Weighted-loss-function CUSUM chart for monitoring mean and variance of a production process

In a production process, when Statistical Process Control (SPC) deals with a quality characteristic (e.g. a dimension) that is a variable, it is usually necessary to monitor both the mean value of the quality characteristic and its variability. The CUSUM scheme comprising a few cooperative CUSUM charts is quicker than the traditional Shewhart (X) over bar &S charts for this purpose. However, the designs and analyses of such a multi-chart CUSUM scheme are mathematically intractable and the operation is very laborious. Based on the Weighted Loss Function, this article proposes a CUSUM chart (called the WLC chart) that detects both mean shift and variance shift by inspecting a single statistic WL (Weighted Loss Function). The most useful feature of the WLC chart is its simplicity for implementation and design compared with the CUSUM scheme using a few CUSUM charts. This is mainly attributable to the use of a single statistic WL. Moreover, based on the results of a factorial experiment, it is found that the WLC chart is, on average, more effective than the (X) over bar &S charts and the multi-chart CUSUM scheme by about 30 and 14%, respectively. A step-by-step procedure is also presented to facilitate practitioners in designing the WLC chart.