Copyright © 2003
by Thomas Pyzdek, all rights reserved

1. In general, a Six Sigma Black Belt should be quantitatively oriented.
2. With minimal guidance, the Six Sigma Black Belt should be able to use data to convert broad generalizations
   into actionable goals.
3. The Six Sigma Black Belt should be able to make the business case for attempting to accomplish
   these goals.
4. The Six Sigma Black Belt should be able to develop detailed plans for achieving these goals.
5. The Six Sigma Black Belt should be able to measure progress towards the goals in terms meaningful
   to customers and leaders.
6. The Six Sigma Black Belt should know how to establish control systems for maintaining the gains
   achieved through Six Sigma.
7. The Six Sigma Black Belt should understand and be able to communicate the rationale for continuous
   improvement, even after initial goals have been accomplished.
8. The Six Sigma Black Belt should be familiar with research that quantifies the benefits firms
   have obtained from Six Sigma.
9. The Six Sigma Black Belt should know or be able to find the PPM rates associated with different
   sigma levels (e.g., Six Sigma = 3.4 PPM)
10. The Six Sigma Black Belt should know the approximate relative cost of poor quality associated
    with various sigma levels (e.g., three sigma firms report 25% COPQ).
11. The Six Sigma Black Belt should understand the roles of the various people involved in change
    (senior leader, champion, mentor, change agent, technical leader,
    team leader, facilitator).
12. The Six Sigma Black Belt should be able to design, test, and analyze customer surveys.
13. The Six Sigma Black Belt should know how to quantitatively analyze data from employee and customer
    surveys. This includes evaluating survey reliability and validity
    as well as the differences between surveys.
14. Given two or more sets of survey data, the Six Sigma Black Belt should be able to determine
    if there are statistically significant differences between them.
15. The Six Sigma Black Belt should be able to quantify the value of customer retention.
16. Given a partly completed QFD matrix, the Six Sigma Black Belt should be able to complete it.
17. The Six Sigma Black Belt should be able to compute the value of money held or invested over
    time, including present value and future value of a fixed sum.
18. The Six Sigma Black Belt should be able to compute present value and future value for various
    compounding periods.
19. The Six Sigma Black Belt should be able to compute the break even point for a project.
20. The Six Sigma Black Belt should be able to compute the net present value of cash flow streams,
    and to use the results to choose among competing projects.
21. The Six Sigma Black Belt should be able to compute the internal rate of return for cash flow
    streams and to use the results to choose among competing projects.
22. The Six Sigma Black Belt should know the COPQ rationale for Six Sigma, i.e., he should be able
    to explain what to do if COPQ analysis indicates that the optimum for a given process is less than Six Sigma.
23. The Six Sigma Black Belt should know the basic COPQ categories and be able to allocate a list
    of costs to the correct category.
24. Given a table of COPQ data over time, the Six Sigma Black Belt should be able to perform a statistical
    analysis of the trend.
25. Given a table of COPQ data over time, the Six Sigma Black Belt should be able to perform a statistical
    analysis of the distribution of costs among the various categories.
26. Given a list of tasks for a project, their times to complete, and their precedence relationships,
    the Six Sigma Black Belt should be able to compute the time to completion
    for the project, the earliest completion times, the latest completion
    times and the slack times. He should also be able to identify which
    tasks are on the critical path.
27. Give cost and time data for project tasks, the Six Sigma Black Belt should be able to compute
    the cost of normal and crash schedules and the minimum total cost
    schedule.
28. The Six Sigma Black Belt should be familiar with the basic principles of benchmarking.
29. The Six Sigma Black Belt should be familiar with the limitations of benchmarking.
30. Given an organization chart and a listing of team members, process owners, and sponsors, the Six
    Sigma Black Belt should be able to identify projects with a low probability
    of success.
31. The Six Sigma Black Belt should be able to identify measurement scales of various metrics (nominal,
    ordinal, etc).
32. Given a metric on a particular scale, the Six Sigma Black Belt should be able to determine if a particular
    statistical method should be used for analysis.
33. Given a properly collected set of data, the Six Sigma Black Belt should be able to perform a
    complete measurement system analysis, including the calculation of
    bias, repeatability, reproducibility, stability, discrimination (resolution)
    and linearity.
