As indicated in Section 11.7.2, the R-chart will undoubtedly continued to be used extensively, despite its shortcomings, especially when 3-sigma limits are used. Therefore, construct the R-chart with 3-sigma limits for the data in Example 11.4, using appropriate software since the expressions used for computing the 3-sigma limits were not given.

 

Example 11.4

A study was performed on the mass of polyvinyl chloride (PVC) bottles produced on a blow molding machine. The study was motivated by records that showed insufficient production of bottle units for PVC consumption. The study was performed for one month and the data that were recorded were on PVC consumption, actual production, and expected production based on a desired nominal mass. This study led to significant savings and motivated a study of the blow molding machine. The variation in the bottle mass was of particular interest. An initial study was performed that consisted of samples of five consecutive bottles drawn from each of the two molds every 15 minutes. This resulted in 14 subgroups of size 5, which unfortunately is short of the minimum number of 100 observations that are preferred to be used to compute the initial control limits, as discussed in Section 11.2. It would have been better if more observations had been used so that the control limits could have been estimated with greater precision, especially since there was considerable variation in the subgroup averages when an X-chart was constructed, which here is shown in Figure 11.6. (The data, given below, are used with the permission of H. M. Wadsworth.)