Economic Design of X Control Charts for Monitoring a First Order Autoregressive Process

Abstract

In this paper we deal with the economic design of an X control chart used to monitor a quality characteristic whose observations fit to a first order autoregressive model. The Duncan cost model is used to select the control chart parameters, namely the sample size (n), the sampling interval (h) and the control limit coefficient (k), that lead to the optimal monitoring cost. We found that the autocorrelation has an adverse effect on the chart’s power, on the false alarm risk and on the cost. It also increases n and h and decreases k. To counteract this undesired effect we considered setting up the subgroups using non-sequential observations. It is shown that this sampling strategy significantly reduces the monitoring cost.

Keywords

• Autocorrelation
• First Order Autoregressive Model
• Economic Design
• Control Chart
• Statistical Process Control