Process capability indices
Process capability indices using subgroup averages and standard deviations
A quality engineer collected process data for five subgroups with each subgroup consisting of four
samples (n=4). The averages and standard deviations of samples in each subgroup are summarized in
Table 1 below. The upper specification limit (USL) of the process is 13.05 and the lower specification
limit (LSL) is 12.95.
Table 1. Subgroup Data
Subgroup 1 2 3 4 5
Average πΜ
13.01 12.97 13.00 12.99 12.98
Standard deviation s 0.04 0.02 0.03 0.04 0.02
(1-1) Calculate the average πΜΏ of subgroup averages πΜ
.
Answer
πΜΏ (average of subgroup averages πΜ
)
(1-2) Calculate the average π Μ
of subgroup standard deviation π .
Answer
π Μ
(average of subgroup standard deviations π )
(1-3) Calculate the estimate πΜ of population standard deviation.
Answer
πΜ (estimate of population standard deviation)
1-4
(1-4) Calculate the process capability index πΆπ.
Answer
πΆπ
(1-5) Answer questions in the below table on this process.
Answer
Is this process capable in terms of πΆπ? Yes or No
Briefly explain reason of your above
answer
Explain
(1-6) Calculate the process capability index πΆποΏ½