Question: A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are in control with regard to

A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are in control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:

Machine Measurement Measurement Measurement Measurement
#1 17 15 15 17
#2 16 25 18 25
#3 23 24 23 22

a. What is the sample mean for machine #1?

b. What is the estimate of the mean of the sampling distribution for the sample mean?

c. What is the estimate of the sample average range based upon this limited sample?

d. What are the x-bar chart three-sigma upper and lower control limits?

e. For upper and lower control limits of 23.29 and 16.71, which machine(s), if any, appear(s) to have an out-of-control process mean?

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