The PDCA and CAPD economic models of the P control chart

Recently, more attention has been paid to the PDCA and CAPD processes of quality management for raising the efficiency of management in the industry (Ikezawa, 1985; Shiba and Walden, 2001; Matsui, 2005). When the P control chart is used in the short production run, in order to raise the efficiency of management, two cases often take place. One case starts from deciding the control lines, and then maintains the process with them; the other case starts from searching an assignable cause in the out-of-control state. In this paper, we propose both the PDCA and CAPD model of P control chart based on these two cases, and show their mathematical formulations. Then, from an economic viewpoint, we discuss the effect of Pa (power) on Ct (the total expectation cost) of the two models, and investigate the optimal value of sampling interval (vi) to minimise Ct in detail. Finally, by numerically analysing the two models, we found the new relationship between the key time parameters and Ct, respectively.