The Use of CUSUM-Charts for Identification the Technological Process Disorder at the Initial Stage

Abstract

The accumulated sum control charts use the data obtained at the current and at all previous control stages. The using of these charts allows to determine the moment when the process goes out of statistically controlled state with less delay than the Shewhart charts. However, the presence of a time delay between the occurred event and its detection on the control chart can lead to large production losses (sometimes irreparable losses). The article considers a new approach that allows to identify violations in the process at the initial stage. For this it was suggested to consider not the average values of sample results at control points, but the standard deviations at these points. Using Pearson statistics, the probabilities of finding the standard deviation in elementary intervals are determined, into which the area of permissible deviations is divided in a statically controlled process. The initial premise is the assumption that the output of the sample dispersion outside the range of tolerances at the control point is evidence that there are violations in the process. The probability of a control point falling beyond acceptable limits is the upper limit in the presence of violations in the process. This probability is a measure to detect violations at the initial stage. As a criterion, the number of consecutive control points falling in elementary intervals was selected. The probability of such a complex event should be less than the value of the measure to identify violations in the process. A concept is introduced and a critical number of points is determined. The efficiency of identifying process violations is determined. Recommendations on the use of the results are given.