Problem 1

An automatic filling machine is used to fill two-litre bottles of cola. The machine's output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of .01 litres. Output is monitored using means of samples of five observations.

a)Determine the two-sigma upper and lower control limits for the sample means.

b)If the means for 6 samples are: 2.005, 2.001, 1.998, 2.002, 1.995, and 1.999, is the process in control?

Problem 2

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

a)Determine the mean of each sample.

b)Estimate the mean of the process.

c)Calculate the standard deviation of the sample means (assuming that the estimate of the std. deviation of the process is 0.192).

d)What are the Three Sigma control limits for the sample mean?

e)Using the control limits of 3.14 and 3.86, are any sample means beyond these control limits? If so, which one(s)?

f)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)?