1. Chapter 15 Control Methods

2. Control is the heart of Six Sigma
Customers are demanding higher levels of product quality at a lower cost, improved responsiveness, and added value. + Producers must struggle to satisfy technical, performance, schedule, and cost expectations of the customer. = Drive the need for control methods used in Six Sigma & TQM Do it right the first time Eliminate product variation ↓ Delivery of offerings, which are defect free at a min. cycle time

3. Six Sigma initiatives to reduce variation
In the past, the pursuit of quality was more a philosophy than an art or science… these tools can change that.
Design
Design to standard parts
Design to standard materials
Robust design
Design for assembly
Design for reliability
Design for simplicity
Process
Short-cycle manufacturing
Process characterization
Process standardization
Statistical process control
Material and Components
Part standardization
Transaction(s) standardization
Supplier statistical process control (SPC)
Supplier certification
Material requirements planning

4. Poka-Yoke Japanese for mistake proofing
Poka (inadvertent error)
Yokeru (avoidance)
Design and implementation of actions to prevent errors, mistakes, or defects in our everyday activities and processes.
Errors should not be considered inevitable. Any error type can be reduced considerably, if not eliminated altogether.

5. Common types of mistakes
Incorrect processing
Work pieces placed incorrectly
Missing parts
Wrong parts
Wrong blue print or instructions
Wrong piece processed
Operation skipped or omitted
Improper adjustment
Equipment not set up properly
Process improperly supersized
Use of the wrong tool

6. How are these examples of daily Poka-Yoke?
Parking garages have low clearance. To insure that cars entering the garage will fit, garages are fitted with a go/no-go gauge at the entrance. Hitting the swinging sign or pipe will not damage the vehicle as much as driving into a concrete beam.
Filling pipe insert keeps larger, leaded-fuel nozzle from being inserted
Gas cap tether does not allow the motorist to drive off without the cap
Gas cap is fitted with ratchet to signal proper tightness and prevent over-tightening
This iron turns off automatically when it is left unattended or when it is returned to its holder
Examples from:

7. Keys to implementing Poka-Yoke
Utilize Failure Mode-Effects Analysis (FMEA) to identify opportunities.
Use the highest principle possible.
Elimination
Replacement
Facilitation
Detection
Mitigation

8. Statistical Process Control (SPC)
SPC is a method of analyzing data over time and using the result of the analysis to solve manufacturing and processing problems
Can be applied to almost anything that can be expressed with numbers of data.
Control = to keep something within boundaries
Process = any set of conditions or causes, which work together to produce an output or result.
Process is a sequence of activities characterized by:
Measureable inputs
Value-added (VA) activities
Measureable Outputs
Repeatability

9. Statistical Control
A process is within statistical control when the process contains only natural, chance variation.
Only when a process is statistically stable can it be treated as a population with constant mean, standard deviation, and distribution.
A process control system is a feedback four element system:
The Process
Information about Performance
Action on the Process
Actions on the Output

10. Prevention vs. Detection
Every process contains several sources of variation
Two product characteristics are not equal
Differences among products, transactions, or services may range from very large to very small.
No matter how small, variation is always present
Time period and conditions under which measurements are made affect the total process variation visible to the user
Strategy of Prevention - It is always more effective to avoid “waste” by not producing it (vs. trying to detect).
Minimum Requirements – If specification limits can be determined then anything within those limits is acceptable and everything outside them is unacceptable.

11. Causes of Variation Common Causes Special Causes Assignable causes
Only natural variation (no patterns, cycles or unusual points.)
Process in statistical control when the only source of variation is common cause.
Values will tend to forma pattern that can be described by a probability distribution.
Assignable causes
Unnatural patterns
Out of control process
Can be detected by simple statistical techniques  such as Control Charts.
=0 1 2 3
95%
99.73%
-1
-2
-3

12. Continuous Statistical Process Control (SPC) Tools
Purposes of Control Charts
Control a CTP characteristic (statistical process control - SPC)
Used to monitor a CTQ,CTC or CTD characteristic (Statistical process monitoring-SPM)
Used as diagnostic tools for any CT Characteristic.

13. Development of Control Charts
Based on in-control data
If non-random causes present, discard data
Correct control chart limits
Combine location and variation charts
Charts must be reviewed and adjusted throughout usage and after acting on information.
Define the problem
Establish the measurement system
Determine the control charts
Prepare data collection
Implement and use control charts
Continuous Improvement

14. Control Charts Commonly based on   3 Sample mean: x-bar-charts  x
Sample range: R-charts
Sample std. deviation: s-charts
Fraction defective: p-charts
Number of defects: c-charts
Consider sample size, desired sensitivity, allowable complexity level of charts and attribute vs. variable data.

