An economic design of cumulative sum charts to control non-normal process means

This paper proposes a method for the economic design of Cumulative sum (Cusum) control charts to maintain the current control of the process means, where the observations are independently, but non-normally distributed. The economic design of the Cusum charts involves the determination of the design parameters that minimize a relevant cost function. The design parameters are the sample size n, sampling interval s, the reference value jk, and the decision interval h. Approximating the non-normal probability density function of the process by an Edgeworth series, and deriving the average run lengths in Cusum control schemes by the use of a system of linear algebraic equations, an expression for the expected loss-cost function for the process is identified. An algorithm for near-optimal determination of the design parameters, by minimizing the loss-cost function, is presented, and its application is demonstrated through a numerical example. Finally, the effects of changes in various parameters and the cost coefficients on the loss-cost function are discussed.