Figure 6.25a shows a casting used in a gas turbine jet aircraft engine. This part is typical of those produced by both casting and machining processes for use in gas turbine engines and auxiliary power units in the aerospace industry—cylindrical parts created by rotating the cross section around a central axis. The vane height on this part is a critical quality characteristic. Data on vane heights are collected by randomly selecting five vanes on each casting produced. Initially, the company constructed
and s control charts on these data to control and improve the process. This usually produced many out-of-control points on the chart, with an occasional out-of-control point on the chart. Figure 6.26 shows typicaland s charts for 20 castings. A more careful analysis of the control-charting procedure revealed that the chief problem was the use of the five measurements on a single part as a rational subgroup, and that the out-of-control conditions on the chart did not provide a valid basis for corrective action. Remember that the control chart for deals with the issue of whether or not the between-sample variability is consistent with the within-sample variability. In this case it is not: The vanes on a single casting are formed together in a common wax mold assembly. It is likely that the vane heights on a specific casting will be very similar, and it is reasonable to believe that there will be more variation in average vane height between the castings. This situation was handled by using the s chart in the ordinary way to measure variation in vane height. However, as this
FIGURE 6.2 5 An aerospace casting.
FIGURE 6.26 Typical
andscontrol charts (from Minitab) for the vane heights of the castings in Fig. 6.26.
standard deviation is clearly too small to provide a valid basis for control of , the quality engineer at the company decided to treat the average vane height on each casting as an individual measurement and to control average vane height by using a control chart for individuals with a moving range chart. This solution worked extremely well in practice, and the group of three control charts provided an excellent basis for process improvement. Figure 6.27 shows this set of three control charts as generated by Minitab. The Minitab package generates these charts automatically, referring to them as “between/within” control charts. Note that the individuals chart exhibits control, whereas the chart
in Fig. 6.26 did not. Essentially, the moving range of the average vane heights provides a much more reasonable estimate of the variability in height between parts. The s chart can be thought of as a measure of the variability in vane height on a single casting. We want this variability to be as small as possible, so that all vanes on the same part will be nearly identical. The paper by Woodall and Thomas (1995) is a good reference on this general subject.
FIGURE 6.27 Individuals, moving-range, andscontrol charts for the vane heights of the castings in Fig. 6.25.