1. Quality Assurance (Quality Control)

2. Phases of Quality Assurance
Acceptance
sampling
Process
control
Continuous
improvement
Inspection
before/after
production
Corrective
action during
Quality built
into the
process
The least
progressive
The most

3. Inspection How Much/How Often Where/When Centralized vs. On-site
Inputs
Transformation
Outputs
Acceptance
sampling
Process
control

4. Inspection Costs Cost Total Cost Cost of inspection Cost of passing
defectives
Optimal
Amount of Inspection

5. 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

6. Examples of Inspection Points

7. Statistical Process Control
The Control Process
Define
Measure
Compare to a standard
Evaluate
Take corrective action
Evaluate corrective action

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

9. Sampling Distribution
Process distribution
Mean

10. Normal Distribution Mean -3s -2s +2s +3s 95.5% 99.7%
s = Standard deviation

11. Control Limits (Type I Error)
Mean
LCL
UCL
a/2
a = Probability of Type I error

12. Control Limits Sampling distribution Process distribution Mean
Lower control limit
Upper control limit

13. Mean Charts Two approaches:
If the process standard deviation (s) is available (x
If the process standard deviation is not available (use sample range to approximate the process variability)

14. Mean charts (SD of process available)
Upper control limit (UCL)
= average sample mean + z (S.D. of sample mean)
Lower control limit (LCL)
= average sample mean - z (S.D. of sample mean)

15. Mean charts (SD of process not available)
UCL = average of sample mean + A2 (average of sample range)
LCL = average of sample mean - A2 (average of sample range)
A2 is a parameter depending on the sample size and is obtainable from table.

16. Example
Means of sample taken from a process for making aluminum rods is 2 cm and the SD of the process is 0.1cm (assuming a normal distribution). Find the 3-sigma (99.7%) control limits assuming sample size of 16 are taken.

17. Example (solution) x = SD of sample mean distribution z = 3
= SD of process / (sample size)
= 0.1 /  (16) = 0.025
z = 3
UCL = 2 + 3(0.025) = 2.075
LCL = = 1.925

18. Example(p.427)
Twenty samples of size 8 have been taken from a process. The average sample range of the 20 samples is 0.016cm and the average mean is 3cm. Determine the 3-sigma control limits.

19. Example Average sample mean = 3cm Average sample range = 0.016cm
Sample size = 8
A2 = 0.37 (From Table 9-2)
UCL = (0.016) = 3.006
LCL = (0.016) = 2.994

20. Control Chart
Abnormal variation due to assignable sources
Out of control
1020
UCL
1010
1000
Mean
Normal variation due to chance
990
LCL
980
Abnormal variation due to assignable sources
970 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample number

21. Observations from Sample Distribution
UCL
LCL 1 2 3 4
Sample number

22. Mean and Range Charts Detects shift x-Chart Does not detect shift
UCL
LCL
x-Chart
Detects shift
UCL
LCL
Does not detect shift
R-chart

23. Mean and Range Charts Does not detect shift x-Chart R-chart
UCL
LCL
UCL
LCL
Does not detect shift
x-Chart
UCL
LCL
R-chart
Detects shift

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

25. Use of p-Charts When observations can be placed into two categories.
Good or bad
Pass or fail
Operate or do not operate
When the data consists of multiple samples of several observations each

26. p-chart
The center line is the average fraction (defective) p in the population if p is known, or it can be estimated from samples is it is unknown.
p = SD of sample distribution
= {p(1-p)/n}
UCLp = p + zp
LCLp = p - zp

27. Example (p.431)
The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

28. Example
The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process
No. of defective items

29. Example (solution)
Population mean not available, to be estimated from sample mean
Total No. of defective items = 220
Estimate sample mean = 220/{20(100)}=.11
SD of sample = {.11(1-.11)/100}= 0.03
z = 2 (2-sigma)
UCLp = (.03) = 0.17
LCLp = (.03) = 0.05
Thus a control chart can be plotted (p.431)

30. Use of c-Charts
Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted.
Scratches, chips, dents, or errors per item
Cracks or faults per unit of distance
Calls, complaints, failures per unit of time

31. Process Capability Process variability matches specifications
Lower Specification
Upper Specification
Process variability matches specifications
Lower Specification
Upper Specification
Process variability well within specifications
Lower Specification
Upper Specification
Process variability exceeds specifications