Question: Refer to the Milling Operation case in problem.
(a) For purposes of process monitoring only, let a target deviation from flatness be μ = 5, and suppose the process standard deviation is σ = 1.40, as in problem 54. (In functional terms a 0 deviation from flatness is ideal.) Compute control limits for individuals based on this set of standards. Give the center line and control limits.
(b) Plot the individuals from problem (b) using your new limits from (a). Does it appear that there has been a process change from standard conditions? Why or why not?
(c) Discuss the practical meaning of the terms "stability," "shift," and "out of control" in light of parts (b) and (d) of problem 54 and part (b) above.
Problem: Milling Operation. A student group studied a milling operation used in the production of a screen fixture mounting. Of primary importance was a "deviation from flatness" measurement. The units of measurement were .001 in. In the past, deviations from flatness had an average of 2.45 and a standard deviation of 1.40. What do the values of these and the fact that deviation from flatness cannot be negative suggest about the plausibility of a normal model for deviation from flatness? For what follows temporarily put aside any misgivings you might rightly have.
(a) Set up standards given control limits for process location. (Monitoring is to be done on the basis of subgroups of size one.)
(b) Ten consecutive mountings produced the deviation from flatness values below (units are .001 in).
.5, 4.5, 2.0, 2.0, 3.0, 3.0, 2.0, 4.5, 3.0, 0.0
Together with the limits in (a), use these data values to make a control chart for monitoring process aim. Has there been a process change away from the standards? Why or why not?
(c) Find the moving ranges of adjacent observations and the mean of these 10 observations.
(d) Make a retrospective individuals chart using the moving ranges and grand average of the 10 data values. Give the center line and control limits. What do you conclude based on this chart?