Interpreting Charts for Individual Measurements and Moving Ranges

IRCHART Statement

Interpreting Charts for Individual Measurements and Moving Ranges

Montgomery (1996) points out that a moving range chart should be interpreted with care because "the moving ranges are correlated, and this correlation may often induce a pattern or runs or cycles on the chart." For this reason Nelson (1982) recommends against plotting the moving ranges. Nelson notes that the assumption of normality is more critical for an individual measurements chart than for an $\bar{X}$ chart. You can use the NOCHART2 option in the IRCHART statement to specify that only the individual measurements chart is to be displayed. See Example 34.3 for an illustration. If, instead, you specify the SEPARATE option, the charts for individual measurements and moving ranges are displayed on separate screens.

An alternative method for creating an individual measurements chart is to use the XCHART statement, which uses an estimate of $\sigma$ based on moving ranges of two consecutive measurements when the subgroup sample sizes are all equal to one. Note that the XCHART statement displays the control limit legend n=1 to indicate the common subgroup sample size, whereas the IRCHART statement displays a legend that indicates the number of consecutive measurements used to compute the moving ranges (the "pseudo subgroup sample size").

Nelson (1982) explains that the reason for estimating the process standard deviation $\sigma$ from moving ranges of two consecutive measurements rather than the sample standard deviation of the measurements is that "the moving range of two minimizes inflationary effects on the variability which are caused by trends and oscillations that may be present." Nelson suggests that any moving range that exceeds 3.5 times the average moving range should be removed from the calculation of the average moving range.

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