Stress-Strength Reliability for First-Order Autoregressive Multivariate Normal Distribution and Its Estimation
Abstract
In this article it is mainly focused on discussion about estimation of stress-strength reliability under first-order autoregressive multivariate normal setup. It is seen in some situations that the components of a system are autoregressive correlated. The form of the first-order autoregressivecorrelation structure within the components of a system is known for a given situation; however parameters that are involved in the autoregressive structure always unknown. In this article, we propose a procedure to compute and estimate the stress-strength reliability R= Pr (a^' x>b^' y) whenxand y are distributed independently multivariate normal distribution with first-order autoregressive structure, where a and b are two known vectors. Here we have proposed the method of Maximum Likelihood Estimator (MLE), Minimum Variance Unbiased Estimator (MVUE) and Method of Moments Estimator (MOM) to estimate these unknown parameters. Actually, we want to find out overall strength is larger than overall stress. In order to do that we take a^' x and b^' y as their representatives e.g. principal components of the respective vectors do the job approximately. The performance of these intervals checked through the simulation study. Finally, we provide a real data analysis.In this article it is mainly focused on discussion about estimation of stress-strength reliability under first-order autoregressive multivariate normal setup. It is seen in some situations that the components of a system are autoregressive correlated. The form of the first-order autoregressivecorrelation structure within the components of a system is known for a given situation; however parameters that are involved in the autoregressive structure always unknown. In this article, we propose a procedure to compute and estimate the stress-strength reliability R= Pr (a^' x>b^' y) whenxand y are distributed independently multivariate normal distribution with first-order autoregressive structure, where a and b are two known vectors. Here we have proposed the method of Maximum Likelihood Estimator (MLE), Minimum Variance Unbiased Estimator (MVUE) and Method of Moments Estimator (MOM) to estimate these unknown parameters. Actually, we want to find out overall strength is larger than overall stress. In order to do that we take a^' x and b^' y as their representatives e.g. principal components of the respective vectors do the job approximately. The performance of these intervals checked through the simulation study. Finally, we provide a real data analysis.
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