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Because the most common types of measures involve variables data we will discuss the XmR control chart in this chapter.
FIGURE 22.11. GROSS ANATOMY OF AN XMR CHART.
X-bar
Moving Range
The XmR chart is both versatile and relatively easy to make. The calculated control limits use simple formulas that require only basic arithmetic (adding, subtracting, multiplying, and dividing) and nothing more. An excellent book that introduces both control chart thinking and the use of the XmR chart is Understanding Variation, by Donald Wheeler (1993); it is a good book for novices to read to gain insight and practical knowledge on the topic of control charts.
Figure 22.11 shows the basic anatomy of an XmR control chart. It is made by using a pair of trend charts. The upper chart (the X-bar display) shows each value and its average over time. The lower chart (the moving range display) shows the amount of difference between successive points and their average difference, each from its predecessor, over time. An example of an actual XmR chart for fasting blood glucose levels in an individual patient is shown in Figure 22.12.
How Do You Make an XmR Control Chart?
You can use the data collection worksheet (Figure 22.5) to turn your run chart into an XmR control chart. Instructions are summarized on the worksheet and discussed in more detail here:
FIGURE 22.12. XMR CHART SHOWING FASTING BLOOD SUGAR VARIANCE IN ONE PATIENT OVER ONE MONTH.
FIGURE 22.12. XMR CHART SHOWING FASTING BLOOD SUGAR VARIANCE IN ONE PATIENT OVER ONE MONTH.
1. Specify the name of your measure (variable, for example, systolic blood pressure), the unit of measure (for example, mm) and the method of measurement.
2. Enter your data:
a. The first two rows provide space for entering the data and the time of data collection and can be used when helpful.
b. Row 3 provides space for entering the value of each measurement that you take.
3. Do these calculations:
a. Moving range. Row 4 provides space to enter the moving range. This is done by calculating the absolute value of the difference between each two time-ordered points: that is, the difference between Points 1 and 2, then the difference between Points 2 and 3, then the difference between Points 3 and 4, and so forth.
b. Average =Xbar. The sum of the measures in Row 3 divided by the number of measures listed in Row 3 (the sum of the As divided by the total number of X's).
c. Average range = R bar. The sum of the measures in Row 4 divided by the number of moving ranges in Row 4 (the sum of the R's divided by the total number of R's).
d. Upper natural process control limit (UCL) = Xbar + (2.66 X R bar).
e. Lower natural process control limit (LCL) = Xbar - (2.66 X R bar).
f. Upper control limit for moving range = UCLR.
4. Plot your data for the upper chart showing the time trend for your measures (values of X), keeping in mind that the upper and lower control limits must fit onto the chart:
a. Plot the data for each point in time order (all the X's), and connect the dots.
b. Draw the center line, using the average value of all the X's (Xbar).
c. Draw in the upper control limit for X, using a dotted line.
d. Draw in the lower control limit for X, using a dotted line.
5. Plot your data for the lower chart, showing the time trend for the moving range between your measures (values of R):
a. Plot the data for each point in time order (all the R's), and connect the dots, keeping in mind that the upper control limit must fit onto the chart.
b. Draw in the center line using the average value of all the R's (R bar).
c. Draw in the upper control limit for R (UCLr), using a dotted line; there is no lower control limit for the moving range because absolute values are used to show point-to-point variation.
6. Interpret the results by studying them and understanding the patterns; use the common rules for interpreting control charts.
7. Overlay the target value (on the upper chart) for the measure that you have set as a performance goal and determine whether your system has or has not yet reached the desired level or whether you are approaching the target level.
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