1. DSQR Training Control Chart Topics
HEATING, COOLING & WATER HEATING PRODUCTS
DSQR Training Control Chart Topics
Ted Fisher/Fred Nunez
Corporate Quality

2. Class Charting Exercise
The Process: Device that “produces” small chips, right in the classroom.
Sample Size: n = 2 for each subgroup. We will pretend that we are doing:
One piece at beginning of the run
One piece at the end of the run
To Do:
Measure both pieces and record the data
Calculate the Average and the Range; plot both points immediately
Evaluate:
If in-control – continue to run
Otherwise, process will be adjusted to bring it back into control in accordance with the attached reaction plan
Control limits are on the chart.
Afterwards, we will discuss what we have learned from this simple exercise.

3. A Basic Control System

4. Reaction Plan for Part #654321

5. Control Plan for P/N
Control Chart Exercise Data Sheet

7. A COMPLETE SPC CONTROL SYSTEM
DETECTION MODE
PREVENTION MODE
CORRECTIVE ACTION &
COMPENSATING ACTION
PREVENTIVE ACTION
(Identify causes and take action after the fact, or take action without finding cause)
(Identify causes and take action before the fact)
“Reaction Plan”: the written compensating and corrective actions alone.

8. Reasons for Out-of-Control (Historical Data)
Question: What would you suggest we do with this data?

10. CONCLUSIONS - Class Charting Exercise - What Did We Learn?
Variation is always present
Values different from target are not justification for process adjustment
Need tool to distinguish “signal” from “noise”
This tool is the control chart
The control chart says when to stop and adjust, and when to leave alone
If the process average changes, the control chart will signal this change
though perhaps not on the very first sample after the change
If the process variability changes, the control chart will signal this change
Always review the range chart before reviewing the X-chart because if
the Range chart goes out-of-control, the X-chart might be meaningless
for that plotted point

11. Point Movements on a Variables Control Chart

12. Point Movements on a Variables Control Chart

13. Summary of Point Movements
Changes in the process average are reflected in the XBar chart but not in the R chart
Therefore the R chart is independent of the XBar chart
Changes in process variability are reflected in both charts
Therefore the XBar chart is not independent of the R chart

14. The Central Limit Theorem
Averages of samples from any (stable) distribution tends to be normally distributed
As n becomes larger and larger, the distribution of averages tends closer and
closer to normality
Generally for n as small as 4-5, the distribution of averages will be close to normal
Many industrial processes are such that the distribution is reasonably normal with
sample sizes as small as n=2

15. Central Limit Theorem Distribution
50 tosses of Three Dice

16. Central Limit Theorem Distribution
Dice Histogram
150 Individual Values
Dice Histogram
50 Subgroups of n=3
(Uniform Distribution)
(Approaching a Normal Distribution)
Value of Die
Average Value

17. Central Limit Theorem Distribution

18. Central Limit Theorem Distribution

19. Increasing Sample Size Reduces the Spread of the Distribution
Averages are less variable than individuals
As sample size (n) increases, the spread of the distribution decreases by
the square root of n
SX = SX n
where,
sx = sample standard deviation (“s-sub x”)
= standard error (“s-sub xbar”)
n = sample size sx

20. Why Use Averages?
See chart on next page.

21. Probability of Getting a Sample Value That Lies Above the Upper 3 Sigma Control Limit
Plots of Individuals
Plots of Averages 4 2 3 1

22. Range Charts vs. Standard Deviation Charts
Statistical Efficiency of the Range for Estimating Sigma
Although Range is an unbiased estimate of standard deviation, its efficiency decreases as sample sizes increases. This is because the Range uses only two pieces of data, the max and min.
For this reason, R-charts should be replaced by s-charts when the subgroup size is larger than some set value. Although there is no general agreement on when to switch, most practitioners will make the switch at subgroups sizes of 6, 8, or 10.
Control charts for Average, Range and Standard Deviation have been constructed for 25 subgroups of size 3 (next page)
Upon review, please note that:
the plotted values for the R and S chars are different, but
the pattern is very similar, and
the conclusions (in-control or not) are the same