34. Given the measurement system metrics, the Six Sigma Black Belt should know whether or not a given
    measurement system should be used on a given part or process.
35. The Six Sigma Black Belt should know the difference between computing sigma from a data set
    whose production sequence is known and from a data set whose production
    sequence is not known.
36. Given the results of an AIAG Gage R&R study, the Six Sigma Black Belt should be able to
    answer a variety of questions about the measurement system.
37. Given a narrative description of “as-is” and “should-be” processes, the Six
    Sigma Black Belt should be able to prepare process maps.
38. Given a table of raw data, the Six Sigma Black Belt should be able to prepare a frequency tally
    sheet of the data, and to use the tally sheet data to construct a
    histogram.
39. The Six Sigma Black Belt should be able to compute the mean and standard deviation from a grouped
    frequency distribution.
40. Given a list of problems, the Six Sigma Black Belt should be able to construct a Pareto Diagram
    of the problem frequencies.
41. Given a list which describes problems by department, the Six Sigma Black Belt should be able to
    construct a Crosstabulation and use the information to perform a Chi-square
    analysis.
42. Given a table of x and y data pairs, the Six Sigma Black Belt should be able to determine if
    the relationship is linear or non-linear.
43. The Six Sigma Black Belt should know how to use non-linearity’s to make products or processes
    more robust.
44. The Six Sigma Black Belt should be able to construct and interpret a run chart when given a
    table of data in time-ordered sequence. This includes calculating
    run length, number of runs and quantitative trend evaluation.
45. When told the data are from an exponential or Erlang distribution the Six Sigma Black Belt should
    know that the run chart is preferred over the standard X control chart.
46. Given a set of raw data the Six Sigma Black Belt should be able to identify and compute two
    statistical measures each for central tendency, dispersion, and shape.
47. Given a set of raw data, the Six Sigma Black Belt should be able to construct a histogram.
48. Given a stem & leaf plot, the Six Sigma Black Belt should be able to reproduce a sample
    of numbers to the accuracy allowed by the plot.
49. Given a box plot with numbers on the key box points, the Six Sigma Black Belt should be able to
    identify the 25th and 75th percentile and the median.
50. The Six Sigma Black Belt should know when to apply enumerative statistical methods, and when
    not to.
51. The Six Sigma Black Belt should know when to apply analytic statistical methods, and when not
    to.
52. The Six Sigma Black Belt should demonstrate a grasp of basic probability concepts, such as
    the probability of mutually exclusive events, of dependent and independent
    events, of events that can occur simultaneously, etc.
53. The Six Sigma Black Belt should know factorials, permutations and combinations, and how to
    use these in commonly used probability distributions.
54. The Six Sigma Black Belt should be able to compute expected values for continuous and discrete
    random variables.
55. The Six Sigma Black Belt should be able to compute univariate statistics for samples.
56. The Six Sigma Black Belt should be able to compute confidence intervals for various statistics.
57. The Six Sigma Black Belt should be able to read values from a cumulative frequency ogive.
58. The Six Sigma Black Belt should be familiar with the commonly used probability distributions,
    including: hypergeometric, binomial, Poisson, normal, exponential,
    chi-square, Student’s t, and F.
59. Given a set of data the Six Sigma Black Belt should be able to correctly identify which distribution
    should be used to perform a given analysis, and to use the distribution
    to perform the analysis.
60. The Six Sigma Black Belt should know that different techniques are required for analysis depending
    on whether a given measure (e.g., the mean) is assumed known or estimated
    from a sample. The Six Sigma Black Belt should choose and properly
    use the correct technique when provided with data and sufficient information
    about the data.
61. Given a set of subgrouped data, the Six Sigma Black Belt should be able to select and prepare
    the correct control charts and to determine if a given process is
    in a state of statistical control.
62. The above should be demonstrated for data representing all of the most common control charts.
63. The Six Sigma Black Belt should understand the assumptions that underlie ANOVA, and be able
    to select and apply a transformation to the data.
64. The Six Sigma Black Belt should be able to identify which cause on a list of possible causes
    will most likely explain a non-random pattern in the regression residuals.
65. If shown control chart patterns, the Six Sigma Black Belt should be able to match the control chart
    with the correct situation (e.g., an outlier pattern vs. a gradual
    trend matched to a tool breaking vs. a machine gradually warming up).
