1. Statistical Quality Control
Chapter 15
Statistical Quality Control
To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

2. Statistical Process Control
Take periodic samples from process
Plot sample points on control chart
Determine if process is within limits
Prevent quality problems
UCL
LCL

3. Variation Common Causes Special Causes Variation inherent in a process
Can be eliminated only through improvements in the system
Special Causes
Variation due to identifiable factors
Can be modified through operator or management action

4. Types of Data Attribute data Variable data
Product characteristic evaluated with a discrete choice
Good/bad, yes/no
Variable data
Product characteristic that can be measured
Length, size, weight, height, time, velocity

5. SPC Applied to Services
Nature of defect is different in services
Service defect is a failure to meet customer requirements
Monitor times, customer satisfaction

6. Service Quality Examples
Hospitals
Timeliness, responsiveness, accuracy of lab tests
Grocery Stores
Check-out time, stocking, cleanliness
Airlines
Luggage handling, waiting times, courtesy
Fast food restaurants
Waiting times, food quality, cleanliness, employee courtesy

7. Service Quality Examples
Catalog-order companies
Order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time
Insurance companies
Billing accuracy, timeliness of claims processing, agent availability and response time

8. Control Charts Graph establishing process control limits
Charts for variables
Mean (x-bar), Range (R)
Charts for attributes
p and c

9. Process Control Chart Out of control Upper control limit Process1 2 3 4 5 6 7 8 9 10
Sample number
Upper
control
limit
Process
average
Lower
Out of control
Figure 15.1

10. A Process is In Control if
No sample points outside limits
Most points near process average
About equal number of points above & below centerline
Points appear randomly distributed

11. Development of Control Chart
Based on in-control data
If non-random causes present discard data
Correct control chart limits

12. Control Charts for Attributes
p Charts
Calculate percent defectives in sample
c Charts
Count number of defects in item

13. p-Chart UCL = p + zp LCL = p - zp where
z = the number of standard deviations from the process average
p = the sample proportion defective; an estimate of the process average
p = the standard deviation of the sample proportion
p =
p(1 - p) n

14. The Normal Distribution
=0 1 2 3
-1
-2
-3
95%
99.74%

15. Control Chart Z Values Smaller Z values make more sensitive charts
Z = 3.00 is standard
Compromise between sensitivity and errors

16. p-Chart Example 20 samples of 100 pairs of jeans 1 6 .06 2 0 .00
NUMBER OF PROPORTION
SAMPLE DEFECTIVES DEFECTIVE
: : :
200
Example 15.1

17. total sample observations
p-Chart Example
20 samples of 100 pairs of jeans
NUMBER OF PROPORTION
SAMPLE DEFECTIVES DEFECTIVE
: : :
200
p =
= 200 / 20(100)
= 0.10
total defectives
total sample observations
Example 15.1

18. p-Chart Example p = 0.10 20 samples of 100 pairs of jeans 1 6 .06
NUMBER OF PROPORTION
SAMPLE DEFECTIVES DEFECTIVE
: : :
200
p = 0.10
UCL = p + z =
p(1 - p) n
0.10( )
100
UCL = 0.190
LCL = 0.010
LCL = p - z =
Example 15.1

19. p-Chart
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Proportion defective
Sample number 2 4 6 8 10 12 14 16 18 20
UCL = 0.190
LCL = 0.010
p = 0.10

20. c-Chart UCL = c + zc c = c LCL = c - zc where
c = number of defects per sample

21. c-Chart The number of defects in 15 sample rooms 1 12 190 2 8 15 3 16
1 12
2 8
3 16
: :
15 15
190
SAMPLE NUMBER OF DEFECTS
c = = 12.67
190 15
UCL = c + zc =
= 23.35
LCL = c + zc =
= 1.99
Example 15.2

22. c-Chart 3 6 9 12 15 18 21 24 Number of defects Sample number 2 4 8 1014 16
UCL = 23.35
LCL = 1.99
c = 12.67

23. Control Charts for Variables
Mean chart ( x -Chart )
Uses average of a sample
Range chart ( R-Chart )
Uses amount of dispersion in a sample

24. Range ( R- ) Chart UCL = D4R LCL = D3R R k R = where
R = range of each sample
k = number of samples

25. Range ( R- ) Chart SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
n A2 D3 D4
SAMPLE SIZE FACTOR FOR x-CHART FACTORS FOR R-CHART
Range ( R- ) Chart
Table 15.1

