Economic Comparisons of Control Charts

Article

Lorenzen, Thomas J.; Vance, Lonnie C.   (1986, ASQC)   General Motors Research Laboratories, Warren, MI

40th Annual Quality Congress, May 1986, Anaheim, CA    Vol. 40    No. 0
QICID: 3188    May 1986    pp. 255-263
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Article Abstract

Statistical process control represents a fundamental set of tools for achieving and maintaining quality and for increasing productivity. One of the primary tools is the statistical quality control chart. The basic chart methodology consists in sampling from a process over time and charting some measurement such as the mean of a continuous process. The X-chart, because of its simplicity and ease of operation, has been in use for 60 years. However, other charts such as cumulative sum (cusum) control charts and geometric moving average control charts have gained in popularity recently, primarily because it is believed they are more efficient in detecting small shifts in the process.Recently, Lorenzen and Vance (1986) have developed a unified approach to the economic design of control charts. A general process model is given and the choice of control chart parameters -- sample size, sampling interval, and control limits -- are chosen to minimize an hourly cost function. This allows use of the same general process model for economically designing different types of control charts.The purpose of this report is to make comprehensive comparisons of the X, cusum, and geometric moving average charts using cost as the criterion. Cost is used because it is easily understood by non-statisticians and is the "yardstick" used by most corporations.Sensitivity analyses are performed to quantify the sensitivity of these charts to process parameter changes such as the amount of shift in the process level that should be detected. In particular, the cost for using a non-optimal choice of sample size is calculated for each chart.The optimum costs for the cusum chart are slightly lower than that for X-chart. The geometric moving average (with r=0.25) chart costs are generally higher than those for the X chart. For small shifts in the process level, the cusum and geometric moving average (r=0.25) charts have smaller costs for the stored design values than the X-chart. Costs for the optimum designs are nearly the same for the X and cusum charts and slightly higher for the geometric moving average charts except for shifts in process level around 0.5.

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