Economic design of x control charts considering process shift distributions

Process shift is an important input parameter in the economic design of control charts. Earlier x control chart designs considered constant shifts to occur in the mean of the process for a given assignable cause. This assumption has been criticized by many researchers since it may not be realistic to produce a constant shift whenever an assignable cause occurs. To overcome this difficulty, in the present work, a distribution for the shift parameter has been considered instead of a single value for a given assignable cause. Duncan's economic design model for x chart has been extended to incorporate the distribution for the process shift parameter. It is proposed to minimize total expected loss-cost to obtain the control chart parameters. Further, three types of process shifts namely, positively skewed, uniform and negatively skewed distributions are considered and the situations where it is appropriate to use the suggested methodology are recommended.