Understanding Type I and Type II Errors in Statistical Process Control

1. 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 UniversityPomona 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

8. 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 Major Concept #2: Process Control

9. Process Capability What it is Process Control Note - no reference to specs ! In Control (Special Causes Eliminated) TIME (continued below) Out of Control (Special Causes Present) Process Capability 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. Type I error: a False alarm, producer’s risk No error Type II error: b Failure to detect, consumer’s risk No error Types of Error Test Says H0 False H0 True H0True State of Reality H0False

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

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?