1. Statistical Process Control
Chapter 3
Statistical Process Control
Russell and Taylor
Operations and Supply Chain Management, 8th Edition

2. Lecture Outline Basics of Statistical Process Control – Slide 4
Control Charts – Slide 12
Control Charts for Attributes – Slide 16
Control Charts for Variables – Slide 27
Control Chart Patterns – Slide 45
SPC with Excel and OM Tools – Slide 52
Process Capability – Slide 54
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

3. Learning Objectives
Explain when and how to use statistical process control to ensure the quality of products and services
Discuss the rationale and procedure for constructing attribute and variable control charts
Utilize appropriate control charts to determine if a process is in-control
Identify control chart patterns and describe appropriate data collection
Assess the process capability of a process
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

4. Statistical Process Control (SPC)
monitoring production process to detect and prevent poor quality
Sample
subset of items produced to use for inspection
Control Charts
process is within statistical control limits
UCL
LCL
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

5. Process Variability Random Non-Random inherent in a process
depends on equipment and machinery, engineering, operator, and system of measurement
natural occurrences
Non-Random
special causes
identifiable and correctable
include equipment out of adjustment, defective materials, changes in parts or materials, broken machinery or equipment, operator fatigue or poor work methods, or errors due to lack of training
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

6. SPC in Quality Management
SPC uses
Is the process in control?
Identify problems in order to make improvements
Contribute to the TQM goal of continuous improvement
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

7. Quality Measures: Attributes and Variables
A characteristic which is evaluated with a discrete response
good/bad; yes/no; correct/incorrect
Variable measure
A characteristic that is continuous and can be measured
Weight, length, voltage, volume
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

8. SPC Applied to Services
Nature of defects is different in services
Service defect is a failure to meet customer requirements
Monitor time and customer satisfaction
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9. SPC Applied to Services
Hospitals
timeliness & quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance & checkouts
Grocery stores
waiting time to check out, frequency of out-of-stock items, quality of food items, cleanliness, customer complaints, checkout register errors
Airlines
flight delays, lost luggage & luggage handling, waiting time at ticket counters & check-in, agent & flight attendant courtesy, accurate flight information, cabin cleanliness & maintenance
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

10. SPC Applied to Services
Fast-food restaurants
waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy
Catalogue-order companies
order accuracy, operator knowledge & courtesy, packaging, delivery time, phone order waiting time
Insurance companies
billing accuracy, timeliness of claims processing, agent availability & response time
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

11. Where to Use Control Charts
Process
Has a tendency to go out of control
Is particularly harmful and costly if it goes out of control
Examples
At beginning of process because of waste to begin production process with bad supplies
Before a costly or irreversible point, after which product is difficult to rework or correct
Before and after assembly or painting operations that might cover defects
Before the outgoing final product or service is delivered
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

12. Control Charts A graph that monitors process quality Control limits
upper and lower bands of a control chart
Attributes chart
p-chart
c-chart
Variables chart
mean (x bar – chart)
range (R-chart)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

13. Process Control Chart Out of control Upper control limit Process
average
Lower
control
limit 1 2 3 4 5 6 7 8 9 10
Sample number
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14. Normal Distribution Probabilities for Z= 2.00 and Z = 3.00 =0 1 23
-1
-2
-3
95%
99.74%
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15. A Process Is in Control If …
… no sample points outside limits
… most points near process average
… about equal number of points above and below centerline
… points appear randomly distributed
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

16. Control Charts for Attributes
p-chart
uses portion defective in a sample
c-chart
uses number of defects (non-conformities) in a sample
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

17. p-Chart UCL = p + zp LCL = p - zp
z = number of standard deviations from process average
p = sample proportion defective; estimates process mean
p = standard deviation of sample proportion
p =
p(1 - p) n
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

18. Construction of p-Chart
20 samples of 100 pairs of jeans
NUMBER OF PROPORTION
SAMPLE # DEFECTIVES DEFECTIVE
: : :
200
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19. Construction of p-Chart
total defectives
total sample observations
p = =
p(1 - p) n
UCL = p + z =
UCL =
p(1 - p) n
LCL = p - z =
LCL =
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

20. Construction of p-Chart
total defectives
total sample observations
p =
= 200 / 20(100) = 0.10
p(1 - p) n
0.10( )
100
UCL = p + z =
UCL = 0.190
p(1 - p) n
0.10( )
100
LCL = p - z =
LCL = 0.010
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

21. Construction of p-Chart
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

22. p-Chart in Excel
Click on “Insert” then “Charts” to construct control chart
I4 + 3*SQRT(I4*(1-I4)/100)
I4 - 3*SQRT(I4*(1-I4)/100)
Column values copied from I5 and I6
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

23. c-Chart UCL = c + zc c = c LCL = c - zc where
c = number of defects per sample
c = c
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

24. c-Chart UCL = c + zc LCL = c - zc
Number of defects in 15 sample rooms
NUMBER OF
DEFECTS
SAMPLE
c =
: :
190
UCL = c + zc
LCL = c - zc
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

