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The traditional Shewhart control chart, the X-bar and R/S chart, cannot give support to decide when it is not economically feasible to stop the process in order to remove special causes. Therefore, the purpose of this paper is to propose a new control chart design – a modified acceptance control chart, which provides a supportive method for decision making in economic terms, especially when the process has high capability indices.

The authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution of C_pk, to compare and analyze the efficiency of the proposed design.

This study suggested a new procedure to calculate the control limits (CL) of the X-bar chart, which allows economic decisions about the process to be made. By introducing a permissible average variation and defining three regions for statistical CL in the traditional X-bar control chart, a new design is proposed.

A framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (C_p and C_pk) in addition to m and n were introduced in the expected ARL equation. The C_pk is a random variable and its probability function is known. Therefore, by using a preliminary sample of a process under control, the authors can test whether the process is capable or not.

The purpose of this paper is to provide a new method to estimate the reliability of series system by using a discrete bivariate distribution. This problem is of great interest in industrial and engineering applications.

The authors considered the Basu–Dhar bivariate geometric distribution and a Bayesian approach with application to a simulated data set and an engineering data set.

From the obtained results of this study, the authors observe that the discrete Basu–Dhar bivariate probability distribution could be a good alternative in the analysis of series system structures with accurate inference results for the reliability of the system under a Bayesian approach.

System reliability studies usually assume independent lifetimes for the components (series, parallel or complex system structures) in the estimation of the reliability of the system. This assumption in general is not reasonable in many engineering applications, since it is possible that the presence of some dependence structure between the lifetimes of the components could affect the evaluation of the reliability of the system.

The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and engineering applications.

The authors introduce copula functions and consider a Bayesian analysis for the proposed models with application to the simulated data.

The use of copula functions for modeling the bivariate distribution could be a good alternative to estimate the reliability of a two components series system. From the results of this study, the authors observe that they get accurate Bayesian inferences for the reliability function considering large samples sizes. The Bayesian parametric models proposed also allow the assessment of system reliability for multicomponent systems simultaneously.

Usually, the studies of systems reliability engineering assume independence among the component lifetimes. In the approach the authors consider a dependence structure. Using standard classical inference methods based on asymptotical normality of the maximum likelihood estimators for the parameters the authors could have great computational difficulties and possibly, not accurate inference results, which there is not found in the approach.