Question 2
Beaver Brothers, Inc., is conducting a study to assess the capability of its 150-gram bar soap
production line. A critical quality measure is the weight of the soap bars after stamping. The
lower and upper specification limits are 162 and 170 grams, respectively. As a part of an
initial capability study, 25 samples of size 5 were collected by the quality assurance group
and the observations in Table 3.7 were recorded.
After analyzing the data by using statistical control charts, the quality assurance group
calculated the process capability ratio, Cp, and the process capability index, Cpk. It then
decided to improve the stamping process, especially the feeder mechanism. After making all
the changes that were deemed necessary, 18 additional samples were collected. The summary
data for these samples are
1
s = 1 gram
All sample observations were within the control chart limits. With the new data, the quality
assurance group recalculated the process capability measures. It was pleased with the
improved Cp but felt that the process should be centered at 166 grams to ensure that
everything was in order. Its decision concluded the study.
a. Draw the control charts for the data obtained in the initial study and verify that the
process was in statistical control.
b. What were the values obtained by the group for Cp and Cpk for the initial capability
study? Comment on your findings and explain why further improvements were necessary.
c. What are the Cp and Cpk after the improvements? Comment on your findings, indicating
why the group decided to change the centering of the process.
d. What are the Cp and Cpk if the process were centered at 166? Comment on your findings.