25. c-Chart Number of defects in 15 sample rooms 15 c = = 12.67 1 12 2 8
: :
190
SAMPLE
c = = 12.67 15
UCL = c + zc =
= 23.35
LCL = c - zc =
= 1.99
NUMBER OF
DEFECTS
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

26. c-Chart
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

27. Control Charts for Variables
Range chart ( R-Chart )
Plot sample range (variability)
Mean chart ( x -Chart )
Plot sample averages
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

28. x-bar Chart:  Known = UCL = x + z x LCL = x - z x = Where - - - =
x1 + x xk k
X =
= process standard deviation
x = standard deviation of sample means =/
k = number of samples (subgroups)
n = sample size (number of observations) n
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

29. x-bar Chart Example:  Known
Observations(Slip-Ring Diameter, cm) n -
Sample k x
We know σ = .08
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

30. x-bar Chart Example:  Known
x1 + x xk k
X = = -
UCL = x + z x = -
LCL = x - z x = -
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

31. x-bar Chart Example:  Known
= (.08 / ) 10
= 4.93
_____
50.09
= 5.01
X = =
LCL = x - z x -
UCL = x + z x
= (.08 / )
= 5.09
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

32. x-bar Chart Example:  Unknown_
UCL = x + A2R LCL = x - A2R =
where
x = average of the sample means
R = average range value
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

33. Control Chart Factors n A2 D3 D4 2 1.880 0.000 3.267
Factors for R-chart
Sample
Size
Factor for X-chart
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

34. x-bar Chart Example:  Unknown
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k x R
Totals
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

35. x-bar Chart Example:  Unknown_
R =
____
∑ R k
UCL = x + A2R =
x = x
___
LCL = x - A2R
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

36. x-bar Chart Example:  Unknown
1.15 10
R = = = 0.115 _
____ _ _
UCL = x + A2R =
50.09 10
_____
x = = = 5.01 cm x k
___
= (0.58)(0.115) = 5.08
LCL = x - A2R
= (0.58)(0.115) = 4.94
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

37. x- bar Chart Example
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

38. R- Chart UCL = D4R LCL = D3R R k R = Where R = range of each sample
k = number of samples (sub groups)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

39. R-Chart Example Totals OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k x R
Totals
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

40. Retrieve chart factors D3 and D4
R-Chart Example
Retrieve chart factors D3 and D4
UCL = D4R =
LCL = D3R = _
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

41. Retrieve chart factors D3 and D4
R-Chart Example
Retrieve chart factors D3 and D4
UCL = D4R = 2.11(0.115) = 0.243
LCL = D3R = 0(0.115) = 0 _
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

42. R-Chart Example
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

43. X-bar and R charts – Excel & OM Tools
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

44. Using x- bar and R-Charts Together
Process average and process variability must be in control
Samples can have very narrow ranges, but sample averages might be beyond control limits
Or, sample averages may be in control, but ranges might be out of control
An R-chart might show a distinct downward trend, suggesting some nonrandom cause is reducing variation
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

45. Control Chart Patterns
Run
sequence of sample values that display same characteristic
Pattern test
determines if observations within limits of a control chart display a nonrandom pattern
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

46. Control Chart Patterns
To identify a pattern look for:
8 consecutive points on one side of the center line
8 consecutive points up or down
14 points alternating up or down
2 out of 3 consecutive points in zone A (on one side of center line)
4 out of 5 consecutive points in zone A or B (on one side of center line)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

47. Control Chart Patterns
UCL
UCL
LCL
LCL
Sample observations
consistently below the
center line
Sample observations
consistently above the
center line
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

48. Control Chart Patterns
LCL
UCL
Sample observations
consistently increasing
consistently decreasing
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

49. 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
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

50. 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
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

51. Sample Size Determination
Attribute charts require larger sample sizes
50 to 100 parts in a sample
Variable charts require smaller samples
2 to 10 parts in a sample
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

52. SPC with Excel
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

53. SPC with OM Tools
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

54. Process Capability Compare natural variability to design variability
What we measure with control charts
Process mean = 8.80 oz, Std dev. = 0.12 oz
Tolerances
Design specifications reflecting product requirements
Net weight = 9.0 oz  0.5 oz
Tolerances are  0.5 oz
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

55. Design Specifications
Process Capability
(b) Design specifications and natural variation the same; process is capable of meeting specifications most of the time.
Design Specifications
Process
(a) Natural variation exceeds design specifications; process is not capable of meeting specifications all the time.
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

56. 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.
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

57. Process Capability Ratio
Cp =
tolerance range
process range
upper spec limit - lower spec limit 6 =
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

58. Computing Cp Net weight specification = 9.0 oz  0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz
Cp =
upper specification limit -
lower specification limit 6
Computing Cp
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

59. 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)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

60. Process Capability Index
Cpk = minimum
x - lower specification limit 3 =
upper specification limit - x ,
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

61. Computing Cpk Net weight specification = 9.0 oz  0.5 oz
Process mean = 8.80 oz
Process standard deviation = 0.12 oz =
x - lower specification limit 3 ,
Cpk = minimum =
upper specification limit - x 3
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

62. 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)
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

63. Process Capability With Excel
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

64. Process Capability With OM Tools
© 2014 John Wiley & Sons, Inc. - Russell and Taylor 8e

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