66. The Six Sigma Black Belt should understand the mechanics of PRE-Control.
67. The Six Sigma Black Belt should be able to correctly apply EWMA charts to a process with serial
    correlation in the data.
68. Given a stable set of subgrouped data, the Six Sigma Black Belt should be able to perform a complete
    Process Capability Analysis. This includes computing and interpreting
    capability indices, estimating the % failures, control limit calculations,
    etc.
69. The Six Sigma Black Belt should demonstrate an awareness of the assumptions that underlie the
    use of capability indices.
70. Given the results of a replicated full-factorial experiment, the Six Sigma Black Belt should be able
    to complete the entire ANOVA table.
71. The Six Sigma Black Belt should understand the basic principles of planning a statistically
    designed experiment. This can be demonstrated by critiquing various
    experimental plans with or without shortcomings.
72. Given a “clean” experimental plan, the Six Sigma Black Belt should be able to find
    the correct number of replicates to obtain a desired power.
73. The Six Sigma Black Belt should know the difference between the various types of experimental
    models (fixed-effects, random-effects, mixed).
74. The Six Sigma Black Belt should understand the concepts of randomization and blocking.
75. Given a set of data, the Six Sigma Black Belt should be able to perform a Latin Square analysis
    and interpret the results.
76. Ditto for one way ANOVA, two way ANOVA (with and without replicates), full and fractional factorials,
    and response surface designs.
77. Given an appropriate experimental result, the Six Sigma Black Belt should be able to compute the direction
    of steepest ascent.
78. Given a set of variables each at two levels, the Six Sigma Black Belt can determine the correct
    experimental layout for a screening experiment using a saturated design.
79. Given data for such an experiment, the Six Sigma Black Belt can identify which main effects are significant
    and state the effect of these factors.
80. Given two or more sets of responses to categorical items (e.g., customer survey responses categorized
    as poor, fair, good, excellent), the Six Sigma Black Belt will be
    able to perform a Chi-Square test to determine if the samples are
    significantly different.
81. The Six Sigma Black Belt will understand the idea of confounding and be able to identify which
    two factor interactions are confounded with the significant main effects.
82. The Six Sigma Black Beltwill be able to state the direction of steepest ascent from experimental
    data.
83. The Six Sigma Black Belt will understand fold over designs and be able to identify the fold
    over design that will clear a given alias.
84. The Six Sigma Black Belt will know how to augment a factorial design to create a composite
    or central composite design.
85. The Six Sigma Black Belt will be able to evaluate the diagnostics for an experiment.
86. The Six Sigma Black Belt will be able to identify the need for a transformation in y and to
    apply the correct transformation.
87. Given a response surface equation in quadratic form, the Six Sigma Black Belt will be able
    to compute the stationary point.
88. Given data (not graphics), the Six Sigma Black Belt will be able to determine if the stationary
    point is a maximum, minimum or saddle point.
89. The Six Sigma Black Belt will be able to use a quadratic loss function to compute the cost
    of a given process.
90. The Six Sigma Black Belt will be able to conduct simple and multiple linear regression.
91. The Six Sigma Black Belt will be able to identify patterns in residuals from an improper regression
    model and to apply the correct remedy.
92. The Six Sigma Black Belt will understand the difference between regression and correlation
    studies.
93. The Six Sigma Black Belt will be able to perform chi-square analysis of contingency tables.
94. The Six Sigma Black Belt will be able to compute basic reliability statistics (mtbf, availability,
    etc.).
95. Given the failure rates for given subsystems, the Six Sigma Black Belt will be able to use
    reliability apportionment to set mtbf goals.
96. The Six Sigma Black Belt will be able to compute the reliability of series, parallel, and series-parallel
    system configurations.
97. The Six Sigma Black Belt will demonstrate the ability to create and read an FMEA analysis.
98. The Six Sigma Black Belt will demonstrate the ability to create and read a fault tree.
99. Given distributions of strength and stress, the Six Sigma Black Belt will be able to compute the probability
    of failure.
100. The Six Sigma Black Belt will be able to apply statistical tolerancing to set tolerances for
     simple assemblies. He will know how to compare statistical tolerances
     to so-called “worst case” tolerancing.
101. The Six Sigma Black Belt will be aware of the limits of the Six Sigma approach.