15. What type of Control Chart depends on what kind of data you have…
Attribute data
Product characteristic evaluated with a discrete choice
Good/bad, yes/no
Variable data
Product characteristic that can be measured
Length, size, weight, height, time, velocity

16. Z Values in Control Charts
Smaller Z values make more sensitive charts (Type I error)
Z = 3.00 is standard
Compromise between sensitivity and Type II errors

17. Process Control Chart Upper control limit Central Line Lower control
=0 1 2 3
95%
99.73%
-1
-2
-3
Central
Line
Lower
control
limit 1 2 3 4 5 6 7 8 9 10
Sample number

18. Is your process in Control?
No evidence of out-of-control, if :
No sample points outside limits
Most points near process average
About equal number of points above & below centerline
Points appear randomly distributed

19. Is your process out-of-control?
Sample data fall outside control limits
Theory of runs
2 out of 3 beyond the warning limits
4 out of 5 beyond the 1 limits
8 consecutive on one side
Patterns

20. Zones For Pattern Tests
UCL
LCL CL
Zone A
Zone B
Zone C

21. Control Chart Patterns
8 consecutive points on one side of the center line.
8 consecutive points up or down across zones.
14 points alternating up or down.
2 out of 3 consecutive points in zone A but still inside the control limits.
4 out of 5 consecutive points in zone A or B.

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

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

24. Control Charts For Variables
Each measures process differently
Process average and variability must be in control
X Bar (Mean chart )– Measure the central tendency of a process over time
Dispersion charts
R (Range) – Measure the gain or loss of uniformity or variability of a process across time
S Chart
X-bar and R Charts often used together and jointly interpreted.

25. X-bar Chart Calculations

26. Example X-bar Chart Sample 4.850 4.900 4.950 5.000 5.050 5.100 X-bar 12 3 4 5 6 7 8 9 10
Sample

27. Range (R) Chart Std. Dev. (s) Chart

28. Slip-ring diameter (cm) (sample size =5)
R-Chart Example
Slip-ring diameter (cm) (sample size =5) R
Obs. 5
Obs. 4
Obs. 3
Obs. 2
Obs. 1
Sample 1
4.96
4.99
4.94
5.01
5.02
4.98
0.08 2
4.96
4.95
5.07
5.03
5.01
5.00
0.12 3
4.99
4.92
4.93
5.00
4.97
0.08 : 10
4.99
5.07
5.08
4.98
5.01
5.03
0.10 
50.09
1.15

29. 3 Control Chart FactorsD3 D4 B3 B4 2
1.880
3.267 3
1.023
2.575
2.568 4
0.729
2.282
2.266 5
0.577
2.115
2.089 6
0.483
2.004
0.03
1.970 7
0.419
0.076
1.924
0.118
1.882 8
0.373
0.136
1.864
0.185
1.815 9
0.337
0.184
1.816
0.239
1.761 10
0.308
0.223
1.777
0.284
1.716 11
0.285
0.256
1.744
0.321
1.679 12
0.266
0.354
1.646 13
0.249
1.692
0.382
1.618 14
0.235
0.329
1.671
0.406
1.594 15
0.348
1.652
0.428
1.572 20
0.180
0.414
1.586
0.510
1.490 25
0.153
0.459
1.541
0.565
1.435

30. Example R-Chart Range Sample 0.00 0.05 0.10 0.15 0.20 0.25 0.30 1 2 34 5 6 7 8 9 10
Sample

31. Other Variable Charts MR (Moving Range) Chart
Average of a series of moving ranges
Use difference between successive pairs of numbers in a series
IM (Individual Measurement) Chart

32. MR (Moving Range) Chart
Moving Range (MR)
Average Moving Range:
Estimation of 
Control Limits

33. IM (Individual Measurement) Chart
Average Value:
Control Limits

34. Control Charts For Attributes
p Charts
Chart percent defectives in sample
c Charts
Display the number of defects per sample
np Charts
u Charts

35. p-Chart

36. p-Chart Example 20 samples of 100 pairs of jeans Sample # # Defects
Proportion Defective 1 6
0.06 2
0.00 3 4
0.04 …. 20 18
0.18
200
0.10

37. p-Chart Calculations

38. Example p-Chart Sample number 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16
0.18
0.20
Proportion defective 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20
Sample number

39. np Chart
np chart
If samples are the same size it is simpler to plot the number of defective in each sample instead of calculating the % defective.

40. c-Chart

41. c-Chart Example Count # of defects in 15 rolls of denim fabric
Sample #
# Defects 1 12 2 8 3 16 …. … 15
Total
190

42. c-Chart Calculations

43. Example c-Chart 3 6 9 12 15 18 21 24 Number of defects 2 4 6 8 10 122 4 6 8 10 12 14
Sample number

44. U Chart Variation of the c chart.
Each point is the average number of defects per unit in a sample of k units
The number of units at are averaged need not be the same for all samples.

45. Pre-Control Not waiting for failure to adjust the process
Upper
control
limit
=0 1 2 3
95%
99.73%
-1
-2
-3
Central
Line
Lower
control
limit 1 2 3 4 5 6 7 8 9 10
Sample number
Establish Green zone 1.5 s, and yellow zone  3 s. Everything outside of 3s would be red.

46. Using Pre-Control
Qualify the process by taking 5 consecutive samples in green zone.
The probability of 2 units falling outside of green should prompt a process adjustment or stop.
After adjustment or stop, it will need to requalify process
State of 2 successive samples
Action
Both A & B inside Green
No action
A is Green, B is yellow
No Action
A is Yellow, B is Green
Both A & B are yellow on same side (high or low)
Adjust Process
Both A & B are yellow on opposite sides (high and low)
Stop Process