1. Statistical Process Control (SPC)
IE 362 Quality Control
Week 2
(X, R charts)
Statistical Process Control (SPC) -
Dr. Sun Olapiriyakul

2. Variation The ability to measure variation is necessary
before it can be controlled
1). Within-piece variation
2). Piece-to-piece variation
3). Time-to-time variation

3. Statistical Process Control
Variability is inherent in every process
Natural or _______ causes
Special or _________ causes
Provides a statistical signal when ________ causes are present
Detect and eliminate assignable causes of variation

4. Causes of variation Random Also called common causes
inherent in a process
depends on ________and machinery, engineering, _______, and system of measurement
natural occurrences
Non-Random
also called special causes or assignable causes
identifiable and ____________
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 _________
when assignable causes are present,
- eliminate the bad causes
- ____________the good causes

5. SPC Applied to Services
Hospitals - timeliness and quickness of care, staff responses to requests, accuracy of lab tests, cleanliness, courtesy, accuracy of paperwork, speed of admittance and 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 and luggage handling, waiting time at ticket counters and check-in, agent and flight attendant courtesy, accurate flight information, passenger cabin cleanliness and maintenance
Fast-food restaurants - waiting time for service, customer complaints, cleanliness, food quality, order accuracy, employee courtesy
Catalogue-order companies - order accuracy, operator knowledge and courtesy, packaging, delivery time, phone order waiting time
Insurance companies - billing accuracy, timeliness of claims processing, agent availability and response time

6. SPC Applied to Services

7. Control Charts Types of charts - Variables mean (X - chart)
range (R - chart)
Attributes
P - chart
C - chart -

8. Variables control chart
Variable measure
a product characteristic that is continuous and can be measured
weight - length
Variables is a product characteristic that is measured on a continuous scale -
Mean chart ( x - Chart )
uses process average of a sample
Range chart ( R - Chart )
uses amount of dispersion in a sample
Must be used together!!

9. X bar Chart: Standard Deviation Known= =
UCL = x + zx LCL = x - zx
where
x = average of sample means
n = sample size Z = no. of sd, usually 3
 = process standard deviation
x = std dev. of sample means =  /√n =

10. X-bar Chart Example: Standard Deviation Known (cont.)

11. x-bar Chart Example: Standard Deviation Known (cont.)
Suppose the process standard deviation is know to be 0.08
UCL =
LCL =
Try to construct the chart

12. x-bar Chart Example: Standard Deviation Unknown= =
UCL = x + A2R LCL = x - A2R
where
x = average of sample means
R = average of ranges =

13. Control Limits

14. x-bar Chart Example: Standard Deviation Unknown
OBSERVATIONS (SLIP- RING DIAMETER, CM)
SAMPLE k x R
Example 15.4

15. x-bar Chart Example: Standard Deviation Unknown (cont.)
1.15 10
R = = = 0.115
UCL = x + A2R = (0.58)(0.115) = 5.08
LCL = x - A2R = (0.58)(0.115) = 4.94 =
x = = = 5.01 cm x k
50.09 10

16. x- bar Chart Example (cont.)
UCL = 5.08
LCL = 4.94
Mean
Sample number | 1 2 3 4 5 6 7 8 9 10
5.10 –
5.08 –
5.06 –
5.04 –
5.02 –
5.00 –
4.98 –
4.96 –
4.94 –
4.92 –
x = 5.01 =
x- bar Chart Example (cont.)

17. R- Chart UCL = D4R LCL = D3R R k R = where R = range of each sample
k = number of samples

18. R-Chart Example (cont.)
UCL = D4R =
LCL = D3R =
Retrieve Factor Values D3 and D4
Example 15.3

19. R-Chart Example (cont.)
UCL = 0.243
LCL = 0
Range
Sample number
R = 0.115 | 1 2 3 4 5 6 7 8 9 10
0.28 –
0.24 –
0.20 –
0.16 –
0.12 –
0.08 –
0.04 –
0 –

20. Using x- bar and R-Charts Together
Process average and process variability must be in control
It is possible for samples to have very narrow ranges, but their averages might be beyond control limits
It is possible for sample averages to be in control, but ranges might be very large
It is possible for an R-chart to exhibit a distinct downward trend, suggesting some nonrandom cause is reducing variation

21. 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
To identify a pattern:
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)

22. Control Chart Patterns (cont.)
UCL
LCL
Sample observations
consistently above the
center line
consistently below the

23. Control Chart Patterns (cont.)
LCL
UCL
Sample observations
consistently increasing
UCL
LCL
Sample observations
consistently decreasing

24. 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

25. Performing a Pattern Test
B — B
B U C
B D A
B U 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

26. 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