Proctor & Gamble (P&G), the manufacturer of Crest toothpaste, is considering subcontracting with a new vendor, Guangzhou Packaging, to provide the caps for their travel-size toothpaste containers. Their first step is to determine if Guangzhou Packaging's cap manufacturing process is able to consistently produce caps of the same dimensions or if their manufacturing process has a lot of variation in it. Therefore, P&G went to the Guangzhou Packaging manufacturing facility and, over the course of 3 days, took 10 samples of 7 caps each. They measured each cap (in millimeters) and put the measurements in a table as shown below.

Use the data collected to answer the following questions. Carry calculations out to at least 2 decimal places. Show your calculations.

a) What is type of control chart(s) should be constructed to completely assess the variation in this process based on the data provided in the table below (i.e., c, p, X-bar, and/or R)? Explain your answer. (4)

b) Calculate the control limits (show your calculations) and construct the control chart(s) making sure all

control chart elements are present. The spacing between the control limits should be wide enough to easily read all data points plotted. (10) Note: The control chart(s) may be created in Excel; however, clear, easy to read copies must be embedded as a picture in your test document.

c) Is the process in control? Explain your answer. (5)

Sample Cap1 Cap2 Cap3 Cap4 Cap5 Cap6 Cap7

1 7.5 2 6.3 3 7.0 4 5.4 5 5.3 6 5.4 7 5.4 8 6.7 9 7.1

10 7.2

8.1 8.0 6.2 6.8 7.0 6.2 5.7 6.9 7.6 5.8 6.4 5.5 6.5 6.0 6.9 7.5 7.8 6.5 5.3 7.0

7.7 7.6 7.7 7.6 7.5 6.8 6.9 5.7 7.6 6.1 5.1 6.4 6.6 8.3 5.4 7.6 6.0 6.9 7.4 5.2

7.2 5.4 6.0 7.7 5.1 8.2 6.8 8.3 7.4 8.0 7.1 6.3 7.9 6.8 5.0 7.5 8.3 7.3 5.8 5.9

The second step in the evaluation is to determine if

the process is capable of meeting P&G's cap specification.

d) Given that P&G's specification for the caps is 6.5mm 1.0mm, calculate the appropriate capability metrics. Show your calculations. Round calculations to 3 decimal places. (6)

e) Comment on the process' capability of meeting P&G's specification. Provide a thorough interpretation of your response. (5)