Martha’s Wonderful Cookie Company in Problem 3.30 has designed its special super-chocolate-chip peanut butter cookies to have 8 chocolate chips with tolerances of ±2 chips. Using the process mean and control limits developed in Problem 3.30, determine the process capability ratio and index, and comment on the capability of the cookie production process. 

Data in Problem 3.30

Martha’s Wonderful Cookie Company makes a special superchocolate-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:

Construct an ^_x-chart in conjunction with an R-chart using 3σ limits for these data and comment on the cookie-production process.

Samples 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 7 7 5 4 8 7 9 7 9 11 5 6 7 6 10 5 6 11 9 8 Chips per Cookie 6 9 7 8 5 5 8 6 8 6 10 9 5 8 3 9 8 6 10 4 5 8 7 9 5 9 10 5 8 9 9 8 7 9 7 9 10 6 5 10 6 8 8 6 9 10 8 8 4 9 10 8 5 8 8 8 9 7 8 7 7 5 10 8 7 8 4 8 5 7 6 8 9 8 8 6 7 3 8 7 3