Problem 1

A technician in a quick oil change shop had the following service times (in minutes) for 20 randomly selected cars:

		Sample
1	2	3	4
3.4	3.5	3.4	3.6
3.1	3.4	3.5	3.5
3.1	3.3	3.3	3.7
3.2	3.6	3.3	3.4
3.2	3.2	3.5	3.8

1. Determine the mean of each sample.
2. Estimate the mean of the process.
3. Calculate the standard deviation of the sample means (assuming that the estimate of the std. deviation of the process is 0.192).
4. What are the Three Sigma control limits for the sample mean?
5. Using the control limits of 3.14 and 3.86, are any sample means beyond these control limits? If so, which one(s)?
6. Construct the control charts for sample mean and sample range using the Alternate method (table provided on slide 19). Are any sample means and ranges beyond the control limits? If so, which one(s)?

Problem 2

The administrator of a small town received a certain number of complaints during the last two weeks.

1. Construct a control chart with Three Sigma limits for the number of complaints received each day using the following data. Is the process in control?

2. If 16 complaints are received today (day 15), using the control chart of part a, is there a change in the average number of complaints per day?

	Day
	1	2	3	4	5	6	7	8	9	10	11	12	13	14
Number of complaints	4	10	14	8	9	6	5	12	13	7	6	4	2	10