Optimal design of (X)over-bar-control chart with Pareto in-control times

Economic control chart models usually assume that the time to occurrence of an assignable cause follows an exponential or Weibull distribution. This paper extends that to the Pareto distribution in order to investigate, in general, the effect on the economic control chart parameters like sample size, time between two successive samples, and the cost per unit time of the distributional assumption. The Pareto distribution arises as a limiting distribution of the waiting time for the number of new observations needed to obtain a value exceeding the greatest among "n" observations. It was found that the economic design of (X) over bar chart is greatly influenced by the distributional assumption. Using the cost model, the sensitivity analysis of the statistical economic design of the (X) over bar chart with respect to the parameters and costs is studied.