Study On Statistical Process Control Methods For Monitoring An Event

While many control charts have been developed for monitoring the time interval between the occurrences of an event, many other charts are employed to examine the magnitude of the event. These two types of control charts have usually been investigated and applied separately with limited syntheses in conventional Statistical Process Control (SPC) methods. This study presents three SPC methods, for simultaneously monitoring the time interval and magnitude of an event. In this research, the time interval (denoted as T) follows an exponential distribution and the event magnitude follows a Poisson distribution (denoted as C) or gamma distribution (denoted as X).This study firstly presents a Shewhart-type control chart (called the rate chart or R chart) for simultaneously monitoring the time interval T and magnitude of an event. R chart is based on the ratio between the event magnitude and T. Our studies show that the R chart is more effective for detecting the out-of-control status of an event compared with an individual T chart or an individual C (or X) chart, in particular for detecting downward R shifts (sparse occurrence and/or small magnitude).A combined T&C (or T&X) chart is then developed for monitoring the time interval and magnitude of an event. It integrates a T chart and a C ( or X) chart. When the occurrence of an event is detected, the time interval T between the current and the last occurrences is checked and meanwhile the magnitude for the current occurrence is measured. Our studies show that the new chart is also more effective than an individual T chart or C (or X) chart, in particular for detecting downward R shifts.This study also proposes a Cumulative Sum (CUSUM) scheme, called the TC-CUSUM (or TX-CUSUM) scheme, for the monitoring of an event. This scheme is developed using a two-dimensional Markov model to evaluate the Average Time to Signal (ATS). It is able to check both the time interval between occurrences of the event and the magnitude of each occurrence. Our comparative studies show that the TC-CUSUM (or TX-CUSUM) scheme is more effective than the other two charts for event monitoring when there is a smaller shift in the magnitude of the event. The T&C (or T&X) chart outperforms other charts when there is a larger shift in the magnitude of the event. However, the R chart only performs best when there are prevailing T shifts for detecting downward R shifts. In order to have a more general and quantitative assessment of the relative effectiveness of the proposed charts, the average ratio AR of ATSs across the whole shift domain is calculated for each chart. Moreover, an average loss AL is proposed as a measure of the overall performance of the control charts for event monitoring.The proposed three charts have demonstrated the potential for both manufacturing systems and non-manufacturing sectors (e.g., health care industry, security management, reliability engineering), especially for the latter.