Modified side-sensitive synthetic double sampling monitoring scheme for simultaneously monitoring the process mean and variability

Abstract

This paper develops a new synthetic double sampling (SDS) monitoring scheme based on the modified side-sensitive (MSS) design for jointly monitoring the process mean and variability. We first give the operation of the proposed scheme and secondly, the closed-form expression of the probability of declaring a specific sampling stage as “conforming” or “nonconforming”. Thirdly, we evaluate the performance of the newly proposed scheme in terms of the zero- and steady-state out-of-control average run-length, standard deviation of the run-length, average number of observations to signal, average extra quadratic loss, average ratio of the average run-length and performance comparison index. Finally, we compare the performance of the new monitoring scheme with some existing monitoring schemes. It is observed that the proposed scheme has attractive run-length properties and outperforms the existing joint X¯ and S SDS monitoring scheme as well as all other competing schemes in many situations.