Section 4 Process Capability

Lesson S04-02

Text: Section 4 pages 9 – 16

Duration: 27 minutes

Calculating the Proportion Nonconforming

Next, we explain a method for determining the proportion of nonconforming parts when the distribution of individuals is Normal. The procedure requires the use of the Standard Normal table (to avoid dealing with Calculus!) We will review the Standard Normal distribution and the table describing it.

The Standard Normal Distribution

The Standard Normal (or “Z” distribution as it is sometimes referred to) has the notable feature that the mean is zero and the standard deviation is 1. Thus, the Z scale is an indicator of the distance from average in number of standard deviations.

The 7-up Example

The Z Table used in this example is in the text in Section 4 page 14.

The Fuel Injector Example

How to Determine Probability with Excel

How to Determine Probability with Minitab

Section 4 Process Capability

Lesson S04-01

Text: Section 4 pages 1 – 8

Duration: 9 minutes

Introduction to Process Capability

Introduction to Process Capability Assessment

Process Capability Assessment addresses how well a process will perform relative to specifications. Highly capable processes have small variation and possess minimal risk of producing nonconforming products.

Several approaches exist to measure process capability. This course will focus on a few of the most common methods.

Is This Process Stable?

Quick Quiz

 

View the next video for answers/discussion.

Is the Process Capable?

Quick Quiz

 

View the next video for answers/discussion.

Drawing a Conclusion

Stability and Capability Concepts Review

More frequently than not, stability and capability are confused with each other. In addition, some think that stability implies capability and vice versa. This is not true. Here, we again demonstrate that stability and capability are independent notions, and there is no relation between the two.

Section 8

Many types of production processes are not well supported by the traditional charting techniques that were first invented in the 1920’s. This topic covers several additional control charting methods that have numerous applications in modern production systems.

Sections 5 through 9 include details on:

• 5. Charts for Short Production Runs (Short Run Charts)
• 6. Charts for Multiple Locations (Within/Between Charts)
• 7. CUSUM Charts
• 8. Trending Charts
• 9. Charts for Attribute Data (Appendix in text)

Section 7

Many types of production processes are not well supported by the traditional charting techniques that were first invented in the 1920’s. This topic covers several additional control charting methods that have numerous applications in modern production systems.

Sections 5 through 9 include details on:

• 5. Charts for Short Production Runs (Short Run Charts)
• 6. Charts for Multiple Locations (Within/Between Charts)
• 7. CUSUM Charts
• 8. Trending Charts
• 9. Charts for Attribute Data (Appendix in text)

Section 6

Many types of production processes are not well supported by the traditional charting techniques that were first invented in the 1920’s. This topic covers several additional control charting methods that have numerous applications in modern production systems.

Sections 5 through 9 include details on:

• 5. Charts for Short Production Runs (Short Run Charts)
• 6. Charts for Multiple Locations (Within/Between Charts)
• 7. CUSUM Charts
• 8. Trending Charts
• 9. Charts for Attribute Data (Appendix in text)

Section 1

Welcome to the Statistical Process Control & Process Capability course!

In this section, you will find information about:

• An introduction to the course along with the purpose, goals, and business drivers involved as you implement SPC and process capability studies.
• A brief course overview
• A link to download the course supporting textbook
• Recommendations to get the most from the course
• An introduction to the mechanics of this online course

Click on the module 1 menu item (in the right sidebar on larger screens or below the content on smaller screens) to view the individual lessons within this section of the course. Note the menu will not work if you are not registered for the course and if you are not logged in to the site.

Section 5

Many types of production processes are not well supported by the traditional charting techniques that were first invented in the 1920’s. This topic covers several additional control charting methods that have numerous applications in modern production systems.

Sections 5 through 9 include details on:

• 5. Charts for Short Production Runs (Short Run Charts)
• 6. Charts for Multiple Locations (Within/Between Charts)
• 7. CUSUM Charts
• 8. Trending Charts
• 9. Charts for Attribute Data (Appendix in text)

Section 4

Process capability assessment is performed to assess how well a product characteristic will meet customer or engineering specifications. Highly capable processes are required in order to provide a consistent and reliable performance for our customers.

This section focuses on the methods used to assess process capability for key characteristics.

