An economic statistical design of the Poisson EWMA control charts for monitoring nonconformities

ABSTRACT

An economic statistical model of the exponentially weighted moving average (EWMA) control chart for the average number of nonconformities in the sample is proposed. The statistical and economic performance of proposed design are evaluated using the average run length (ARL) and the hourly expected cost, respectively. A Markov chain approach is applied to derive expressions for ARL. The cost model is established based on the general cost function given in Lorenzen and Vance [The economic design of control charts: a unified approach. Technometrics. 1986;28:3–11]. An example is provided to illustrate the application of the proposed model. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments (DOE) technique.

KEYWORDS:

• EWMA $c$ control chart
• Markov chain
• economic statistical design
• design of experiments

Disclosure statement

No potential conflict of interest was reported by the authors.