Economic design of x¯ control charts considering process shift distributions

Process shift is an important input parameter inthe economic design of control charts. Earlier x controlchart designs considered constant shifts to occur in themean of the process for a given assignable cause. Thisassumption has been criticized by many researchers since itmay not be realistic to produce a constant shift wheneveran assignable cause occurs. To overcome this difficulty, inthe present work, a distribution for the shift parameter hasbeen considered instead of a single value for a givenassignable cause. Duncan’s economic design model for xchart has been extended to incorporate the distribution forthe process shift parameter. It is proposed to minimize totalexpected loss-cost to obtain the control chart parameters.Further, three types of process shifts namely, positivelyskewed, uniform and negatively skewed distributions areconsidered and the situations where it is appropriate to usethe suggested methodology are recommended.