Problem:
Martha's Wonderful Cookie Company makes a special super chocolate-chip peanut butter cookie. The company would like the cookies to average approximately eight chocolate chips apiece. Too few or too many chips distort the desired cookie taste. Twenty samples of five cookies each during a week have been taken and the chocolate chips counted. The sample observations are as follows:
| Sample |
Chips per Cookie |
| 1 |
7 |
6 |
9 |
8 |
5 |
| 2 |
7 |
7 |
8 |
8 |
10 |
| 3 |
5 |
5 |
7 |
6 |
8 |
| 4 |
4 |
5 |
9 |
9 |
7 |
| 5 |
8 |
8 |
5 |
10 |
8 |
| 6 |
7 |
6 |
9 |
8 |
4 |
| 7 |
9 |
8 |
10 |
8 |
8 |
| 8 |
7 |
6 |
5 |
4 |
5 |
| 9 |
9 |
10 |
8 |
9 |
7 |
| 10 |
11 |
9 |
9 |
10 |
6 |
| 11 |
5 |
5 |
9 |
8 |
8 |
| 12 |
6 |
8 |
8 |
5 |
9 |
| 13 |
7 |
3 |
7 |
8 |
8 |
| 14 |
6 |
9 |
9 |
8 |
8 |
| 15 |
10 |
8 |
7 |
8 |
6 |
| 16 |
5 |
6 |
9 |
9 |
7 |
| 17 |
6 |
10 |
10 |
7 |
3 |
| 18 |
11 |
4 |
6 |
8 |
8 |
| 19 |
9 |
5 |
5 |
7 |
7 |
| 20 |
8 |
8 |
6 |
7 |
3 |
Required:
Question 1) Construct an /x chart in conjunction with an R-chart using 3? limits for this data.
Question 2) What is the mean of the x-chart?
Question 3) What is the average range of the data?
Question 4) What is the UCL of the x-chart?
Question 5) Does the process appear to be in control?
Provide detailed solution of the given problem.