6.19) Samples of n = 4 items are taken from a process at regular intervals. A normally distributed quality characteristic is measured, and x-bar and s values are calculated at each sample. After 50 subgroups have been analyzed, we have Σ x̄i = 1,000 and Σ si = 72
a) Compute the control limit for the x-bar and s charts
b) Assume that all points on both charts plot within the control limits. What are the natural tolerance limits of the process?
c) If the specification limits are 19+/-4, what are your conclusion regarding the ability of the process to produce items conforming to specifications?
d) Assuming that if an item exceeds the upper specification limit it can be reworked and if it is below the lower limit it must be scrapped, what percent scrap and rework is the process now producing?
e) A If the process were centered on at u = 19.0, what would be the effect on the percent scrap or rework?
6.46) Control charts for x bar and s are maintained on a quality characteristic. The sample size is n=4. After 30 samples, we obtain
∑ ¯xi=12,870 and ∑ sj=410
A. Find the centerline and three sigma control limits for the s chart.
B. Assuming that both charts exhibit control, estimate the parameters μ and σ