| While many control charts have been developed for monitoring the time interval (t) between the occurrences of an event, many other charts are employed to examine the size (c) 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 article presents two SPC methods, t&c chart and r chart, for simultaneously monitoring the time interval t and size c. Essentially, a t&c chart combines a t chart and a c chart, and r chart is based on the ratio between c and t. In this article, t follows an exponential distribution and c follows a Poisson distribution.In this study, t chart, c chart, t&c chart and r chart are first designed. Control limits and Average Time to Signal (ATS) of every chart are evaluated. These four charts are operated as follows: (1) detection of upward r shifts (increasing c and/or decreasing t), (2) detection of downward r shifts (decreasing c and/or increasing t). In this paper a program is written to calculate ATS of four control charts when t or c shifts. In order to have a more general and quantitative assessment of the relative effectiveness of the charts, the average of the ratios of ATS values across the whole shift domain is calculated for each chart.Both t&c chart and r chart are more effective than an individual t chart or individual c chart for detecting the out-of-control status of the event, in particular for detecting downward shifts. Compared with t&c chart, r chart performs well especially for detecting upward shifts. More profound is that, comparing with an individual t or c chart, t&c chart and r chart perform more uniformly for detecting both t shift and c shift, as well as the joint shift in t and c. The t&c chart and r chart have demonstrated their potential not only for manufacturing systems, but also for non-manufacturing sectors such as supply chain management, office administration and health care industry. |
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