This section includes details on:

• Types of capability assessments
• Review of stability vs. capability
• Estimating ppm (parts per million defective)
• Defining and estimating capability indices (e.g. C_pk)
• Interpretation and limitations of capability indices
• Handling nonnormal data

Section 3 Control Charts

Lesson S03-14

Text: Section 3 pages 76 – 80

Duration: 6 minutes

Control Chart Selection

A large variety of charts are available for use and the proper chart selection depends on several factors. These include:

• Data Type (Variable or Attribute)
• Sensitivity Required
• Ability to Obtain Rational Samples
• Production Volumes and Cycle Times
• Constancy of Sample Size

Control Plan Updates

As Statistical Process Control charts are implemented, the Control Plan should be updated to reflect the following information:

• Type of control chart(s)
• Sample size
• Sampling frequency

Control Charts Summary

Section 3 Control Charts

Lesson S03-13

Text: Section 3 page 75 and Section 9 pages 11 – 12

Duration: 10 minutes

Introduction to Exercise 6

a. It is wise to ignore the first chart signal and wait for another to be sure the process is out-of-control before reacting (true/false).

Solution/Discussion: Exercise 6 a

b. When should control limits be recomputed?

Solution/Discussion: Exercise 6 b

c. Provide an example (from your operation, if possible) where obtaining a rational sample may be problematic.

Solution/Discussion: Exercise 6 c

d. How does the subgroups size affect the sensitivity (ability to detect process changes) of an X̄ chart?

Solution/Discussion: Exercise 6 d

e. A beer bottler labels the product as a 12 fluid oz container. The filling process standard deviation (for volume) is 0.12 fluid oz. The fill volumes follow a normal distribution and the bottler decides to center the process at 12.36 to protect from “underfills.”

What is the sample size required to detect a shift of 0.18 fl oz with 80% probability (type II error is 0.20)?

Hint: Use MINITAB or the Excel worksheet Control Chart Sample Size.XLS

Solution/Discussion: Exercise 6 e

f. This is a continuation of the previous problem. Following a variation reduction effort, the standard deviation for the fill volume has been reduced from 0.12 to 0.08 fl oz.

What is the sample size required now to detect a shift of 0.18 fl oz with 80% probability (type II error is 0.20)?

Solution/Discussion: Exercise 6 f

Section 3 Control Charts

Lesson S03-12

Text: Section 3 pages 73 – 75

Duration: 19 minutes

Sample Size Guidance

The sample size for an X̄ control chart is a function of:

• The process standard deviation
• The size of the shift we want to detect
• The allowable level of Type II Error (probability that the specified shift is not detected when the shift occurs)

We have already seen that the smaller the size of the shift that we want to detect, the larger the sample size we need. Also, reducing Type II error requires a larger sample size. Finally, the larger our standard deviation is, the larger the sample size that is needed to detect a specified process change.

The Sample Size Worksheet

An Excel file called “Control Chart Sample Size” (download with the link) and it allows sample sizes to be calculated for X̄ charts in order to detect a specified mean shift with a specified power. This worksheet allows the user to specify:

• Process Standard Deviation
• Amount of Shift to be Detected
• Power (Probability of Detection)

Download the Excel worksheet here: control-chart-sample-size.xls

Sample Size Calculations in Minitab

Sampling Frequency

For ongoing process monitoring, the sampling frequency is a function of the: – Risk of Undetected Process Changes

• Current Process Capability
• Type II Error Probability (probability that a process change is NOT detected on a given sample)
• Cost of Sampling

Section 3 Control Charts

Lesson S03-11

Text: Section 3 pages 64 – 72

Duration: 24 minutes

Sample Size Sensitivity

Our discussion now moves to the issue of sample size, although the term “sensitivity” is sometimes used. It will become evident why sample size controls the sensitivity of control charts. By sensitivity, we mean the ability of a control chart to detect change.

Control charts are supposed to detect change when change occurs. The question is, “what kind of change do charts detect?” Are all X̄ charts equivalent in their ability to detect changes?

Example: Ice Cream Filling Process

Sample Size Summary

Section 3 Control Charts

Lesson S03-10

Text: Section 3 pages 55 – 63

Duration: 15 minutes

Types of Samples

There are a multitude of statistical sampling types, but in this section, only three will be described. Of the three, only one is fundamental to the traditional control charting methods presented in this course. Let’s discuss a Random Sample, a Systematic Sample, and a Rational Sample.

Example: A Choice Between Two Plans

Rational Samples

Discussion on the sample plan selection and the various considerations.

Violations of Rational Sampling

Examples include:

• Sampling from multiple locations on the same unit
• Multi-Cavity Molding Operations
• Machining Operations where multiple units are machined together
• Continuous Flow processing

Subgroups vs. Individuals

A common question is, “Why plot subgroup averages rather than individual values?” As we have seen earlier, individual measurements often do NOT follow a normal distribution. Therefore, determining appropriate control limits requires methods for nonnormal data. Averages follow a normal distribution due to the Central Limit Theorem so plotting averages is convenient.