Question

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 sampling. 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 given were recorded.

Sample OBS.1OBS.2OBS.3OBS.4 OBS.5 165.3 165.3 165.4 165.4 1 161.6 161.7 162.9 2 8 162.9 159.6 160.0 164.0 168 8.03 167.0 156.3 164,() 4 162.9 164.2 163.9 160.6 163.1 liil_а 3GEs.co 161 asano 163.2 157.0 161.2 164.5 158.4 161.3 164.7 162.5 163.6 15 163.6 164.5 ได้ 29 35129 155.0162.2 16 162.3 163.7 164 162.0 165.2 163.7 165.7 165.9 165.5 20 163.9 161.6 159.9 165.6 165.9 165.6 21 165.1 15O. 167.7 165.8 166.0 163.1 163.7 165.6 165.6 | 166.2 | 25

After analyzing the data by using statistical control charts, the T’Challa’s 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 X̅̅ = 163 grams R̅= 2.323 grams σ = 1 gram All sample observations were within the control chart limits. With the new data, Wakanda Forever’s 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 T’Challa’s 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 analysis, 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 analysis.

Answer 1

16 164.5 158.5 160.3 163.4 164.6 17 164.9 157.9 162.3 163.7 165.1 18 19 1621 163.9 165.1 159.3 162 20 165.2 159.1 161.6 163.9 165.2 21 164.9 165.1 159.9 162 163.7 22 1676 165.6 165.6 156.7 165.7 23 167.7 165.8 165.9 156.9 165.9 24 166 166 165.6 165.6 165.5 25 163.7 163.7 165.6 165.6 166.2 162.69 162.69 162.69 162.69 162.69 163.7163.12 162.69 162.69 162.69 162.69 162.69 4.1469 4.1469 4.1469 4.1469 4.1469 4.1469 4.1469 4.1469 4.1469 4.1469 166.8369 166.8369 166.8369 166.8369 166.8369 166.8369 166.8369 166.8369 166.8369 166.8369 16226 16278 16106 16248 163 13823 13823 13823 13823 13823 13823 13823 13823 13823 13823 155 1622 163.7 164.8 159.6 164.24 164.44 165.74 164.96