26. R-Chart Example OBSERVATIONS (SLIP-RING DIAMETER, CM)
SAMPLE k x R
Example 15.3

27. R-Chart Example R k R = = = 0.115 1.15 10
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0
OBSERVATIONS (SLIP-RING DIAMETER, CM)
SAMPLE k x R
UCL = 0.243
LCL = 0
Range
Sample number
R = 0.115 | 1 2 3 4 5 6 7 8 9 10
0.28 –
0.24 –
0.20 –
0.16 –
0.12 –
0.08 –
0.04 –
0 –
Example 15.3

28. x-Chart Calculations x1 + x2 + ... xk = k x = =
UCL = x + A2R LCL = x - A2R =
where
x = the average of the sample means =

29. x-Chart Example UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08
OBSERVATIONS (SLIP-RING DIAMETER, CM)
SAMPLE k x R
UCL = x + A2R = (0.58)(0.115) = 5.08
LCL = x - A2R = (0.58)(0.115) = 4.94 =
x = = = 5.01 cm x k
50.09 10
Example 15.4

30. x-Chart Example UCL = x + A2R = 5.01 + (0.58)(0.115) = 5.08
LCL = 4.94
Mean
Sample number | 1 2 3 4 5 6 7 8 9 10
5.10 –
5.08 –
5.06 –
5.04 –
5.02 –
5.00 –
4.98 –
4.96 –
4.94 –
4.92 –
x = 5.01 =
OBSERVATIONS (SLIP-RING DIAMETER, CM)
SAMPLE k x R
UCL = x + A2R = (0.58)(0.115) = 5.08
LCL = x - A2R = (0.58)(0.115) = 4.94 =
x = = = 5.01 cm x k
50.09 10
Example 15.4

31. Using x- and R-Charts Together
Each measures the process differently
Both process average and variability must be in control

32. Control Chart Patterns
LCL
UCL
Sample observations
consistently below the
center line
UCL
LCL
Sample observations
consistently above the
center line
Figure 15.3

33. Control Chart Patterns
LCL
UCL
Sample observations
consistently increasing
UCL
LCL
Sample observations
consistently decreasing
Figure 15.3

34. Zones for Pattern Tests
UCL
LCL
Zone A
Zone B
Zone C
Process average
3 sigma = x + A2R =
3 sigma = x - A2R
2 sigma = x (A2R) 2 3
2 sigma = x (A2R)
1 sigma = x (A2R) 1
1 sigma = x (A2R) x
Sample number | 4 5 6 7 8 9 10 11 12 13
Figure 15.4

35. Control Chart Patterns
8 consecutive points on one side of the center line.
8 consecutive points up or down across Zones.
14 points alternating up or down.
2 out of 3 consecutive points in Zone A but still inside the control limits.
4 out of 5 consecutive points in Zone A or B.

36. Performing a Pattern Test
B — B
B U C
B D A
B D A
B U C
— U C
A U C
A U B
A U A
A D B
SAMPLE x ABOVE/BELOW UP/DOWN ZONE
Example 15.5

37. Sample Size Determination
Attribute control charts
50 to 100 parts in a sample
Variable control charts
2 to 10 parts in a sample

38. Process Capability Range of natural variability in process
Measured with control charts.
Process cannot meet specifications if natural variability exceeds tolerances
3-sigma quality
Specifications equal the process control limits.
6-sigma quality
Specifications twice as large as control limits

39. Design Specifications Design Specifications
Process Capability
(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.
Design Specifications
Process
(b) Design specifications and natural variation the same; process is capable of meeting specifications most the time.
Design Specifications
Process
Figure 15.5

40. Design Specifications Design Specifications
Process Capability
(c) Design specifications greater than natural variation; process is capable of always conforming to specifications.
Design Specifications
Process
(d) Specifications greater than natural variation, but process off center; capable but some output will not meet upper specification.
Design Specifications
Process
Figure 15.5

41. Process Capability Measures
Process Capability Ratio
Cp = =
tolerance range
process range
upper specification limit -
lower specification limit 6

42. Computing Cp Net weight specification = 9.0 oz  0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cp =
= = 1.39
upper specification limit -
lower specification limit 6
6(0.12)
Example 15.6

43. Process Capability Measures
Process Capability Index
Cpk = minimum
x - lower specification limit 3 =
upper specification limit - x ,

44. x - lower specification limit upper specification limit - x
Computing Cpk
Net weight specification = 9.0 oz  0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cpk = minimum
= minimum , = 0.83
x - lower specification limit 3 =
upper specification limit - x ,
3(0.12)
Example 15.7