Acceptance X-bar chart considering the sample distribution of capability indices, C ˆ p and C ˆ p k

Abstract

PurposeThe 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.Design/methodology/approachThe authors made a modeling expectation average run length (ARL), which incorporates the probability density function of the sampling distribution ofCpk, to compare and analyze the efficiency of the proposed design.FindingsThis 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.Originality/valueA framework is presented to help practitioners in the use of the proposed control chart. Two new parameters (CpandCpk) in addition tomandnwere introduced in the expected ARL equation. TheCpkis 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.