Phases of Quality Assurance

1
Phases of Quality Assurance
Figure 1
2
Inspection
Figure 2

• How Much/How Often
• Where/When
• Centralized vs. On-site

3
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

4
Examples of Inspection Points
Table 4
5
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

6
Sampling Distribution
Figure 5
7
Normal Distribution
Figure 6
????Standard deviation
???
???
???
???
Mean
95.5
99.7
8
Control Limits
Figure 7
9
Type I Error
Figure 8
10
Control Chart
Figure 9
11
Control Limits

• X-Bar Chart
• R Chart

12
Factors for Control Limits
Sample Size
n
A
D
D
2
3
4
2 3 4 5 6 7 8 9 10
1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.
308
0 0 0 0 0 0.076 0.136 0.184 0.223
3.268 2.574 2.282 2.114 2.004 1.924 1.864 1.816 1.
777
13
Factors for Control Limits
Sample size
n
A
D
D
2
3
4
11 12 13 14 15 16 17 18 19 20
.285 .266 .249 .235 .223 .212 .203 .194 .187 .180
.256 .283 .307 .328 .347 .363 .378 .391 .403 .415
1.744 1.717 1.693 1.672 1.653 1.637 1.622 1.608 1.
597 1.585
14
Samples from Soft-Drink Machine
Sample
R
1
2
3
4
5
X
1 2 3 4 5 6 7 8 9 . . . . . . 25
9 9.7 10.2 10.1 9.6 10.1 9.7 10.2 9.9 . . . . . .
10.0
9.7 10.1 10.1 9.2 10.1 9.1 10.1 9.3 10.2 . . . . .
. 9.8
10.1 10.5 9.8 9.5 9.9 9.2 10.1 9.5 10.1 . . . . .
. 10.2
9.2 10.2 9.6 9.2 9.7 9.6 9.8 9.9 9.7 . . . . . .
10.3
9.5 10.5 9.8 9.0 9.7 9.5 10.3 9.1 10.1 . . . . . .
10.2
9.5 10.2 9.9 9.4 9.8 9.5 10.0 9.6 10.0 . . . . . .
10.1 9.8
1.1 .8 .6 1.1 .5 1.0 .6 1.1 .5 . . . . . . .5 .78
R
X
µ (target)10 oz, sample size n 5, number of
samples K25
15
X-bar and R Charts for10-Ounce Soft Drinks
UCL9.80.577 x 0.78 10.25
LCL9.8-0.577 x 0.78 9.35
16
X-bar and R Charts for10-Ounce Soft Drinks
Samples 9.1, 8.5, 10.2, 9.5, 10.1
17
Control Charts withOut-of-Control Warnings
(Slide 1 of 2)
18
Observations from Sample Distribution
Figure 10
UCL
LCL
Sample number
19
Mean and Range Charts
Figure 11
(process mean is shifting upward)
Sampling Distribution
Detects shift
Does notdetect shift
R-chart
20
Mean and Range Charts
Figure 12
Sampling Distribution
(process variability is increasing)
R-chart
Reveals increase
LCL
21
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

22
Process Control for Attributes

• Proportion defective
• Number of defects per unit

23
Examples
Mails not delivered in 12 hours
UCLp 0.02 3(0.0044) 0.0332 LCLp 0.02 -
3(0.0044) 0.0068
Bank errors with UCLc 5 3(2.24) 11.72 LCLc
5 - 3(2.24) 0
24
Use of p-Charts
Table 13

• When observations can be placed into two
  categories.
• Good or bad
• Pass or fail
• Operate or dont operate
• When the data consists of multiple samples of
  several observations each

25
Use of c-Charts
Table 14

• 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
• Breaks or Tears per unit of area
• Bacteria or pollutants per unit of volumn
• Calls, complaints, failures per unit of time

26
Process Capability
Figure 15
27
Causes of Variation

• Random Causes (common/chance)
• difficult or expensive to control
• e.g., outside humidity, line voltage
• waiting time for banking
• Assignable Causes (special)
• easier to correct
• e.g., employee error, new materials, bank tellers
  absence

28
Comparing Process Variation to Tolerance Limits
Out of control assignable / special causes
29
High Process Capability After Technological
Process Change
Only random variations or common variations and
in control
30
Process Capability

• UTL - LTL
• Cp -------------- gt 1.33
• 6?
• UTL Upper Tolerance Limit
• LTL Lower Tolerance Limit
• Engineers decide on UTL and LTL
• ???? Standard Deviation of Process Output
• natural variations
• Example Temperature of food (38ºC, 49º), ? 1ºC
• Cp (49-38)/6 1.83 gt 1.33

31
Figure 16
3 Sigma and 6 Sigma Quality
Upperspecification
Lowerspecification
1350 ppm
1350 ppm
1.7 ppm
1.7 ppm
Processmean
? 3 Sigma
? 6 Sigma