After comparing the R values obtained in Step 3 with the control limits for the R-chart ([LCL.sub.R] = 0, [UCL.sub.R] = 4.698) and [bar.x] values with the control limits for the [bar.x]-chart ([LCL.sub.[bar.x]] = -1.5, [UCL.sub.[bar.x]] = 1.5), the proportion of values falling below LCL ([P.sub.L)] and above UCL ([P.sub.U)] were determined for each chart.
For both stratified and random sampling methods, the R-chart is found to be more sensitive than the [bar.x]-chart in detecting the shifts of different magnitude in the mean of a single stratum.
The R-chart shows higher sensitivity in detecting shifts in a single stratum mean under stratified sampling when compared to random sampling.
We define it as the threshold shift level ([[delta].sub.threshold] = 3.5[[sigma].sub.x]) where the relative superiority of R-chart under stratified sampling gets balanced by that of [bar.x]-chart under random sampling.
It is due to the relative superiority of R-chart for stratified sampling plan far exceeding that of [bar.x]-chart for random sampling when 3.5 < 5 [less than or equal to] 6.
There are several variations of the R-chart. First, it is possible to construct an R-chart using individual data, although reservations have been expressed concerning the accuracy of this chart (Doty, 1996; Ostle et al., 1996).
If the outcome is continuous, an X-mR-chart or m [bar]X-mR-chart should be used if the sample sizes equal 1 (the latter with a slowly changing, more variable process), an [bar]X-R-chart and R-chart should be used if the sample sizes are equal and range from 2 through 10, and an [bar]X-S-chart and S-chart should be used if the sample sizes are equal and greater than 10.
Thus far, we have developed spreadsheets for the X-mR-chart, [bar]X-R-chart, R-chart, p-chart, and c-chart.
SPSS allows the user to select among four categories of SPC charts: (1) [bar]X-R-charts, [bar]X-S-chart, R-charts, and S-charts; (2) X-mR-charts and mR-charts; (3) p-and np-charts; and (4) c- and u-charts.