Section 7 CUSUM Charts

Lesson S07-01

Text: Section 7 pages 1 – 4

Duration: 10 minutes

Introduction to CUSUM Charts

Control charts are supposed to detect change when change occurs. One problem with traditional control charting procedures is that they are not sensitive enough to detect small shifts.

Charts of averages may be designed to detect very small shifts by selecting a large enough sample size. Unfortunately, sometimes the required sample size is too large for practical purposes. Furthermore, there are instances when the largest possible sample size is one (n=1). In these instances, a CUSUM chart may be beneficial.

CUSUM Approaches

Appendix II Attribute Charts

Lesson A2-08

Text: Appendix II additional notes and summary

Duration: 7 minutes

Summary and One More Thing

Appendix II Attribute Charts

Lesson A2-07

Text: Appendix II pages 33 – 34 and 37 – 38

Duration: 9 minutes

Introduction to Exercise

The exercise Excel worksheet: Attribute Chart Exercises.xlsx

Solution / Discussion of Exercise

Appendix II Attribute Charts

Lesson A2-06

Text: Appendix II pages 30 – 38

Duration: 14 minutes

Introduction to Standardized Charts

When the sample size fluctuates by more than plus or minus 20% of the average sample size, standardized charts should be used to account for the varying size. Consider how the situation of varying sample size may arise, and also observe its adverse consequence if not properly accounted for.

p Chart Standardization

Standardized p Chart Example

Download the spreadsheet for computing standardized p or u charts: standardized-p-and-u-charts-calculations.xlsx

Standardized u Chart

Appendix II Attribute Charts

Lesson A2-05

Text: Appendix II pages 28 – 29

Duration: 2 minutes

Introduction to u Charts

u charts look identical to c charts when the sample size is constant. To use a c chart, the sample size must be constant. The u chart offers flexibility in the sense that the sample size can fluctuate.

Download the exercise data (and solution) within the file: attribute-u-chart-exercise.xlsx

Appendix II Attribute Charts

Lesson A2-04

Text: Appendix II pages 21 – 27

Duration: 9 minutes

Introduction to c Charts

c charts are used to monitor the number of flaws or errors in a process. The random variable, c, follows a Poisson distribution. The Poisson distribution is a discrete distribution (as is the Binomial).

A c Chart Example

Download the calculations worksheet for a c chart: calculation-worksheet-for-c-chart.pdf

Appendix II Attribute Charts

Lesson A2-03

Text: Appendix II pages 18 – 20

Duration: 5 minutes

Introduction to np Charts

np charts look identical to p charts when n is constant (except for the scale). In fact, np charts can only be used when n is constant, even though p charts can be modified to handle changing sample sizes.

A np chart Minitab Example

Download the exercise data (and solution) within the file: attribute-p-chart-exercise.xlsx

Appendix II Attribute Charts

Lesson A2-02

Text: Appendix II pages 8 – 18

Duration: 21 minutes

Introduction and Sample Size Determination

Many people argue that tracking attribute data is inspection. However, any time we monitor statistics over time, we are implementing SPC, even if the data is attribute in type. We begin with p charts because they are commonly employed. Furthermore, percentages of scrap, absenteeism, flawed units, incorrect forms, and so on are often tracked. Although attribute data is less informative than variable type data (yes/no or counts versus actual measurement values), we can perform statistical process control on attribute data.

p Chart Control Limits and Normal Approximation

A p Chart Example

Calculate p̄

Constructing the p Chart

Download the  Calculations Worksheet for p Chart. Or view workbook page Appendix II: Page 16 and 17.

Appendix II Attribute Charts

Lesson A2-01

Text: Appendix II pages 1 – 7

Duration: 11 minutes

Introduction to Attribute Charts

All of the material covered up to now assumes variable type data. However, this topic is an introduction to managing attribute data for statistical process control purposes. Although attribute data may not be as informative as variable type, there are many situations where only attribute type data is available.

Exercise Introduciton

Discussion of Quick Exercise Solution

Section 9

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 Charts for Multiple Locations

Lesson S06-07

Text: Section 6 page 48 and Section 9 page 21

Duration: 3 minutes

Introduction to Exercise 13

For the following data, determine whether an S or d chart would be necessary. The data may be found in the file named Exercise13.MTW.

Solution / Discussion of Exercise 13

Section 6 Charts for Multiple Locations

Lesson S06-06

Text: Section 6 page 38 – 48

Duration: 6 minutes

Analysis of Variance

One of the most common methods for statistically testing for differences between locations is called an Analysis of Variance. It is typically abbreviated as “ANOVA.” At first thought, one might perform what is called a “one way ANOVA” to test for differences between groups (locations in our case).

Conceptually, a one way ANOVA statistically compares the average of each location to identify whether the averages are statistically the same or whether at least one of the averages is different.

Section 6 Charts for Multiple Locations

Lesson S06-05

Text: Section 6 page 37 and Section 9 page 19

Duration: 4 minutes

Introduction to Exercise 12

Determine whether the two cavities are consistent with each other or whether they are significantly different from each other. The data may be found in the file named Exercise12.MTW.

Solution / Discussion of Exercise 12

Section 6 Charts for Multiple Locations

Lesson S06-04

Text: Section 6 pages 22 – 36

Duration: 16 minutes

Testing Two Locations

In the example just completed, the need for the d chart was obvious because a simple chart of the three locations demonstrated a significant difference between the locations.

An obvious discrepancy between locations is often not apparent. In many situations, an objective test is required to determine whether location to location differences exist.

The appropriate statistical methods to test for significant differences between locations are a Paired t-Test or an ANOVA (2-way)

The use of Paired t-Test is covered next.

S or d Chart

Paired t-Test

An Example

Paired t-Test Background

Section 6 Charts for Multiple Locations

Lesson S06-03

Text: Section 6 pages 14 – 22

Duration: 15 minutes

Introduction to X̄, Rb, and D Charts

When the differences between locations are not random, that is, one location produces larger values than the other location, we may use a “d” (differences) chart to monitor the consistent difference that is expected between the locations. “d” represents the (largest) “difference” that is expected between the locations.

Chart Using Minitab

Consider the Source of Variation

Use the 3-way Charts

Download the  X̄, Rb, and D Charts Calculations Worksheet. Or view workbook page Section 6: Pages 19 and 20.

Summary