Study On Quality Control Chart Application In Auto-correlated Processes

The purpose of statistical process control is to help quality managers to monitor the production process, identify outliers in the production process, and then adjust the production process in order to maintain the production process in acceptable and stable state, to finally meet the customers’ demand for product or service level. Control chart is one of the main tools of statistical process control. Conventional control chart application provided that the sample data is sufficient and meets the assumption of independent and identically distributed. However, with the improvement of the level of automation, now a lot of the production process does not meet the above premise, but there are a lot of self-related phenomena. If we continue to use the conventional control chart, it will cause a lot of false alarms occurs, and process capability index used in conventional control charts does not reflect the true process capability in auto-correlation situations.To solve the above question, this paper presents residual control chart. After fitting the data to auto-correlation ARMA model, the generated residuals meet the assumption of independent and identically distributed, then set up the conventional control chart for the residuals. Firstly, by way of an example, we analyze the drawbacks of conventional control chart in auto-correlation case. The results show that the auto-correlation production process control limits will become tighter when we ignore the auto-correlation phenomenon, thus resulting in more time points beyond the control limits, and a large number of false alarms issued, causing unnecessary losses. Secondly, we use the simple and widely used AR(1) model to analyze the calculation of Process Capability Indices of residual control chart in the theoretical level. Studies show that, due to the overall standard deviation of conventional control chart is undervalued, so the conventional process capability index is higher than the calculated result when taking the auto-correlation into consideration. When the auto-correlation coefficient becomes larger, the gap also will become larger. This can easily lead to the false judgments that the already inadequate production process capability is in line with production requirements, miss the best opportunity to improve, resulting in the rise of a large number of unqualified products. Finally, this paper simulates the auto-correlation process of different auto-correlation coefficient to specify the comparison process.The second part of the article is to apply the residual control chart to the increasingly flourishing field of electronic business. The selected data is auto-correlation but non-stationary. Therefore, this paper smoothes the data firstly by a first-order differential, and then identify the model by auto-correlation function and partial auto-correlation function. Then through hypothesis testing to identify the most appropriate model, and finally establish control chart for the residuals. The comparison results between the residual control chart and the actual situation show that the residual control chart accurately identifies the abnormal situation out, and can help instruct quality management personnel to take the appropriate marketing strategy in the future.