Quality Control Worksheet

ProblemThe data that follow (Table 1) give the number of nonconforming bearing and seal assemblies in
samples of size 100. Determine the control limits for the fraction and number of nonconforming
units these data.
Sample Number
Table 1
Number of
Sample Number
Nonconforming
Assemblies
Number of
Nonconforming
Assemblies
10
5
9
12345or∞a
10
11
2
12
8
13
11
16
14
10
17
15
13
6
7
16
8
7
18
17
23
8
29
18
13
13
19
2
10
9
20
13
Problem 2
An item is made in lots of 100 each. The lots are given 100% inspection. The record sheet for the first 15
lots inspected showed that a total of 55 items did not conform to specifications.
(a) Determine the trial control limits and the centerline for a p chart using 3-sigma control limits.
(b) What is the minimum lot size for this process to ensure that the chart has a positive lower control
limit?
Problem 3
In designing a fraction nonconforming chart with center line p = 0.3 and three-sigma control limits,
what is the value of n necessary to give a probability of 0.50 of detecting a shift in the process to 0.26?Problem 4
A control chart for nonconformities is to be constructed with c = 5.0, LCL=0, and UCL such that the
probability of a point plotting outside control limits when c = 5.0 is only 0.005.
(a) Develop the expression to calculate the UCL. Find the UCL.
(b) What is the type I error probability if the process is assumed to be out of control only when two
consecutive points fall outside the control limits?
Problem 5
In a textile finishing plant, dyed cloth is inspected for the occurrence of defects per 50 square meters. The
data on ten rolls of cloth are shown in Table 2. Use these data to set up a control chart for nonconformities
per unit. Construct the standardized control chart for nonconformities per unit.
Table 2
Roll #
# of Square
Meters
# of
Non-Conformities
1
500
14
2
400
15
3
650
20
4
500
9
5
475
10
6
500
11
7
600
21
8
525
13
9
600
21
10
625
23