23. Range Charts vs. Standard Deviation Charts
X-Bar Chart
Range Chart
S Chart

24. Why 3 Sigma Limits?
A discussion of errors and risks

25. Why 3 Sigma Limits?

26. Why 3 Sigma Limits?

27. 3-D Charts (or I-R-MR)
Developed to handle situations where the within-piece, within-coil, within-batch or
within-lot variability is expected to be significant (relative to piece-to-piece,
coil-to-coil, batch-to-batch, or lot-to-lot variation )
The IX chart displays the average, the MR chart displays the part-to-part average
and the R(within) chart displays the within part variation

28. 3-D Chart Example
Conventional Xbar/R chart for Tank Height; Subgroup size of 2 – two consecutive tanks are sampled.
Out-of-control – majority of points are beyond control limits. .
If it is reasonable to assume that the subgroup-to-subgroup variability can be made as small as the within-subgroup variability, then an Xbar/R chart above is the correct choice.
Caution: This approach should not be used indiscriminately. The moving range calculated from the subgroup averages should only be used when the physical situation warrants its use.
Source: “Understanding Statistical Process Control”, 2d Edition, Wheeler & Chambers, pg 225

29. 3-D Chart Example
3-D Chart shows much better control than the conventional Xbar/R chart
Standard IX/MR chart calculations are used for the IX/MR chart
The R chart is calculated in the normal manner

30. CONTROL CHARTS FOR DEVIATION FROM TARGET
“Target Charts”
Conventional control charts assume that the process average is constant (or at least intended to be constant). Some processes however are intended to run with different targets for different part numbers.
Typical example:
The same process is used to
make various diameters of steel
rods as shown. The process is the same but the target for each P/N is different.
In this case, a conventional control chart would be meaningless since the process average is not intended to be constant. Depending on part number, the target varies between 0.35 and 0.65 inches. A practical approach is to use a Target Chart, plotting only the deviations from target. .
Let’s look an example where a company uses the same process to make parts with three different OD’s for three customers.

31. A DEVIATION FROM TARGET CONTROL CHART
For Use When Target Values Are Not Constant

32. Incorrect Handling of The O.D. Data

33. Correct Handling of The O.D. Data

34. SPC IMPROVEMENT CYCLE
Determine your sampling scheme, sample size, sampling frequency, measurement device, etc.
These 3 steps are repeated for continuing process improvement
1. Collection:
3. Capability:
Gather data
Plot on a chart
Determine process capability
Action to improve process capability
2. Control:
Calculate control limits from the data
Identify causes for out-of-control points
Action to correct

35. Common Questions2
Common Questions to Ask for an Out of Control Process:
Are there differences in the measurement accuracy/precision of the of the instruments used?
Are there differences in the methods used by different operators or crews?
Were any untrained workers involved in the process at that time?
Is the process affected by the environment?
Is the process affected by tool wear?
2 - Adapted from The Memory Jogger by GOAL/QPC

36. Common Questions Has there been any change in raw materials?
Is the process affected by operator fatigue?
Has there been any change in maintenance procedures?
Is the machine being adjusted frequently?
Did the parts come from different processes (e.g. machines, shifts or operators)?
Are operators afraid to report “bad news”?

37. Develop an SPC Control System
An SPC Control System is a specific plan of action to bring a process back within spec or into a state of control
It documents what action to take when the process is out-of-control or out-of-spec
Types of action (in order of increasing effectiveness)
Compensating
Corrective
Preventive
Can you think of examples for each of these?
not blaming people.
Focus on improving the process

38. A COMPLETE SPC CONTROL SYSTEM
DETECTION MODE
PREVENTION MODE
CORRECTIVE ACTION &
COMPENSATING ACTION
PREVENTIVE ACTION
(Identify causes and take action after the fact, or take action without finding cause)
(Identify causes and take action before the fact)
“Reaction Plan”: the written compensating and corrective actions alone.

39. Ingredients For SPC Success
Technical & Process Knowledge
Statistical Process Control Tools
Teamwork
65%
25%
10%
Appropriate portions plus good mixing produces the best results.

40. Criteria for SPC The Characteristic To Be Controlled:
Must be IMPORTANT
Customer fitness for use requirements
History of (or potential for) high costs due to nonconformance
History of frequent, costly process adjustments
Is one that you have authority and responsibility for controlling
Is one in which you have (or can gain) adequate knowledge of
how the process affects the characteristic being controlled
Can be monitored early in the process, close to the causes
(e.g. raw materials, process variables, etc.)
Is quantifiable (objective) rather than subjective or judgmental
Can be easily measured (for timely feedback of information)
BOXED ITEMS ARE CRITICAL