Using CUSUM Charts To Detect Small Process Shifts

In order to monitor a process, quality practitioners frequently use Shewhart control charts (e.g. X –R, P-charts, etc.), so named after the pioneering work of Dr. Walter Shewhart. It can be shown that if there are sharp, intermittent changes to a process, these types of charts are highly effective. However, if one is interested in a small, sustained shift in a process, other types of control charts may be preferred, for example the Cumulative Sum (CUSUM) chart, originally developed by Page (1954). With exponential increases, an Exponentially Weighted Moving Average (EWMA) chart may be appropriate; for an example see Bower (2000). The CUSUM chart Though CUSUM charts have been well researched and developed, it is true that many quality practitioners do not use them, even though there may be justifiable reasons to make use of this technique for their process. Possibly this may be due to a lack of instruction on CUSUM charts in many classes on SPC. In practice, however, I find that many of these same quality practitioners play the game of golf; hence they are in fact already well versed in the technique behind CUSUM charts. In essence, for each hole in a round of golf, there are a specified number of times in which one should strike the ball, until it eventually drops into the hole. For example, on a par 4, if you strike the ball 4 times and it falls into the cup, then you held par. If you were able to do this task with only three shots (a “birdie”) then you are "1 under par" hence your cumulative sum is -1. This is continued throughout the course, the ultimate winner therefore having the lowest CUSUM. Picture a golfer who is holding par for the first 13 holes, then suddenly hits form and has five successive birdies towards the end of the round. The final CUSUM is therefore –5, though from viewing a CUSUM chart it would be clear to see when the “process” shifted.