a) Colonial Electric is a large company that produces lightbulbs and other electrical appliances. One particular lightbulb is supposed to have an average life of about 1,000 hours before it burns out. Periodically the company will test 5 of these and measure the average time before these burn out. The following table gives the result of 10 such samples:

Sample 1 2 3 4 5 6 7 8 9 10
Mean 979 1087 1080 934 1072 1007 952 986 1063 958
Range 50 94 57 65 135 134 101 98 145 84

1. What is the overall average of these means? What is the average range?

2. What are the upper and lower control limits for a 99.7% control chart for the mean?

3. Does this process appear to be in control? Explain.

4. Explain why a process can be out of control even though all the samples fall within the upper and lower control limits.

b) Claire Underwood has been concerned about Machine 8 at the Collard Factory. To make sure that the machine is operating correctly samples are taken and the average and the range of each sample is calculated. Each sample consists of 12 items produced from the machine. Recently, 12 samples were taken and for each the sample range and average were calculated. The sample range and sample average were 1.1 and 46 for the first sample, 1.31 and 45 for the second sample, 0.91 and 46 for the third sample, and 1.1 and 47 for the fourth sample. After the fourth sample the sample averages increased. For the fifth sample the range was 1.21, and the average was 48; for sample 6, it was 0.82 and 47, for sample 7 it was 0.86 and 50, for sample 8 it was 1.11 and 49. After the eight sample the sample average continued to increase never getting below 50. For sample 9 the range and average were 1.12 and 51; for sample 10 they were 0.99 and 52; for sample 11 they were 0.86 and 50 and for sample 12 they were 1.2 and 52.

Although Claire's boss wasn't overly concerned, Claire was. During installation the supplier had set a value of 47 for the process average and an average range of 1.0. It was Claire's feeling that something was definitely wrong with machine number 8. Do you agree? Explain your view.