using the asymptotic normality property and delta method, and the bootstrap confidence intervals are obtained using the sampling theory. Finally, Monte Carlo simulation is conducted to support the proposed model and methods, and one real data set is analyzed to demonstrate the applicability of our study

Estimating Discrete Markov Models From Various Incomplete Data Schemes

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a case, the estimation of transition probabilities is straightforwardly made by counting one-step moves from a given state to another. In many real-life problems, however, the inference is much more difficult as state sequences are not fully observed, namely the state of each individual is known only for some given values of the time variable. A review of the problem is given, focusing on Monte Carlo Markov Chain (MCMC) algorithms to perform Bayesian inference and evaluate posterior distributions of the transition probabilities in this missing-data framework. Leaning on the dependence between the rows of the transition matrix, an adaptive MCMC mechanism accelerating the classical Metropolis-Hastings algorithm is then proposed and empirically studied.Comment: 26 pages - preprint accepted in 20th February 2012 for publication in Computational Statistics and Data Analysis (please cite the journal's paper

Constant-Stress Partially Accelerated Life Testing for Weibull Inverted Exponential Distribution with Censored Data

The novelty of this article is estimating the parameters of Weibull inverted exponential (WIE) distribution with a constant stress partially accelerated life test (PALT) under adaptive type-II progressively censored samples. Moreover, the maximum likelihood estimators (MLEs), their asymptotic variances confidence intervals, and Bayes estimators (BEs) of the model parameters and the acceleration factor are obtained. Furthermore, the approximate bootstrap and credible confidence intervals of the estimators are acquired. The accuracy of the MLEs and BEs for the model parameters and the acceleration factor is investigated through the simulation studies

Modified weibull distributions in reliability engineering

Ph.DDOCTOR OF PHILOSOPH

Investigation the generalized extreme value under liner distribution parameters for progressive type-Ⅱ censoring by using optimization algorithms

Several random phenomena have been modeled by using extreme value distributions. Based on progressive type-Ⅱ censored data with three different distributions (i.e., fixed, discrete uniform, and binomial random removal), the statistical inference of the generalized extreme value distribution under liner normalization (GEVL distribution) parameters is investigated in this study. Since there is no analytical solution, determining the maximum likelihood parameters for the GEVL distribution is considered to be a problem. Standard numerical methods are frequently insufficient for this dilemma, requiring the use of artificial intelligence algorithms to address this difficulty. Here, nonlinear minimization and a genetic algorithm have been used to tackle that problem. In addition, Lindley approximation and Monte Carlo estimation were implemented via Metropolis-Hastings algorithms to carry out the Bayesian point estimation based on both the squared error loss function and LINEX loss functions. Moreover, the highest posterior density intervals were applied. The proposed theoretical inference techniques have been applied in a numerical simulation and a real-life example