1. Chapter 7- Additional SPC Techniques for Variables
Quality Improvement
Chapter 7- Additional SPC Techniques for Variables
PowerPoint presentation to accompany
Besterfield, Quality Improvement, 9e 1

2. Outline Continuous and Batch Processes Multi-Vari Chart Short-Run SPC
Gauge Control 2

3. Learning Objectives
When you have completed this chapter you should be able to:
Explain the difference between discrete, continuous, and batch processes.
Construct and use a group chart.
Construct a multi-vari chart.
Calculate the central line and control limits of a specification chart 3

4. Learning Objectives-Continued
When you have completed this chapter you should be able to:
Calculate the central line and central limits for a Zbar & W and Z & MW charts
Explain how to use precontrol for set up and run activities.
Determine a PTPC chart
Understand the concept of GR&R 4

5. Continuous Processes
Usually operates 24 hrs a day, 7 days a week, stops for scheduled maintenance.
Often involves a conveyor or moving assembly line
Associated with product involving hazardous materials

6. Continuous Processes Examples Paper-making machines Oil refineries
Soft drinks (continuous then discrete)
Control charts for each value (multiple stream output)

7. Continuous Processes
It is extremely important to have knowledge about the process and objectives for the control chart. When it is difficult to obtain samples from a location, sensors may be helpful to collect data, compare to control limits, and automatically control the process.

8. Continuous & Batch Processing
A good example of a continuous process is depicted by the paper-making process. They operate 24 hrs a day, 7 days a week, and stop only for scheduled maintenance or emergencies.Observed values are taken in the machine direction(md) or cross-machine direction (cd). 8

9. Continuous & Batch Processing
If the flow of pulp is controlled by 48 valves, then 48 md control charts would be required to control each valve.In this case it is very important for the practitioner to be knowledgeable about the process and have definite objectives for the control chart. 9

10. FIGURE 7-1 Paper-Making Machine

11. FIGURE 7-2 Paper Web and Observed Valves for md and cd Control Charts
MD = machine direction
CD = Cross-machine direction
FIGURE 7-2 Paper Web and Observed Valves for md and cd Control Charts

12. Group Chart
Eliminates the need for a chart for each stream; however, it does not eliminate the need for measurements at each stream
Uses the same methodology outlined in Chapter 6, 25 subgroups for each stream.
Use lowest and highest averages for Xbar chart and the highest range for the R chart. Each stream has a number.

13. Group Chart
Any out-of-control situation would call for corrective actions
We have the out-of-control situation when the same value streams gives the highest or lowest value r times in succession

14. Group Chart Each stream has the same target Same variation
See Table 7-1 for the r values
The technique is applicable to machines, test equipment, operators, or suppliers as long as:
Each stream has the same target
Same variation
Variation is as close to normal as required by conventional Xbar and R charts.

15. Batch Processes Paint, soft drinks, bread, soup, etc
SPC of batches has two forms:
Within batch variation
Only one observed value of a particular quality characteristic can be obtained
They need to be obtained at different locations within the batch
Between-batch variation
Does not always occur

16. FIGURE 7-3 Example of Multiple Streams: A Four-Spindle Filling Machine

17. Batch Chart
It is not a control chart, it might be more appropriately called a run chart
Can provide information for effective quality improvement

18. Batch Chart
Figure 7-4 Batch chart for different batches with differet specifications

19. Multi-Vari Chart
For detecting different types of variation that are found in products and services
The chart will lead to a problem solution much faster than other techniques
Shows the different types of variation within a single unit or service (within unit variation, unit-to-unit variation, time-to-time variation)

20. Multi-Vari Chart Procedure: Select 3 to 5 consecutive units
Plot the highest and lowest observed value of each piece
Draw a line between them
Repeat the process

22. Short-Run SPC Specification Chart
Used for small lot sizes – common in JIT
Gives some measure of control and a method of quality improvement
Central line and control limits are established using the specification
σ = (USL-LSL) / 6 Cp
JIT = Just in time
USL – LSL instead of range

23. Specification Chart
Cp is unknown since we do not have enough data
This is an approximation.
Do /- .12
These limits represent what we would like the process to do.

24. Cp = 1, 1.33, .67
FIGURE 7-7 Comparison for Different Capabilities for Specification Chart

25. Deviation Chart Deviation Chart
The plotted points are the deviation from the target
Even though the target changes, the central line for the X chart is always zero
Because the target changes, we require the variance (S2) of the different targets or nominal to be identical. This requirement is verified by ANOVA or by using
Target changes from different runs with different targets
ANOVA = Analysis of variances
Slide 18

26. Deviation Chart Advantages:
Provide the opportunity to convey enhanced information
Can plot different quality characteristics on the same chart
Can use this on Xbar R charts too.

