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 𝑋̅ 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 𝑋̿ of subgroup averages 𝑋̅.
Answer
𝑋̿ (average of subgroup averages 𝑋̅)
(1-2) Calculate the average 𝑠̅of subgroup standard deviation 𝑠.
Answer
𝑠̅(average of subgroup standard deviations 𝑠)
(1-3) Calculate the estimate 𝜎̂ of population standard deviation.
Answer
𝜎̂ (estimate of population standard deviation)
1-4
(1-4) Calculate the process capability index 𝐶𝑝.
Answer
𝐶𝑝
(1-5) Answer questions in the below table on this process.
Answer
Is this process capable in terms of 𝐶𝑝? Yes or No
Briefly explain reason of your above
answer
Explain
(1-6) Calculate the process capability index 𝐶𝑝