Practice Problems: Supplement 6 (S6), Statistical Process Control
Problem 1:
Twenty-five engine mounts are sampled each day and found to have an average width of 2 inches,
with a standard deviation of 0.1 inches. What are the control limits that include 99.73% of the
sample means ( Z  3) ?
Problem 2:
Several samples of size n  8 have been taken from today’s production of fence posts. The average
post was 3 yards in length and the average sample range was 0.015 yard. Find the 99.73% upper
and lower control limits.
Problem 3:
The average range of a process is 10 lbs. The sample size is 10. Use Table S6.1 to develop upper
and lower control limits on the range.
Problem 4:
Based on samples of 20 IRS auditors, each handling 100 files, we find that the total number of
mistakes in handling files is 220. Find the 95.45% upper and lower control limits.
Problem 5:
There have been complaints that the sports page of the Dubuque Register has lots of typos. The last
6 days have been examined carefully and the number of typos/page is recorded below. Is the
process in control using Z  2?
Day
Number of Typos
Monday
2
Tuesday
1
Wednesday
5
Thursday
3
Friday
4
Saturday
0
1
ANSWERS:
Problem 1:

 2  3  0.1
UCLX  X  Z X  2  3 0.1
LCLX  X  Z X

25   2  0.06  1.94 inches
25  2  0.06  2.06 inches
Problem 2:
X  3 yds
R  0.015 yds
A2 = 0.373 from Table S6.1
UCL  X  A2 R  3  0.373(0.015)  3.006 yds
LCL  X  A2 R  3  0.373(0.015)  2.994 yds
Problem 3:
From Table S6.1, D4 = 1.78 and D3 = 0.22
UCLR  D4 R  (1.78)(10)  17.8 lbs
LCLR  D3 R  (0.22)(10)  2.2 lbs
Problem 4:
P
Total number of mistakes
220

 0.11
Total number of files
(100)(20)
P 
(011
. )(1  011
. )
 0.03
100
UCLP  P  z P  0.11  (2)(0.03)  0.17
LCLP  P  Z P  0.11  (2)(0.03)  0.05
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Problem 5:
C  15 6  2.5
UCLC  C  2 2.5  2.5  2(1.58)  5.66
LCLC  C  2 2.5  2.5  2(1.58)  0.66 (or 0)
As none of the observations are outside the control limits, the process is in statistical control.
However, it might be a worthwhile effort to investigate why no typos were made on Saturday. We
would like to better understand this effort so it can be repeated on other days.
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