ACCEPTANCE CONTROL CHARTS FOR MONITORING FIRST-ORDER AUTOREGRESSIVE PROCESS

The idea that any deviation should be recognized as soon as possible will often be impractical. Despite the existence of numerous assignable causes in the process, their eects may be so small and minor against the permissible tolerance. Identifying them seems uneconomical from practical sights. If the process reaches a high level of capability, the production may be acceptable even though assignable causes befall. Since customer expectation will not be aected in this case, it is not economical to stop the process. By considering the level of speci- cations, some changes in the average can be allowed. Dividing the conditions of the monitored process into just black and white can be simplistic. In such cases, traditional control charts with two zones are not applicable. By dening the zone of indierence, permissible deviations can be tolerated. For such a situation, Acceptance Control Chart (ACC) is developed based on three zones. Suppose that a statistically assignable cause is detected using the traditional control charts; however, no signal is observed by the ACC. Thus, this change does not result in a nonconforming output, and there is no need to stop production since no operational loss occurs. The most important assumptions of the ACC are the normality and independence of the monitored data. In some industrial/non-industrial processes (e.g., continuous production processes, nancial processes, network monitoring, and environmental phenomena), serial correlation can be extracted among samples which violates the assumption of independence. Autocorrelation reduces the performance of traditional control charts by producing frequent false signals in the in-control state or makes them respond slowly to the detection of the outof- control state. The main purpose of this study is to develop an ACC for monitoring the data of the most widely used autocorrelated process, namely the rst-order autoregressive process AR(1). In this regard, two types of ACC are extended for the residuals of AR(1) processes. Upon evaluating the performance of monitoring methods using the average run length (ARL), it is found that the proposed EWMA chart has better results. Moreover, the economic-statistical design of the proposed chart is carried out at a lower cost.