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Webinar: Using Average Run Length to Optimize Advanced Control Charts

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John Noguera
John NogueraP.Eng. CTO & Co-founder SigmaXL, Inc.

Webinar: Using Average Run Length to Optimize Advanced Control Charts

One of the issues for Six Sigma and Quality practitioners using basic or advanced control charts has been what tests for special causes to use and what settings to use with those tests, or what parameters to use for an EWMA or CUSUM chart. This presentation introduces the concept of the average run length (ARL) as an approach to help the practitioner make these decisions. The average run length is the average number of runs before an out-of-control signal is given on the control chart. We desire the “In-Control” average run length (ARL 0) to be as large as possible and the “Out-of-Control” average run length (ARL 1) to be as small as possible. The economic consequences are clear, if ARL 0 is too low, we will be frequently chasing false alarms. If the ARL 1 is too high, we will fail to detect a significant shift in the process mean.

The calculations for ARL are quite complex, involving either Markov Chains or Monte Carlo simulation to solve. ARL Templates will be demonstrated that take care of these calculations and are easy to use.

The EWMA and CUSUM will be compared to the Shewhart Individuals chart with tests for special causes.

We will also introduce the Poisson and Binomial EWMA and CUSUM as alternatives to the classical attribute C and P charts.

The problem of robustness to non-normality will be considered by using the Pearson family to simulate any specified value of skewness and kurtosis and estimate the ARLs.


  • Introduction to Average Run Length (ARL)
  • Shewhart Charts with Tests for Special Causes
  • EWMA
  • EWMA Binomial Proportions
  • EWMA Poisson Counts
  • CUSUM Binomial Proportions
  • CUSUM Poisson Counts
  • Robustness to Non-normality
  • Limitations of Average Run Length
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About John Noguera

John Noguera is Co-founder and Chief Technology Officer of SigmaXL, Inc., a leading provider of user-friendly Excel add-ins for Lean Six Sigma tools, statistical & graphical analysis and Monte Carlo simulation. John leads the development of SigmaXL and DiscoverSim with a passion for ease-of-use, practical & powerful features, and statistical accuracy. John is a certified Six Sigma master black belt and was an instructor at Motorola University. He co-developed Motorola’s External Six Sigma Green Belt program which utilized the SigmaXL software tool. John was fortunate to have started his involvement with Six Sigma being mentored by the originator of Six Sigma, Bill Smith. John has specialized in teaching statistical methods and consulting in the implementation of Six Sigma Quality – with a focus on practical application with return on investment, in manufacturing, service and transactional areas. Since 1989, he has provided consulting and training services to more than 5000 black belts, green belts, managers, engineers, and business professionals in North America, Central America, Australia, Asia, Middle East and Europe. John has a B.A.Sc. in Electrical Engineering (1981) from the University of Waterloo. He is a member of the Professional Engineers of Ontario (PEO), American Statistical Association (ASA), INFORMS and Senior Member of the American Society for Quality (ASQ). He has authored conference papers on Statistical Process Control and Six-Sigma Quality and has been a guest lecturer at the University of Notre Dame. He is a contributing author in the Encyclopedia of Statistics in Quality and Reliability (Wiley).

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