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In this study, we propose a Bayesian Extended Exponentially Weighted Moving Average (BEEWMA) control chart. We have considered that the control chart statistic follows a normal distribution and the location parameter has an informative prior (normal). Average run length (ARL) has been used to evaluate the performance of the BEEWMA control chart. A simulation study has been performed to evaluate the new BEEWMA control chart’s performance for different smoothing constants values. The performance of the proposed control chart is also measured using a real-life application.

We aim to extend the Markov System Dynamic method (MSD) to evaluate the reliability of repairable systems in two-state weather (2SW) models. Increasing the number of components in real practices has limited the use of the Markov method, because of increasing the number of equations and the complexity of the problem. There is no such restriction in the MSD method. Thus, it can be applied to complex systems. Theoretically, we indicate that the 2SW model is a type of linear dynamical system. Therefore, we can use MSD to solve it. Through an example, the validity of the proposed method is confirmed in comparison to the Markov method for the 2SW model. Since the MSD method does not use equations, it can be a preferred alternative for calculating the reliability of 2SW models. Accordingly, we apply the MSD method for assessing the reliability of a four-component system.

In this article, time truncated attribute control chart is proposed for logistic-exponential distribution based on four acceptance sampling plans. The performance of the proposed control chart is evaluated in terms of average run length. Furthermore, the efficiency of the proposed attribute control chart is compared for all given acceptance sampling plans, viz., single sampling plan, repetitive sampling plan, multiple dependent state sampling plan and multiple dependent state repetitive sampling plan. Also, the application of the proposed control chart is illustrated by using real life example.

In the present work we first discuss the structure and properties of the ageing function of the Gumbel–Barnett copula in the exchangeable case. Then we define and illustrate the ageing notions such as IFR, DMRL, NBU etc for copulas using the weak copula ageing property of the Gumbel–Barnett copula.

In this article, we consider classical and Bayesian estimations of some economic measures, specially Bonferroni Curve and Bonferroni Index of the Pareto distribution. We obtain the Maximum Likelihood Estimator and Uniform Minimum Variance Unbiased Estimator in the classical setup, and their properties are studied. Additionally, we conduct Bayesian estimation procedures based on symmetric loss functions and a truncated gamma prior. The precision of the estimators is evaluated under different sample sizes via Monte Carlo simulation. Furthermore, a real dataset is provided to compute all the estimators.