1. ASQ Orange Empire Section October 11, 2016
The Importance of Understanding Type I and Type II Error in Statistical Process Control Charts
Phillip R. Rosenkrantz, Ed.D., P.E. California State Polytechnic University Pomona
ASQ Orange Empire Section
October 11, 2016

2. Goals
Provide a brief review of the concepts of process control and process capability
Explain Type I and Type II error with colorful examples
Give examples of Type I and Type II error for common decision rules
Illustrate how the improper use of decision rules creates excessive Type I error and creates mistrust in the use of SPC
Suggest simple approaches for reducing Type I error in SPC

3. Assignable vs. Common Cause Variation
Dr. Walter Shewhart developed Statistical Process Control (SPC) during the 1920s. Dr. W. Edwards Deming promoted SPC during WWII and after.
Premise is that there are three types of variation
Common Cause Variation
Assignable (or Special Cause) variation
Tampering (or over-adjusting)
Each of these types of variation require a different approach or type of action.

4. Quinconx Demonstration
Common cause (natural) variation - Built-in random variation in the system. Difficult to reduce without changing the system or process. Responsibility of management because they are responsible for the system.
Assignable or Special cause variation - Variation caused by identifiable events usually under control of the work group
Tampering - Over adjusting of the process resulting in increased variation.

5. Common Cause vs. Assignable Cause Variation
According to Dr. Deming’s research, more than 85% of problems are the result of “common cause” variation. Management is responsible for the system and it is their responsibility to work on reducing this type of variation. Later research puts the estimate at over 94%.
The work group is responsible for preventing and reducing “assignable cause” variation.
Management needs to understand these concepts.

6. Tampering – The Third Type of Variation
Tampering is over-adjusting the system caused by a lack of understanding of variation.
Sometimes large built in variation is mistaken for a process going “out of calibration” and needing adjustment
Over adjusting actually increases variation by adding more variation each time the process is changed
Tampering is a difficult habit to break because many machine operators consider it their “job” to constantly adjust their machine.
SPC reduces or eliminates unnecessary adjustments.

7. Major Concept #1: Process Capability
The ability of a process to produce within specification limits
Able to produce within specifications – process is “capable”
Not able to produce within specifications – “not capable”
Often quantified with process capability indices
Cp, Pp – Ability to stay within specs if centered
Cpk, Ppk – Ability based on current distribution
There are two very important concepts that are central to this presentation. If a student could remember only two things from this chapter it would be the difference between process capability and process control. Along with that would be some appreciation for how they would be managed.
#1 is the concept of Process Capability
The ability of a process to produce within specification limits
Able to produce within specifications – process is “capable”
Not able to produce within specifications – “not capable”
Often quantified with process capability indices
Cp – Ability to stay within specs if centered
Cpk – Ability based on current distribution

8. Major Concept #2: Process Control
Process Control refers to how stable and consistent the process is.
“In-control” - stable and only experiencing systematic or “common cause” variation.
“Not in-control” – Process is not stable. Mean and variation are changing due to identifiable or “special” causes (usually controllable by those running the operation).
Represents <10% of the problems
#2 is the concept of Process Control
Process Control refers to how stable and consistent the process is.
“In-control” - stable and only experiencing natural or “common cause” variation.
“Not in-control” – Process is not stable. Mean and variation are changing due to identifiable or “special” causes (usually controllable by those running the operation).
Represents <10% of the problems

9. Process Capability What it is Process Control Process Capability
Note - no reference to
specs !
In Control
(Special Causes Eliminated)
TIME (continued below)
Out of Control
(Special Causes Present)
Process Capability
Sometimes a picture is helpful. The top figure illustrates the concept of Process Control. First we acknowledge that the system itself produces a certain amount of variation that is hard to identify and eliminate. Special cause problems exist caused by identifiable sources of variation. They cause quality problems. Eliminating and control these problems brings a process into a state of “control” or stability.
Once a process is in control, the next objective is to reduce common cause (built in) variation so parts are within specification. Reducing this variation may mean changing the system or doing scientific experiments to understand the factors causing this. Note that if you consider all problems to be special cause problems there is a tendency to blame the workers and not the system.
In Control and Capable
(Variation from Common
Causes Reduced)
Lower Spec Limit
Upper Spec Limit
TIME (continued from above)
In Control but not Capable
(Variation from Common Causes
Excessive)

10. Control Charts
Walter Shewhart developed control charts that help management and workers identify common cause and special cause variation
Management’s responsibility to reduce common cause variation
The work group is primarily responsible for controlling special or assignable cause variation
Small samples are taken periodically with statistics (e.g., average, range) plotted on charts and reveal the amount and type of variation. Control limits are traditionally +/- 3 standard deviations from the process average.

