Quality Control

1. McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
10
Quality Control

2. 10-2
Learning Objectives
 List and briefly explain the elements of the
control process.
 Explain how control charts are used to
monitor a process, and the concepts that
underlie their use.
 Use and interpret control charts.
 Use run tests to check for nonrandomness
in process output.
 Assess process capability.

3. 10-3
Phases of Quality Assurance
Acceptance
sampling
Process
control
Continuous
improvement
Inspection of lots
before/after
production
Inspection and
corrective
action during
production
Quality built
into the
process
The least
progressive
The most
progressive
Figure 10.1

4. 10-4
Inspection
 How Much/How Often
 Where/When
 Centralized vs. On-site
Inputs Transformation Outputs
Acceptance
sampling
Process
control
Acceptance
sampling
Figure 10.2

5. 10-5
Cost
Optimal
Amount of Inspection
Inspection Costs
Cost of
inspection
Cost of
passing
defectives
Total Cost
Figure 10.3

6. 10-6
Where to Inspect in the Process
 Raw materials and purchased parts
 Finished products
 Before a costly operation
 Before an irreversible process
 Before a covering process

7. 10-7
Examples of Inspection Points
Type of
business
Inspection
points
Characteristics
Fast Food Cashier
Counter area
Eating area
Building
Kitchen
Accuracy
Appearance, productivity
Cleanliness
Appearance
Health regulations
Hotel/motel Parking lot
Accounting
Building
Main desk
Safe, well lighted
Accuracy, timeliness
Appearance, safety
Waiting times
Supermarket Cashiers
Deliveries
Accuracy, courtesy
Quality, quantity
Table 10.1

8. 10-8
Statistical Process Control:
Statistical evaluation of the output of a
process during production
Quality of Conformance:
A product or service conforms to
specifications
Statistical Control

9. 10-9
Control Chart
 Control Chart
 Purpose: to monitor process output to see
if it is random
 A time ordered plot representative sample
statistics obtained from an on going
process (e.g. sample means)
 Upper and lower control limits define the
range of acceptable variation

10. 10-10
Control Chart
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UCL
LCL
Sample number
Mean
Out of
control
Normal variation
due to chance
Abnormal variation
due to assignable sources
Abnormal variation
due to assignable sources
Figure 10.4

11. 10-11
Statistical Process Control
 The essence of statistical process
control is to assure that the output of a
process is random so that future output
will be random.

12. 10-12
Statistical Process Control
 The Control Process
 Define
 Measure
 Compare
 Evaluate
 Correct
 Monitor results

13. 10-13
Statistical Process Control
 Variations and Control
 Random variation: Natural variations in the
output of a process, created by countless
minor factors
 Assignable variation: A variation whose
source can be identified

14. 10-14
Sampling Distribution
Sampling
distribution
Process
distribution
Mean
Figure 10.5

15. 10-15
Normal Distribution
Mean
   
95.44%
99.74%
Standard deviation
Figure 10.6

16. 10-16
Control Limits
Sampling
distribution
Process
distribution
Mean
Lower
control
limit
Upper
control
limit
Figure 10.7

17. 10-17
SPC Errors
 Type I error
 Concluding a process is not in control
when it actually is.
 Type II error
 Concluding a process is in control when it
is not.

18. 10-18
Type I and Type II Errors
In control Out of control
In control No Error Type I error
(producers risk)
Out of
control
Type II Error
(consumers risk)
No error
Table 10.2

19. 10-19
Type I Error
Mean
LCL UCL
/2 /2
Probability
of Type I error
Figure 10.8

20. 10-20
Observations from Sample
Distribution
Sample number
UCL
LCL
1 2 3 4
Figure 10.9

21. 10-21
Control Charts for Variables
 Mean control charts
 Used to monitor the central tendency of a
process.
 X bar charts
 Range control charts
 Used to monitor the process dispersion
 R charts
Variables generate data that are measured.

