Statistical Methods for Six Sigma

October 19, 2010
School of Engineering, Coimbatore

sixsigmaIt is said that that which cannot be measured cannot be controlled and that which cannot be controlled cannot be perfected.

There are several test-based statistical methods that can be used for measuring and by extension, quality-control, but many quality practitioners are not aware of these methods.

A paper that attempts to address this gap was published in a recent issue of Statistical Papers of Springer.

Titled A Review of Preliminary Test-based Statistical Methods for the Benefit of Six Sigma Quality Practitioners, the paper was authored by Dr. J. Ravichandran, Associate Professor, Department of Mathematics at Coimbatore.

“In the paper, I have highlighted the significance of preliminary test-based statistical methods and their use in achieving quality improvement and business excellence,” explained Dr. Ravichandran.

Dr.J.Ravichandran“Six Sigma quality practitioners will benefit by learning about the application of these methods to their field.”

A method for perfection that organizations follow to maximize effective output, the Six Sigma process developed in the late eighties. The test-based statistical methods came later, and so it is that most Six Sigma practitioners even today remain unaware of its benefits, especially in preliminary stages of testing.

Six-sigma implies that 99.99966% of manufactured products are free of defects; the process tolerates a mere 3.4 defects per million. This, in turn, implies that the quality of intermediate outputs at every stage of the manufacturing process has to be within strict quality-control limits.

“This is where statistics comes to the rescue,” further explained Dr. J Ravichandran. “A sample containing smaller numbers of units is drawn and measured for its quality and other features. Inferences are drawn about the entire population using its sample units.”

“The population can be represented by statistical models (distributions) that contain some unknown parameters viz. the overall quality and other features. Most of the classical statistical procedures assume that the model parameters are known in advance.”

student“However, there exist situations where the model parameters are not clearly known (dilemma) to the experimenter and thus there exists suspicion. Preliminary test-based statistical methods are used to clear this suspicion.”

“With its extensive literature review, the paper details preliminary test-based inference methods and their applicability to people who can benefit from it the most – Six Sigma practitioners,” the author summed up.


Paper Abstract: Ever since Professor Bancroft developed inference procedures using preliminary tests there has been a lot of research in this area by various authors across the world. This could be evidenced from two papers that widely reviewed the publications on preliminary test-based statistical methods. The use of preliminary tests in solving doubts arising over the model parameters has gained momentum as it has proven to be effective and powerful over to that of classical methods. Unfortunately, there has been a downward trend in research related to preliminary tests as it could be seen from only few recent publications. Obviously, the benefits of preliminary test-based statistical methods did not reach Six Sigma parishioners as the concept of Six Sigma just took off and it was in a premature state. In this paper, efforts have been made to present a review of the publications on the preliminary test-based statistical methods. Though studies on preliminary test-based methods have been done in various areas of statistics such as theory of estimation, hypothesis testing, analysis of variance, regression analysis, reliability, to mention a few, only few important methods are presented here for the benefit of readers, particularly Six Sigma quality practitioners, to understand the concept. In this regard, the define, measure, analyze, improve and control methodology of six sigma is presented with a link of analyze phase to preliminary test-based statistical methods. Examples are also given to illustrate the procedures.

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