Martha's Wonderful Cookie Company makes a special super chocolate-chip peanut butter cookie. Martha's used the number of chocolate chips as a proxy measure for the weight of chocolate chips in a cookie. The company would like the cookies to average approximately eight chocolate chips a piece and wants to base its statistical process control on eight chocolate chips per cookie. Too few or too many chips affect the desired cookie taste. Ten samples of five cookies each during a week have been taken and the chocolate chips counted. The sample observations are as follows:
Chips per cookie
Sample Cookie 1 Cookie 2 Cookie 3 Cookie 4 Cookie 5
1 7 6 9 8 5
2 7 7 8 8 10
3 5 5 7 6 8
4 8 8 5 10 8
5 7 6 9 8 4
6 7 6 5 4 5
7 9 10 8 9 7
8 11 9 9 10 6
9 5 5 9 8 8
10 6 8 8 5 9
Assume that we have sufficient data to prepare and analyze control charts.
a) Construct the appropriate control chart(s) to analyze the cookie-production process based on how the company is actually performing.
b) Comment on the cookie-production process based on the results of your control chart analysis.
c) Suppose it is industry standard practice for a chocolate chip cookie to have on average 4.5 to
7.5 chocolate chips. What would you conclude about this company's performance relative to the industry standards?
See excel, attached, for control chart. There are several ways to do the chart so this is just one way. Typically the chart would compare the sample averages to the desired level (8 chips) and make sure all sample means are within a corridor of three standard deviations from the desired 8-chip level. However, the process can be "out of control" by several standards, not just having a sample average outside the three standard deviation corridor. See ...
Your tutorial is 402 words plus a graph in Excel that is interpreted for you. Two references are provided. This is an informal control chart that permits you to view both the "three standard deviation corridor" and the pattern above and below the 8-chip standard.