22. 10-22
Mean and Range Charts
UCL
LCL
UCL
LCL
R-chart
x-Chart Detects shift
Does not
detect shift
Figure 10.10A
(process mean is
shifting upward)
Sampling
Distribution

23. 10-23
x-Chart
UCL
Does not
reveal increase
Mean and Range Charts
UCL
LCL
LCL
R-chart Reveals increase
Figure 10.10B
(process variability is increasing)
Sampling
Distribution

24. 10-24
Control Chart for Attributes
 p-Chart - Control chart used to monitor
the proportion of defectives in a process
 c-Chart - Control chart used to monitor
the number of defects per unit
Attributes generate data that are counted.

25. 10-25
Use of p-Charts
 When observations can be placed into
two categories.
 Good or bad
 Pass or fail
 Operate or don’t operate
 When the data consists of multiple
samples of several observations each
Table 10.4

26. 10-26
Use of c-Charts
 Use only when the number of
occurrences per unit of measure can be
counted; non-occurrences cannot be
counted.
 Scratches, chips, dents, or errors per item
 Cracks or faults per unit of distance
 Breaks or Tears per unit of area
 Bacteria or pollutants per unit of volume
 Calls, complaints, failures per unit of time
Table 10.4

27. 10-27
Use of Control Charts
 At what point in the process to use
control charts
 What size samples to take
 What type of control chart to use
 Variables
 Attributes

28. 10-28
Run Tests
 Run test – a test for randomness
 Any sort of pattern in the data would
suggest a non-random process
 All points are within the control limits -
the process may not be random

29. 10-29
Nonrandom Patterns in Control
charts
 Trend
 Cycles
 Bias
 Mean shift
 Too much dispersion

30. 10-30
Counting Above/Below Median Runs (7 runs)
Counting Up/Down Runs (8 runs)
U U D U D U D U U D
B A A B A B B B A A B
Figure 10.12
Figure 10.13
Counting Runs

31. 10-31
NonRandom Variation
 Managers should have response plans to
investigate cause
 May be false alarm (Type I error)
 May be assignable variation

32. 10-32
 Tolerances or specifications
 Range of acceptable values established by
engineering design or customer
requirements
 Process variability
 Natural variability in a process
 Process capability
 Process variability relative to specification
Process Capability

33. 10-33
Process Capability
Lower
Specification
Upper
Specification
A. Process variability
matches specifications
Lower
Specification
Upper
Specification
B. Process variability
well within specifications
Lower
Specification
Upper
Specification
C. Process variability
exceeds specifications
Figure 10.15

34. 10-34
Process Capability Ratio
Process capability ratio, Cp =
specification width
process width
Upper specification – lower specification
6
Cp =







 

 3
X
-
UTL
or
3
LTL
X
min
=
Cpk
If the process is centered use Cp
If the process is not centered use Cpk

35. 10-35
Limitations of Capability Indexes
1. Process may not be stable
2. Process output may not be normally
distributed
3. Process not centered but Cp is used

36. 10-36
Example 8
Machine
Standard
Deviation
Machine
Capability Cp
A 0.13 0.78 0.80/0.78 = 1.03
B 0.08 0.48 0.80/0.48 = 1.67
C 0.16 0.96 0.80/0.96 = 0.83
Cp > 1.33 is desirable
Cp = 1.00 process is barely capable
Cp < 1.00 process is not capable

37. 10-37
Process
mean
Lower
specification
Upper
specification
1350 ppm 1350 ppm
1.7 ppm 1.7 ppm
+/- 3 Sigma
+/- 6 Sigma
3 Sigma and 6 Sigma Quality

38. 10-38
Improving Process Capability
 Simplify
 Standardize
 Mistake-proof
 Upgrade equipment
 Automate

39. 10-39
Taguchi Loss Function
Cost
Target
Lower
spec
Upper
spec
Traditional
cost function
Taguchi
cost function
Figure 10.17

40. 10-40
Video: Defect Prev.