This month, we will continue our discussion on the use of control charts for setting key performance indicator (KPI) threshold levels. In its basic form, the control chart is a simple plot of a time sequence of group statistics (i.e., KPI data points). The points are then compared to control limits (i.e., KPI threshold levels), which capture the bandwidth of the variation due to the common causes (see April 2005, p. 47). As long as the KPI data points are within the control limits, then the underlying process being measured is statistically in control. This concept can also be used to develop KPI warning limits.

As you may recall from your college Stat 101 course, stable business process outputs are randomly distributed with a mean µ and a variance s2 (or standard deviation of s). The baseline on the control chart is typically the arithmetic mean for all the KPI sample data plotted. If the outputs are normally distributed, it is a well-known statistical result that 99.74 percent of these output averages are within three standard deviations of the mean. In statistical parlance, the three standard deviations are referred to as the upper control limit (UCL) at +3s or the lower control limit (LCL) at -3s. In addition, there are also upper warning limits (UWLs) at +2s and lower warning limits (LWLs) at -2s that capture 95.0% of the output averages (or KPIs). The control and warning limits will be extremely helpful in identifying KPIs that are out of control, KPIs that are experiencing problematic trends and KPIs that are within the allowable process variability. The basic elements of the control chart are illustrated in Figure 1. In addition to this x-bar chart, a companion range chart can also provide information about the spread of the sample KPI metrics. Figure 1: KPI x-bar Control Chart

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