Question 4.

A key step in the manufacturing of interior doors is drilling holes for the know. The desired diameter is 2 and 1/8 inches. A local manufacturer had collected the following data for quality control purposes. They collected seven samples with five measurements in each. The table below contains the data.

	Samples
	1	2	3	4	5	6	7
Measurement 1	2.145	2.155	2.105	2.135	2.095	2.135	2.135
Measurement 2	2.155	2.155	2.155	2.155	2.145	2.115	2.125
Measurement 3	2.145	2.095	2.135	2.115	2.095	2.155	2.135
Measurement 4	2.115	2.125	2.105	2.095	2.095	2.105	2.145
Measurement 5	2.125	2.135	2.095	2.155	2.155	2.145	2.155

1. Please calculate the upper and lower control limits for the Xbar and R charts the company can use to monitor if the process is remaining in control. Please specify the upper and lower control limits and the centerline for each type of chart.

2. A few weeks later, the quality manager collected the following three samples. Is the process still in control? Please answer using the control charts you developed for part (i).

		Measurements
		1	2	3	4	5
Samples	1	2.125	2.125	2.155	2.095	2.095
2	2.115	2.115	2.155	2.115	2.135
3	2.105	2.125	2.145	2.145	2.155

Part b

The same manufacturer from part (a) would like to measure the capability of the drilling process. Their measurements indicate that the process is drilling holes with a mean of 2.123 inches and standard deviation of 0.0009 inches. Their customer specified the upper and lower specification limits as 2.128 and 2.122 inches.

1. Is the process capable of meeting the customer's standards? Please provide the necessary calculations (i.e., cp and cpk) to back your response.
2. After some process improvement efforts, the bottling process is now operating with a mean of 2.125 inches (standard deviation remained the same). Is the process in capable now? Please justify your answer.