In Six Sigma Black Belt Curriculum and Body of Knowledge – 2012, a universal, highly technical body of knowledge was proposed to equip Black Belts with the expertise and abilities needed to lead nontrivial process improvement efforts over a full spectrum of diverse scenarios. But what additional technical knowledge should be expected for a Master Black Belt?

This article addresses the minimum additional technical knowledge that a Master Black Belt should possess beyond the topics already defined for Black Belts. There are many statistical tools not mentioned here that could be useful as part of a Master Black Belt’s toolbox – this list is not intended to limit the body of knowledge for a Master Black Belt.

An effective Master Black Belt must possess skills and knowledge outside of these Six Sigma technical topics. A Master Black Belt should have a mastery of Lean, total productive maintenance and Design for Six Sigma along with leadership skills, project management skills, change management skills, and instructional and presentation skills. Years of experience in project work, coaching, classroom instruction and higher-level strategic planning are also critical for an effective Master Black Belt.

A Master Black Belt who is advising or guiding an organization must be able to identify the roadmap made up of individual projects based on assessments of the operation against the business needs in order to close the gap on perfect operation. Without this broad, strategic view of the improvement efforts, all the work is pointless. Thus, technical knowledge represents only a portion of the makeup of a successful Six Sigma practitioner. Nonetheless, a Master Black Belt must be able to provide a high degree of technical expertise when called upon, and consequently there should be a corresponding minimum body of knowledge associated with that title.

As a baseline, a Master Black Belt should have a mastery of these following advanced Six Sigma topics:

1**General linear model (GLM)**: This is the basis for the ANOVA (analysis of variance) and regression topics that Black Belts are expected to understand. Factors, covariates, crossed, nested and mixed structures all have important applications and are important to master, particularly when teaching ANOVA to Black Belts.

2**Advanced regression**: A Master Black Belt should be able to apply general and nonlinear regression to data sets when appropriate. General regression allows for interactions between predictors while nonlinear regression allows an arbitrary prediction equation to be defined and fitted to the data.

3**Advanced DOE (design of experiments)**: Black Belts should be able to perform 2^{k} full and fractional factorials, general full factorials, multiple response optimization, central composite design, response surface methods and evolutionary operation DOEs. In addition to these types of DOEs, Master Black Belts should be able to perform the following advanced designs:

**Robust design**: This type of DOE analyzes the variation of an output so that a design can be determined that will minimize this variation over the conditions and operational settings of the product or service.**Mixture design**: This DOE is useful when there are constraints on the factor settings as is the case for recipe or mixture settings where the inputs must add up to 100 percent.**Split plot design**: This is a useful technique when dealing with hard-to-change factors in the experimental design.

4**Ordinal and nominal logistic regression**: Black Belts should understand binary logistic regression, but Master Black Belts should also be well versed in applying the logistic regression approach to ordinal and nominal data.

5**Measures of association**: This is essentially correlation analysis with discrete data. It is particularly useful for analyzing and interpreting survey results or performing an attribute gage R&R study using an attribute agreement analysis. Survey design and analysis should be part of this topic to ensure that surveys are created to give meaningful results when analyzed using measures of association or other analytical techniques.

6**Principle components/factor analysis**: This type of analysis is useful when there are highly correlated factors in the data. A principle components/factor analysis can help to reveal underlying root causes that may be manifested as different combinations of factors in the data set.

7**Advanced probability distributions**: Black Belts should understand and be able to analyze normal, *t*, *F*, chi-squared, binomial, Poisson, exponential, Weibull and lognormal distributions. In addition to these, a Master Black Belt should be able to derive the hypergeometric distribution and should have a solid understanding of the basic event probability concepts, and also permutations and combinations that are the key concepts behind this fundamental distribution. Other probability distributions such as gamma, geometric and negative binomial should also be understood.

8**Data transformations**: Performing data transformations without understanding when they are necessary and how to properly apply them has led to many errors and much confusion throughout the history of Six Sigma. A Master Black Belt should know when a transformation is appropriate (e.g., non-normality or heteroskedasticity), what is the simplest effective technique (Box-Cox, Johnson, etc.) and how to communicate the results of a transformed set of data.

9**Extended gage R&R**: This is essentially an application of the GLM to a variable gage R&R study. Whenever there are factors beyond parts and operators (such as test stands or facilities), the standard gage R&R design is not sufficient. An extended gage R&R study is also necessary when there are combinations of crossed and nested factors in the measurement system.

10**Advanced time series analysis**: Forecasting is one of the most commonly flawed undertakings of businesses. Understanding such advanced time series analysis concepts as autocorrelation, cross correlations and auto regressive integrated moving average (referred to as ARIMA) can be extremely useful in improving a company’s forecasting accuracy and comprehension of forecasting limitations.

11**Reliability basics**: Reliability is a crucial factor in many businesses for both internal equipment and products being used by customers. A Master Black Belt should have an excellent understanding of reliability concepts such as hazard rates, mean time between failure, censored data, parallel and series designs, as well as the applications of exponential, lognormal and Weibull distributions to reliability scenarios.

There are, of course, many other useful statistical and analytical tools that may be valuable for Master Black Belts depending on the environment in which they are working. These tools can be taught in a two-week Master Black Belt technical training course.

Keep in mind that superior technical knowledge alone does not translate to an effective Master Black Belt. Given that the role’s title implies a “mastery” of Six Sigma tools, these topics should be considered a minimum body of knowledge for someone who goes by the designation of Master Black Belt.