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Applying Change Point Detection in Vaccine Manufacturing. Hesham Fahmy, Ph.D. Merck & Co., Inc. West Point, PA 19486 hesham_fahmy@merck.com. Midwest Biopharmaceutical Statistics Workshop (MBSW) - MAY 23 - 25, 2011. Outline. Definitions Detection methods CUSUM and EWMA estimators

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applying change point detection in vaccine manufacturing

Applying Change Point Detection in Vaccine Manufacturing

Hesham Fahmy, Ph.D.

Merck & Co., Inc.

West Point, PA 19486

hesham_fahmy@merck.com

Midwest Biopharmaceutical Statistics Workshop (MBSW) - MAY 23 - 25, 2011

outline
Outline
  • Definitions
    • Detection methods
    • CUSUM and EWMA estimators
  • Case studies
    • CUSUM and EWMA
    • SSE
  • Conclusions
methods of detection
Methods of Detection
  • Visual (Simple but Subjective)
    • Raw data; run chart
    • CUSUM chart
    • EWMA chart
  • Analytical (Complicated but Objective)
    • Change-Point estimators; i.e. CUSUM, EWMA
    • Mathematical Modeling; i.e. MLE, SSE
types of variation
Types of Variation
  • Common Causes– natural (random) variations that are part of a stable process
    • Machine vibration
    • Temperature, humidity, electrical current fluctuations
    • Slight variation in raw materials
  • Special Causes – unnatural (non-random) variations that are not part of a stable process
    • Batch of defective raw material
    • Faulty set-up
    • Human error
    • Incorrect recipe
cumulative sum control chart
Cumulative Sum Control Chart
  • CUSUM: cumulative sum of deviations from average
  • A bit more difficult to set up
  • More difficult to understand
  • Very effective when subgroup size n=1
  • Very good for detecting small shifts
  • Change-point detection capability
  • Less sensitive to autocorrelation
exponentially weighted moving average
Exponentially Weighted Moving Average
  • EWMA: weighted average of all observations
  • A bit more difficult to set up
  • Very good for detecting small shifts
  • Change point detection capability
  • Less sensitive to autocorrelation

“EWMA gives more weight to more recent observations and less weight to old observations.”

0

1

Shewhart

CUSUM

slide7

Process Shifts

Step

Linear

Nonlinear

Others

process model

t

Process Model

Change point, "Unknown"

in-control state

out-of-control state

example
Example:

Actual Change-Point= 20

Most Recent Reintialization at t =22

example1

Most Recent time

at t =19

Example:

Actual Change-Point= 20

UCL=11

LCL=9

simulated case studies
Simulated Case Studies
  • To test different methods' (control charts/analytical) capability for identifying change-points
    • Case # 1: small shifts/drifts
    • Case # 2: mirror image of case # 1
    • Case # 3: large shifts/drifts
case 11
Case # 1

1 & 6: In-control process; N(0,1)

2 : -ve linear trend; 0.1 sigma

3 : Step shift; N(-3,1)

4 : Step shift; N(-1.5,1)

5 : +ve linear trend; 0.1 sigma

cusum v mask
CUSUM (V-Mask)

Diagnostic Sequence Plot

Detection Criterion: Slope Change

cusum
CUSUM;

Exact Profile

slide21
EWMA;

Detection Criterion: Slope Change

slide22
EWMA;

Same Profile

CUSUM

case 2 mirror image
Case # 2 “Mirror Image”

1 & 6: In-control process; N(0,1)

2 : +ve linear trend; 0.1 sigma

3 : Step shift; N(3,1)

4 : Step shift; N(1.5,1)

5 : -ve linear trend; 0.1 sigma

cusum chart
CUSUM Chart

Case # 2

Mirror Image

Case # 1

case 3
Case # 3

1 & 6: In-control process; N(0,1)

2 : +ve linear trend; 0.5 sigma

3 : Step shift; N(12.5,1)

4 : Step shift; N(9.5,1)

5 : -ve linear trend; 0.38 sigma

detection by sse
Detection by SSE
  • Pick a window of about 30 points including the “investigated point”
  • Fit a two-phase regression using all possible change-points & calculate the SSE
  • Plot possible change-points vs. their SSEs
conclusions
Conclusions
  • Change-point problem is general and can be applied in many applications such as 4 parameter logistic regression and degradation curves.
  • Another application in manufacturing processes includes detection of the change-point for process variance.
  • It is preferred to combine both analytical and visual techniques; in addition to process expertise; to get accurate results.
references
References
  • Fahmy, H.M. and Elsayed, E.A., Drift Time Detection and Adjustment Procedures for Processes Subject to Linear Trend. Int. J. Prod. Research, 2006, 3257–3278.
  • Montgomery, D. C., Int. to Stat. Quality Control, 1997, (John Wiley: NY).
  • Nishina, K., A comparison of control charts from the viewpoint of change-point estimation. Qual. Reliabil. Eng. Int., 1992, 8, 537–541.
  • Pignatiello, J.J. Jr. and Samuel, T.R., Estimation of the change point of a normal process mean in SPC applications. J. Qual. Tech., 2001, 33, 82–95.
  • Samuel, T.R., Pignatiello Jr., J.J. and Calvin, J.A., Identifying the time of a step change with X control charts. Qual. Eng., 1998, 10, 521–527.
acknowledgements
Acknowledgements
  • Lori Pfahler
  • Julia O’Neill
  • Jim Lucas