Quality control

Quality Control

Slide 1

Shakeel Nouman
M.Phil Statistics

Quality Control By Shakeel Nouman M.Phil Statistics Govt. College University Lahore, Statistical Officer

13

Slide 2

Quality Control

• Using Statistics
• W. Edwards Deming Instructs
• Statistics and Quality
• The x-bar Chart
• The R Chart and the s Chart
• The p Chart
• The c Chart
• The x Chart
• Summary and Review of Terms

13-3 Statistics and Quality

Slide 3

A control chart is a time plot of a statistic, such as a sample mean, range,
standard deviation, or proportion, with a center line and upper and lower
control limits. The limits give the desired range of values for the statistic.
When the statistic is outside the bounds, or when its time plot reveals certain
patterns, the process may be out of control.
Value
This point is out of the control limits

UCL
3

Center
Line

3

LCL
Time

A process is considered in statistical control if it has no assignable causes,
only natural variation.

Control Charts

Slide 4

Value

Process is in control

Time
Value

Process mean varies
over time: process is
out of control
Time


Control Charts (Continued)

Slide 5

Value

Process variance
changes over time:
process is out of
control.
Time

Process mean and
variance change
over time: process is
out of control.

Value

Time


Pareto Diagrams – Using the
Template

Slide 6

A Pareto diagram is a bar chart of the various problems in
production and their percentages, which must add to 100%.
A Pareto chart helps
to identify the most
significant problems
and thus one can
concentrate on their
solutions rather than
waste time and
resources on
unimportant causes.


13-4 The Chart: A Control
Chart forXthe Process Mean
Elements of a control chart for the process mean:
k
 xi
Center line: x  i 1
k
LCL: x  A2 R
UCL: x  A2 R
where: k = number of samples, each of size n
xi = Sample mean for sample i
R  Range of sample i
i
k
R
i=1 i
R =
k
If the sample size in each group is more than 10:
s / c4
s / c4
LCL = x - 3
UCL = x + 3
n
n
where s is the average of the standard deviations of all groups.

Slide 7

n

A2

c4

2
3
4
5
6
7
8
9
10
15
20
25

1.880
1.023
0.729
0.577
0.483
0.419
0.373
0.337
0.308
0.223
0.180
0.153

0.7979
0.8862
0.9213
0.9400
0.9515
0.9594
0.9650
0.9693
0.9727
0.9823
0.9869
0.9896


The X Chart: A Control Chart for
the Process Mean (Continued)

Slide 8

• Tests for assignable causes:
One point beyond 3 (3s)
Nine points in a row on one side of the center line
Six points in a row steadily increasing or decreasing
Fourteen points in a row alternating up and down
Two out of three points in a row beyond 2 (2s)
Four out of five points in a row beyond 1 (1s)
Fifteen points in a row within 1 (1s) of the center line
Eight points in a row on both sides of the center line, all
beyond 1 (1s)


Tests for Assignable Causes

Slide 9

Value
3
2
1
1
2
3


Test 1: One value beyond
3 (3s)

Time
Value
3
2
1
1
2
3


Test 2: Nine points in a
row on one side
of the center line.

Time

(Continued)

Slide 10

Value

Test 3: Six points in a
row steadily
increasing or
decreasing.

3
2
1
1
2
3


Time

Value
3
2
1
1
2
3


Test 4: Fourteen points in
a row alternating
up and down.

Time

(Continued)

Slide 11

Value
3
2
1
1
2
3


Test 5: Two out of three
points in a row
beyond 2(2s)

Time

Value
3
2
1
1
2
3


Test 6: Four out of five
points in a row
beyond 1(1s)

Time

(Continued)

Slide 12

Value
3
2
1
1
2
3


Test 7: Fifteen points in a
row within 1
(1s) of the center
line.

Time

Value
3
2
1
1
2
3


Test 8: Eight points in a
row on both sides
of the center line,
all beyond 1
(1s)
Time


X-bar Chart: Example 13-1 –
Using the Template

Slide 13


X-bar Chart: Example 131(continued) – Using the
Template

Slide 14

Note: The X-bar chart cannot be interpreted unless the
R or s chart has been examined and is in control.


13-5 The R Chart and s Chart
Elements of a control chart for the process range:
Center line: R
LCL: D3 R
UCL: D4 R
k
R
i
where: R = i=1
k

Elements of a control chart for the process standard
deviation:
Center line: s
LCL: B3 s
UCL: B4 s
k
s
i=1 i
where: s =
k

n
2
3
4
5
6
7
8
9
10
15
20
25

D3
0
0
0
0
0
0.076
0.136
0.184
0.223
0.348
0.414
0.459

Slide 15

D4

B3

3.267
2.575
2.282
2.115
2.004
1.924
1.864
1.816
1.777
1.652
1.586
1.541

0
0
0
0
0.030
0.118
0.185
0.239
0.284
0.428
0.510
0.565


B4
3.267
2.568
2.266
2.089
1.970
1.882
1.815
1.761
1.716
1.572
1.490
1.435

R Chart: Example 13-1 using the
Template

Slide 16

The process range seems to be in control.


s Chart: Example 13-1 using the
Template

Slide 17

The process standard deviation seems to
be in control.


Example 13-2 using the
Template

Slide 18


Template - Continued

Slide 19


Template - Continued

Slide 20

Based on the x-bar, R, and s charts, the process
seems to be in control.


13-6 The p Chart: Proportion of
Defective Items

Slide 21

Elements of a control chart for the process
proportion:
Center line: p
p(1 - p)
p(1 - p)
LCL: p - 3
UCL: p + 3
n
n
where: n is the number of elements in each
sample
p is the proportion of defectives in
the combined, overall sample

13-6 The p Chart: Proportion of
Defective Items – Using the
Template for Example 13-3


13-7 The c Chart: (Defects Per
Item)

Slide 23

Elements of a control chart for the number
of imperfections per item, c:
Center line: c
LCL: c - 3 c UCL: c + 3 c
where: c is the average number of defects
or imperfections per item (or area,
volume, etc. )


The c Chart: Example 13-4 using
the Template

Slide 24

Observe that one observation is outside the upper control limit,
indicating that the process may be out of control. The general
downward trend should be investigated.

13-8 The x Chart
Sometimes we are interested in
controlling the process mean, but
our observations come so slowly
from the production process that
we cannot aggregate them into
groups. In such case we may
consider an x chart. An x-chart
is a chart for the raw values of
the variable in question.

Slide 25

The chart is
effective if the
variable has an
approximate
normal
distribution. The
bounds are 3
standard 
deviations from
the mean of the
process.


Name
Religion
Domicile
Contact #
E.Mail
M.Phil (Statistics)

Shakeel Nouman
Christian
Punjab (Lahore)
0332-4462527. 0321-9898767
sn_gcu@yahoo.com
sn_gcu@hotmail.com
GC University, .
(Degree awarded by GC University)

M.Sc (Statistics)
Statitical Officer
(BS-17)
(Economics & Marketing
Division)

GC University, .
(Degree awarded by GC University)

Livestock Production Research Institute
Bahadurnagar (Okara), Livestock & Dairy Development
Department, Govt. of Punjab


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