The CAPD Model of -x Chart with Tardiness Penalty for Improving Supplier Quality

This paper proposes the CAPD model of the _-x control chart with tardiness penalties in order to improve supplier quality of offering higher quality products in a short due time. The CAPD model is based on cases which start from (Check) searching the assignable cause occurring passively in the out-of-control state. In addition, clarifying and treating this assignable cause in due time with minimum cost are demanded. When the _-x chart is used in the short production run process, clarifying the relation between the time parameters and the total expectation cost of Ct, and setting the optimal due time have become new problems for the quality manager. To study these questions, the mathematical formulations which correspond to this case are shown. Moreover, by numerically analyzing the proposed model, the new relationships between the key time parameters (mean out of control time 1/μ, mean in control time 1/λ, and due time T) and Ct (the total expectation cost) are found, and the setting of optimal due time T is discussed