This month, we will continue our discussion on the use of control charts for setting key performance indicator (KPI) threshold levels. In the past two columns, we discussed the concepts of variation and x-bar control charts in detail. The final piece of the puzzle is the KPI range chart which tracks the sample variation of the process being captured by the KPIs. The KPI range chart can then be combined with the KPI x-bar chart (see the May 2005 issue of DM Review, p. 8) to understand whether the existing KPI metrics (and the processes they monitor) are stable and in control. As you may recall, when a series of KPI metrics are analyzed, the variation comes from two sources: variation between the individual subgroup samples as captured by differences in the KPI means (the x-bar chart) and variations within the individual subgroup samples as captured in the KPI standard deviation (the range chart). Statistical control requires that both sources of variation be in control and that the KPI range be in control first (i.e., control variance within samples before controlling variance across samples).

Figure 1: Range Control Chart

Range Chart Elements

The basic elements of the x-bar chart - the centerlines and control limits - are also employed in development of the range chart. In the process of creating both KPI x-bar and range control charts, sample observations are collected into subgroups of two or more observations. Associated with each subgroup is a range which is simply the difference between the largest and smallest value in a subgroup sample. This range (R-bar) is then the average range for each subgroup and is plotted on the KPI range chart as the centerline (see Figure 1: Range Control Chart). The lower control limit (RLCL) and upper control limit (RUCL) are then calculated by multiplying the range by the "control limit factors" (D3 and D4 respectively) that are dependent on the subgroup sample size. For example, the RUCL for a sample size of four = 2.28 x R-bar (see Figure 2: Control Limit Factor Table).

Figure 2: Control Limit Factor Table

Control Chart Tests and Implications

With the range chart control limits now in place, points plotted on the chart can be used to determine the stability of the KPI metric. A portfolio of statistical and pattern detection rules is available to alert management to any problems concerning range stability. Several examples of these rules follow:

A KPI range visual would appear red if any of the following conditions occurred:

Individual data points rules:

  • Any individual KPI subgroup range outside upper or lower control limits.

Trend rules:

  • Any run of 7 consecutive KPI subgroup ranges above or below the centerline.
  • Any run of 7 consecutive KPI subgroup ranges upward or downward.
  • Any pattern with 2/3 of KPI subgroup ranges in the middle 1/3 of the control limits.
  • Any pattern with 2/3 of KPI subgroup ranges in the outer 2/3 of the control limits.

Alternatively, a KPI range visual would appear green if none of these criteria are met. It is essential to interpret the range chart before the x-bar chart. If the range chart is not in control, then no meaningful information and insight can be leveraged from the x-bar chart.Next month, we will illustrate how both x-bar and range control charts can assist development and tracking of KPI metrics in the hospitality industry.

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