1. Chapter 13 Statistical Quality Control Method

2. Statistical Quality Control Methods
Acceptance Sampling
Statistical Process
Control
Attributes
Variables
Attributes
Variables
Type of Data

3. Statistical Quality Control Methods
Attribute Data: data which count items, such as the
number of defective items on a sample
Variable Data: data which measure a particular product
characteristic such as length or weight

4. Statistical Quality Control Methods
Sampling Error
Sample results are not representative of the actual
population or process
Customer’s
risk
In agreement
The population
or process is actually
Good or in control
Bad or out of control
or Type II error
 or Type I error
Good or
in control
Bad or out
of control
The sample
says that the
population or
process is
Prducer’s risk

5. Acceptance Sampling Designing a Sampling Plan for Attribute
Costs to justify inspection
Full or 100% inspection or not?
Cost to Inspect
Cost incurred by
passing a reject

6. Acceptance Sampling Purpose of Sampling Plan Find its quality
Ensure that the quality is what it is supposed to be

7. Acceptance Sampling Designing a Sampling Plan for Attribute
n: Number of units in the sample depended on the lot size
c: the acceptance number
AQL (acceptable quality level): maximum percentage of
defects that a company is willing to accept
LTPD (lot tolerance percent defective): minimum percentage of
defects that a company is willing to reject
: producer’s risk
: consumer’s risk

8. Acceptance Sampling Designing a Sampling Plan for Attribute
c LTPD/AQL nAQL
=0.05
=0.10
MIL-STD-105E

9. Operating Characteristic Curve

10. Operating Characteristic Curve
P(r  c) p np 1%
0.99
0.97 2%
1.98
0.95 …

11. Acceptance Sampling Determine a Sampling Plan for Variables
Control Limit: Points on an acceptance sampling chart that distinguish
the accept and reject regions. Also, points on a process
control chart that distinguish between a process being
in and out of control.

12. Acceptance Sampling
Determine a Sampling Plan for Variables

13. Acceptance Sampling
LCL

14. Statistical Process Control
Statistical process control (SPC)
Statistical method for determining whether a particular
process is in or out of control.
Central Limit Theorem

15. Statistical Process Control

16. Statistical Process Control

17. Statistical Process Control
SPC Using Attribute Measurement
Attribute data are data that are counted, such as good or bad
units produced by a machine.
Samples
defects
Sample size=6
defects=2

18. Statistical Process Control
SPC Using Attribute Measurement
Center line =
= Long-run average percent defective
Standard deviation of sample =
Note: X~Bernoulli distribution E(x)=p V(x)=p(1-p)

19. Statistical Process Control
Variable Measurements Using X and R Charts
An X chart tracks the changes in the means of samples by plotting
the means that were taken from a process.
An R chart tracks the changes in the variability by plotting the
range within each sample.

20. Statistical Process Control
Variable Measurements Using X and R Charts
Setup Control Chart:
At least 25 samples
Setup control limits
Control limits for
Upper control limit for
Lower control limit for

21. Statistical Process Control
n A D D4
n A D D4

22. Statistical Process Control

23. Process Capability

24. Process Capability Process Capability Ratio
The larger the ratio, the greater the potential for producing
parts within tolerance from the specified process.

25. Process Capability Capability Index
To determine whether the process mean is closer to the
upper specification limit, or the lower specification limit.

26. Six Sigma Quality improvement program developed by Motorola to reduce
process variation to 50% of design tolerance
Cp=1; defect rate = 2700 per million parts
Cp=2; defect rate = 3.4 per million parts