Economic and economic-statistical designs of the side sensitive group runs chart

Abstract

The idea of proposing the economic and economic-statistical designs of the side sensitive group runs (SSGR) chart is presented in this paper. In the economic design, a simplified algorithm is used to search for the optimal design parameters that minimize the expected hourly cost. Nevertheless, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, in order to improve the effectiveness of the control chart in detecting process shifts, the economic-statistical design takes into account the statistical properties while the cost is minimized by placing statistical constraints upon the cost model of the economic design. Besides formulating the economic and economic-statistical designs based on the average run length (ARL), the economic and economic-statistical designs of the SSGR chart are also formulated based on the expected average run length (EARL) since the process shift size is usually unknown in real situations. In this paper, the sensitivity analyses of the optimal cost and the optimal design parameters are implemented for various input parameters. The effects of misspecification of the shift size on the performance of the SSGR chart are also illustrated based on numerical examples for different input parameters. This paper will also look at whether the SSGR chart performs economically better than the Shewhart X‾, synthetic, group runs (GR) and EWMA charts in the economic-statistical design based on the EARL. From the results of comparison, it is shown that the economic performance of the SSGR chart is better than that of the other four control charts in most practical situations.