QUESTION 1:
Suppose that products were randomly sampled from each of the 10 machines and their weights were measured in micrograms (????) as given in the table below.
Suppose the process standard deviation is to be estimated using sample standard deviations using 3-sigma criterion.
(a) Copy and complete the given table.
(b) Determine the control limits for X' chart.
(c) Construct the Shewhart X' chart.
(d) Using Shewhart decision rules, determine whether the process mean is in state of statistical quality control.
(e) If the process mean is out of statistical quality control, list all machines which are out of control.
(f) What is the estimate for the process mean?
(g) What is the estimate for the process standard deviation?
QUESTION 2:
Use the information given in question 1 to answer the following.
(a) Determine the control limits for ?? chart for the given data.
(b) Construct the ?? chart.
(c) Combining both X' chart and ?? chart, what would you advise the operations manager about machine 9?
QUESTION 3:
(a) Define in-quality-control Average Run Length (ARL0).
(b) Define out-of-quality-control Average Run Length (ARL1).
(c) Define Average Time to Signal (ATS).
(d) Control charts for ??' and ?? are in use with the following parameters:
The sample size is n = 9. Both charts exhibit control. The quality characteristic is normally distributed. The specifications on this quality characteristic are 358 ± 6.
i. What is the type I error associated with these charts?
ii. What percentage of all observations would be in nonconformance?
iii. What are your conclusions regarding the process capability?
iv. Determine and interpret the ARL0 for this process.
v. Determine and interpret the ATS for this process if the samples were observed every half hour.
vi. Suppose the process goes out-of-quality control by shifting its mean to 358.
Determine and interpret the ARL1 for this process.
vii. What would be the appropriate control limits for both of these charts if the type I error probability were to be 0.01?