11. Sample Statistical Process Control (SPC) Chart

12. Use of Control Charts
When the process remains within control limits with only a random pattern, process variation can be attributed to common cause variation (random variation in the system) and is deemed “in control.” The process is stable and continues.
When the process goes beyond control limits or is non-random, it is assumed that an assignable cause is present and deemed “out of control.” The process is not stable and predictable. Find and eliminate the assignable cause.

13. Implementing SPC
SPC was designed to be a tool for first line workers to monitor for the presence of assignable causes
Requires that management not to use results for evaluating performance, but rather only for improving processes--otherwise data will be biased
Implies that the work group and support personnel take time from their other duties to permanently eliminate assignable causes that reoccur
Requires a culture of trust to work effectively

14. Where to Use SPC Use strategically on: Critical customer requirements
Major problems
Six Sigma project related processes
Use tactically on:
Processes that are not “capable” and need to be monitored closely

15. Managing SPC
Any Black Belt or Master Black Belt should be able to set up the proper SPC Charts and monitor them.
Issues to address when designing SPC charts:
Proper type of chart to use for the situation
Sample size and sample frequency
Sampling method
Decision rules being used
How assignable causes will be resolved
Is the process capable or not capable

16. Decision or Sensitizing Rules
Decision Rules (a.k.a. Sensitizing rules) are used by operators to determine if a pattern of points indicates a process is no longer stable, that is: “out-of-control”.
Some rules are designed to detect changes or shifts in the process center (mean)
Some rules are designed to detect changes in the process variation (standard deviation)
Some rules are designed to detect a non-normal patterns (e.g. trends or cycles)

18. Types of error when you use sampling
Control charts are based on sampling. Sampling is subject to two kinds of error:
Type I error (α): “False Alarm” – The sample indicates the process is “out-of-control” but is not
Type II error (β): “Failure to detect” – The sample indicates the process is stable, but it really is “out-of- control”
In most quality situations the larger concern is avoiding Type II error: “Failure to detect”. However, with SPC probably the larger concern is Type I error: “False alarms”

19. Types of Error Test Says State of Reality H0 True H0 False
No error
Type I error: a
False alarm, producer’s risk
Type II error: b
Failure to detect, consumer’s risk
H0 True
State of
Reality
H0 False

20. Examples Ho: Part is good Ha: Part is bad
Ho: Person did not commit the crime Ha: Person did commit the crime
Ho: The appendix is good Ha: The appendix is bad
Ho: The process is in control Ha: The process in not in control

22. A look at two decision rules and the probability of Type I and Type II errors

23. The Central Limit Theorem is the basis for assuming that a process “in control” follows a Normal Distribution
Before going farther in the study of variation, we need to take a moment and understand the Normal Distribution. The normal distribution is sometimes called the Bell Curve. In scientific circles is called the Gaussian Distribution.
The normal distribution describes the shape, center and spread of data such as measurements.
The measurements are centered around the mean or average.
We can calculate a statistic called the standard deviation that shows how far the measurement vary from the center.
The frequency of each value found in the measurements form the shape, or distribution.
The normal distribution is significant because is often found to be the best model for describing variation found in nature and for describing random variation in human-made processes.

24. Probability zones for the normal distribution

25. Rule 1 – Any point outside the 3σ control limits (probability shown for a sequence of 8 points)
False Alarm
Failure
To Detect
Failure
To Detect

26. Rule 4 – A run of 8 points on the same side of the centerline but within the 3σ control limits
False Alarm
Failure
To Detect
Failure
To Detect

27. Overall Type I Error for both rules

28. Cumulative effect of Type I error on a sequence of 8 points as decision rules are added
The probability of a False Alarm
Increases dramatically as decision rules
are added. It does not take too many
false alarms before operators begin
to lose faith in control charts and
start to ignore them.

29. Type I Error - A Common Problem That Makes SPC Ineffective
Too much Type I error eventually renders SPC ineffective. People get tired of chasing false alarms.
Many experts recommend using two decision rules (three at the most) to minimize Type I error. Rules 1 and 4 are commonly used.
Often, upon set up, software installers toggle on all decision rules thinking that is desirable.
If you use SPC software, ask to see which rules are in effect.

30. Tactics for Managers Ask to see SPC Charts
Ask how it was decided which type of chart to use.
Ask which decision rules are being used.
Look for out-of-control points on the chart and what the response was in removing the causes.
Ask if the work group is having trouble resolving assignable causes. Were Pareto Charts, Cause & Effect Diagrams, or other tools used to prioritize efforts?