An optimal economic design of control chart for correlated Poisson variables: The double-dimension LCP chart

Abstract

This work proposes a control chart that uses a statistic that is a linear combination of Poisson variables considering the sampling methodology called Double Dimension. This proposal aims to reduce costs when the Poisson variables used in process monitoring are expensive or difficult to measure. Therefore, they are not measured every time the control is performed but only when there are indications that the process is out of control. A user-friendly program was developed to obtain the performance of this chart and estimate the parameters that optimize the out-of-control ARL (average run length) for a shift that the user wants to detect as quickly as possible, restricted to a fixed value of in-control ARL. In addition, numerical results are presented in different scenarios, which allows verifying the performance and sensitivity of the proposed methodology. The results show that implementing the double dimension methodology offers similar performance as always measuring the cheap and expensive variables but with significant sampling savings.