27. Deviation Chart
Example 7.2, 7.3
HW 5, 6, 7
Figure 7-8 Deviation chart for individuals (X’s) and moving range(R’s)

28. Short-Run SPC

29. ZBar and W Charts Very good for short runs
Different quality characteristics such as length, width etc. may be plotted on the same chart
Can be used to monitor an operator’s daily performance
Can track an entire part history
Subgroup size MUST remain constant
Calculations are more involved

30. Zbar and W Charts Those are very good for short runs
LCLr < R < UCLr
D3Rbar < R < D4Rbar
D3 < R/Rbar < D4
LCL xbar < X bar < UCLxbar
Xbarbar – A2Rbar < Xbar < Xbarbar + A2Rbar
etc

31. Zbar and W Charts Figure 7-10 Zbar chart
W Chart CL = 1 and UCL = D4, LCL = D3
Since the scale and CLs are the same, we can plot different characteristics
Figure 7-10 Zbar chart

32. Z and MW Charts MW chart uses the absolute value
CL always the same
MW chart uses the absolute value
Individuals values are plotted

33. FIGURE 7-11 Central Lines and Control Limits for Z and MW Charts

34. Precontrol Was developed originally with machining operations in mind.
Operator faced with the problem of first setting up the machine and then deciding if the machine is ready for full production.
Small lot sizes with each piece taking a long time to produce.

35. Precontrol
Well suited for machining operations where one can devise simple feedback algorithms to bring the process back on target.
Requires operators who are very knowledgeable about the process.

36. Precontrol Steps for the construction:
Be sure that the process capability is less than the specifications.
PC lines are established to divide the tolerance into five zones (Figure 7-12)
The PC procedure has two stages:
Start-up
Run
Cp>1 This is management’s responsibility

37. Precontrol
Show for spec of /- .1 mm
For Cp >1.33 middle part is almost 1.
Normal Distribution, Cp and Cpk = 1.00 or greater. Specifications (Print Tolerance) at 6σ

38. Precontrol PRE-Control Rules: Start up Process
5 consecutive units in green zone –o.k. to run
1 yellow, restart counting
2 yellow in a row, adjust the process
1 red, adjust the process
< 5 signifies:
Process capability << 1
PRE-control is not appropriate

39. FIGURE 7-13 Precontrol Procedure

40. Precontrol Precontrol Rules cont’d: Sampling n = 2 units
Sample six pairs between adjustments. See Table 7-2 stoppages
1 unit in red zone
2 consecutive units in opposite yellow zone
2 consecutive yellow zones , process adjusted and procedure goes back to start up

41. FIGURE 7-16 Precontrol Chart

43. Precontrol Precontrol can be used for single specifications
Precontrol can be used for attributes
Precontrol is also used for visual characteristics by assigning visual standards for the Precontrol lines
For single spec, use ¾ of the tolerance
Attributes are yes/no decisions
Advantages
Short or long productions
No recording or plotting necessary
Applicable to startup
Works with tolerance vs control limits
Applicable to attributes
Simple to understand
Monitoring only, not problem solving!!!!

45. % Tolerance Precontrol Chart
Z Charts: Ability to accommodate more than one quality characteristic
We can combine Z chart into one technique by the use of percent tolerance precontrol chart (PTPCC)
Target or nominal
X*= (X – nominal) / [(USL-LSL)/2]
A negative value indicates that the observed value is below the nominal
Percent tolerence precontrol chart
vs target R

46. Out of control at 11:30

47. Gage Repeatability and Reproducibility
Gage Repeatability and Reproducibility (GR&R) studies provide information on measurement system performance by analyzing measurement error from various sources. Typically the sources of variation are divided into three categories: part-to-part, operator or appraiser, and gage or equipment. In some instances another category, interaction between parts and operators, can provide additional information about the gaging process.

48. Gauge Control All data have measurement errors
An observed value has two components
Observed value = True value Measurement error
Total Variation = Production Variation (process) + Measurement Variation
Measurement Variation = Repeatability (equipment variation) + Reproducibility (inspector or appraiser variation)

49. Gauge R&R
METHODS:
In instances such as automated measuring processes, the GR&R studies are not affected by operator influence. These data then are analyzed using a calculation method.

50. Gauge R&R Gage has to be calibrated using standards Data is collected
2 or 3 appraisers
2 or 3 trials
10 parts
Part characteristic is measured in a random order
These numbers are considered optimum
Trials should be in random order

51. Gauge Control
The preferred method is to use ANOVA, which is discussed in Chapter 13
A P/T is determined which compares the measurement variation (P) to the total variation (T)

52. Gage Control Guidelines for acceptance of GR&R using the P/T ratio:
Under 0.10 (10%) error
Gage system is satisfactory
0.10 to 0.30 (10% to 30%) error
May be acceptable based upon importance of application, cost of gage, cost of repairs, etc.
Over 0.30 (30%) error
Gage system is not satisfactory. Identify the causes and take corrective action
>0.3: May have bad parts that are declared good or good parts that are declared bad.

53. Evaluation If repeatability is large compared to reproducibility:
The gage needs maintenance
The gage should be redesigned to be more rigid
The clamping or location for gaging needs to be improved
There is excessive within-part variation

54. Evaluation If reproducibility is large compared to repeatability:
The operator needs to be better trained in how to use and read the gage
Calibrations on the gage are not legible
A fixture may be needed to help the operator use the gage consistently
HW 13,16

55. Homework
Chapter 7 Problems 5, 6, 7, 13, 16, 17
HW 13,16

56. Computer Program
EXCEL program files on the website solve for Zbar & W charts and PTPC chart.
GR&R (Gauge Repeatable and Reproducibility) can be affected by environmental factors such as temp, humidity, air cleanliness, and should be controlled