How SPC Enhances Budgeting and Standard Costing-Another Look

THE AUTHORS EXAMINE A STATISTICAL PROCESS CONTROL EXAMPLE AND COME TO A NEW CONCLUSION ABOUT WHAT CONSTITUTES BEING "IN CONTROL" OR STABLE. The Fall 2000 issue of Management Accounting Quarterly contained an article by Harper Roehm, Larry Weinstein, and Joseph Castellano titled "Management Control Systems: How SPC Enhances Budgeting and Standard Costing." In that article, the authors make a good point that setting unattainable targets is not really conducive to improvement efforts. One may, as the authors suggest, use the average value of past performance as the "standard." Or, alternatively, one might set the target slightly higher than the average of past performance to provide a driving force for continuous improvement. In either case, it is important that the process be stable in order to have confidence that the use of the average value as the standard is meaningful. The authors applied a Statistical Process Control (SPC) technique, an X-Moving Range Chart, to test the stability of productivity data for J&J Inc.'s widget production. From their analysis, they conclude that their process is "in control" (stable) with an average value of 55 units produced per hour using 40 workers. This value, they suggest, should be adopted as the standard rather than the current standard of 60. The data used in their analysis are shown as Table 1. We present an alternate analysis and conclusion. We believe there is no statistically significant difference between the production levels of the two shifts. Thus, keeping the shift information may cloud our view of what is happening on a day-to-day basis. We will use the total daily production for our analysis of "in control" (or stability). The X-Moving Range Chart for total daily production is shown in Figure 1. All the data points are indeed within the control limits, but unusual patterns in the data set also imply that the process is not stable. Unusual patterns observed in a data set indicate that nonrandom events have occurred even if all of the data points are within the control limits.1 Knowledge of the behavior of chance variations is the foundation on which control chart analysis rests. If the observed data produce a variation that conforms to a statistical pattern that might reasonably be produced by chance causes, then we presume that no assignable, and therefore no controllable, causes are present. On the other hand, if the variation in the data produces a discernable pattern, then we conclude that there are one or more assignable or controllable causes within the production environment. In the article being discussed, the last eight days of production were below the average value of 110, and the previous seven days were all above the average.2 This is a strong signal that the process is not stable. The probability of eight points consecutively below the average is about 0.008 (see Table 2 for the derivation of the value of the probability of 0.008). The probability of a pattern of seven consecutive points above the average followed by a pattern of eight below the average from a random process is considerably less than 0.008. Hence, one must conclude that there are nonrandom events occurring in the production process described in the article. This means that management should investigate the possible causes for the unusually high and unusually low production periods. Management also should identify the reasons for the high production periods and implement changes to make high production permanent (assuming that the quality level is not compromised) and should identify the reasons for low production and implement changes to avoid such periods in the future. Causes for these changes might be different raw materials, different work teams, different products, and the like. A more complete database including such factors would be of great assistance in determining the root causes of these nonrandom events. But let's explore this another way to see if the signals of instability we just mentioned are real. …