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Advanced Control Charts

Learning Objective

By the end of this lesson, learners will be able to:

  • Understand why advanced control charts are used in Six Sigma.
  • Explain how CUSUM and EWMA detect small or persistent process shifts.
  • Understand the purpose of multivariate monitoring.
  • Select an appropriate advanced control-chart approach for a process.
  • Recognize the role of advanced charts in sustaining process improvements.

1. Introduction

Basic control charts are effective for monitoring process stability, but some process changes may be small or gradual and therefore difficult to detect using conventional charts.

Advanced control charts provide additional sensitivity for detecting subtle, persistent, or complex changes in process performance.

They are particularly useful when the objective is to identify process deterioration early, before it develops into significant defects or customer problems.

2. Why Advanced Control Charts Matter

A Six Sigma improvement does not end when the improved process is implemented.

The process must continue to be monitored to ensure that:

  • The improvement is maintained.
  • Small shifts are detected early.
  • Process deterioration does not go unnoticed.
  • Corrective action can be initiated before performance becomes unacceptable.

Advanced control charts support this ongoing monitoring by providing greater sensitivity to certain types of process changes.

3. CUSUM — Cumulative Sum Control Chart

CUSUM stands for Cumulative Sum.

Instead of considering each observation independently, CUSUM accumulates information from successive observations.

This makes it particularly useful for detecting persistent small shifts in a process mean.

Key Concept

A small shift may not immediately produce a signal on a conventional control chart.

However, if the process continues moving in the same direction, the cumulative effect becomes increasingly visible in a CUSUM chart.

Typical Application

CUSUM can be useful when early detection of gradual process drift is important.

4. EWMA — Exponentially Weighted Moving Average

EWMA stands for Exponentially Weighted Moving Average.

EWMA gives greater weight to more recent observations while still considering previous observations.

This makes the chart sensitive to small, sustained changes in process performance.

Key Concept

A conventional chart may react strongly to a large individual shift.

EWMA is especially useful when the concern is a smaller change that develops progressively over time.

5. Multivariate Monitoring

Some processes have several quality characteristics that must be monitored simultaneously.

These characteristics may also be related or correlated.

Multivariate monitoring considers multiple characteristics together rather than treating every characteristic completely independently.

This can provide a more appropriate view of overall process behavior when several related variables are important.

Example

A semiconductor manufacturing process may require monitoring several wafer characteristics simultaneously.

A multivariate approach can help identify an overall change in the process that may not be obvious when individual characteristics are examined separately.

6. Tools & Techniques

The major tools covered in this lesson are:

  • CUSUM Control Chart
  • EWMA Control Chart
  • Hotelling’s T²
  • Multivariate Monitoring

The selection of the method should depend on the nature of the process and the type of change that needs to be detected.

7. Application Example

Pharmaceutical Tablet Weight

Consider a pharmaceutical manufacturing process where tablet weight is monitored continuously.

A conventional X-bar chart may show the process as being within its control limits while the average tablet weight is gradually drifting.

A CUSUM chart accumulates the small changes and may identify the developing drift earlier.

This allows the process team to investigate the cause before the drift becomes a significant quality problem.

8. Case Study

Semiconductor Wafer Manufacturing

A semiconductor manufacturing process requires very precise control of wafer thickness.

A small and persistent change in thickness can eventually affect product quality.

The organization uses advanced control-chart techniques to monitor the process.

CUSUM or EWMA can provide increased sensitivity to gradual changes, while multivariate monitoring can be considered when several related wafer characteristics need to be monitored together.

The objective is to detect process deterioration early and support timely corrective action.

9. Black Belt Perspective

A Black Belt should understand that control-chart selection should match the nature of the process and the type of change being monitored.

The important question is not simply:

“Which control chart should I use?”

The better question is:

“What type of process change am I trying to detect?”

For example:

  • Persistent small shifts → CUSUM
  • Small sustained changes → EWMA
  • Multiple related characteristics → Multivariate monitoring
  • Multivariate statistical monitoring → Hotelling’s T²

Advanced charts should be used when their additional sensitivity or multivariate capability provides value to the project.

10. Lesson Practice

Consider a process where the average output is gradually increasing by a small amount over time.

Answer the following:

  1. Why might a conventional control chart fail to detect the change quickly?
  2. Which advanced control-chart technique could be considered for detecting a persistent small shift?
  3. How does CUSUM differ from monitoring each observation independently?
  4. When might EWMA be useful?
  5. When would multivariate monitoring be appropriate?
  6. What is the role of advanced control charts in sustaining Six Sigma improvements?

11. Key Learning Points

  • Advanced control charts provide additional sensitivity for detecting subtle process changes.
  • CUSUM accumulates information and is useful for detecting persistent small shifts.
  • EWMA gives greater weight to recent observations and is sensitive to small sustained changes.
  • Multivariate monitoring considers several related characteristics together.
  • Hotelling’s T² is a tool used for multivariate statistical monitoring.
  • Advanced control charts support early detection and sustained process control.
  • The chart should be selected according to the type of process behavior and change being monitored.

12. Lesson Conclusion

Advanced control charts extend the capability of Statistical Process Control beyond basic monitoring.

For a Black Belt, the key is to recognize when a process requires greater sensitivity to small or gradual changes, or when several related characteristics must be monitored together.

By applying CUSUM, EWMA, Hotelling’s T², and multivariate monitoring appropriately, Black Belts can strengthen process monitoring and help sustain improvements over time.