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

Abstract

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

Keywords

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