Economic design of x¯-control charts for continuous flow process with multiple assignable causes

Extending Koo and Case's model (1990) for the case of a single assignable cause to allow for the second occurrence of an assignable cause following the first occurrence and the probability of the assignable causes following exponential distribution, the process-failure mechanism having a fixed hazard rate. We present a cost model and determine the optimal values of the design parameters, the sample size, the sampling intervals and control limit coefficient by minimizing the expected cost per unit time with respect to exponential parameters change. Finally, suggesting the performance of the loss-cost and sensitivity analyses of the design parameters and loss-cost which depend on the model parameters and shift amounts closely are also presented.