Pyzdek Institute » black belt http://www.sixsigmatraining.org Lean Six Sigma Training and Information Wed, 08 Feb 2012 18:11:08 +0000 en hourly 1 http://wordpress.org/?v=3.2.1 Six Sigma Project Presentations in a Nutshell http://www.sixsigmatraining.org/introduction-to-six-sigma/six-sigma-project-presentations-in-a-nutshell.html?source=rss http://www.sixsigmatraining.org/introduction-to-six-sigma/six-sigma-project-presentations-in-a-nutshell.html#comments Sat, 14 Aug 2010 16:55:16 +0000 Thomas Pyzdek http://www.sixsigmatraining.org/?p=2610 I’ve reviewed thousands of improvement projects. I’ve lost count of how many project presentations I’ve attended, either for certification purposes or for presentations to leaders. I’ve come to the conclusion that most Green Belts and Black Belts simultaneously present too much information, and not enough information. If I may speak to Green Belts and Black Belts on behalf of leaders and Master Black Belts everywhere, here’s what I’d like to say. What we’re asking is actually very simple, namely how did you apply the Six Sigma process to pursue a real opportunity? In other words, for your project just walk us through the L1 Six Sigma process shown in the figure, and do so in 45 minutes or less. I actually don’t even care if you use a PowerPoint template, or even if you have any slides whatever. I just want to hear a great Six Sigma success story.

Six Sigma L1 Map

]]> http://www.sixsigmatraining.org/introduction-to-six-sigma/six-sigma-project-presentations-in-a-nutshell.html/feed 0 Jumping to Statistical Conclusions http://www.sixsigmatraining.org/statistical-tools-for-six-sigma/jumping-to-statistical-conclusions.html?source=rss http://www.sixsigmatraining.org/statistical-tools-for-six-sigma/jumping-to-statistical-conclusions.html#comments Tue, 08 Sep 2009 07:00:08 +0000 Thomas Pyzdek http://www.sixsigmatraining.org/?p=1758 Have you attributed your results to the right base data?

It may come as a surprise that the biggest challenge facing black belts and master black belts is usually not in selecting the best statistical technique for analyzing a particular data set. Most statistical techniques work fairly well even if the underlying assumptions are not precisely correct. If a black belt supplements the numerical analysis with graphical evaluation, the chance of making grossly erroneous decisions is negligible.

A mistake that is far more serious–but far more common–is comparing the results of a study to the wrong base data. These “apples to oranges” comparisons often lead to poor decisions and, worse still, to inaccurate beliefs that can derail faith in the Six Sigma approach itself. A recent incident with a client brought this point home for me.

The situation involved a project in the sales organization of a software company. The company had several sales teams and wanted to know if a new approach to closing the sale would improve the rate of closing sales. The company didn’t have a Six Sigma program, and the project was planned and carried out without black belts. The results were presented to management in a classic form: a bar chart (see Figure 1). The team had declared victory, and management–convinced by the “data”–prepared to revamp the sales training to incorporate the new approach companywide. All of the leaders looked forward to the bottom-line improvement they’d see from a 29-percent improvement in the sales closing rate.

Figure 1: Sales Closing Rate Improved by New Approach

All of the leaders, that is, except Lorraine. She’d received green belt training from her previous employer, and she’d seen enough black belt presentations to know that the analysis of the sales team was seriously flawed. It was undeniable that the project team’s sales close rate was 2.53 percent higher than the sales close rate for the rest of the sales department during the 16 weeks of the test, and, yes, the 2.53 percent did represent a 29-percent improvement over the 8.83-percent rate for the rest of the team. Despite these “facts” and the air of scientific objectivity surrounding the analysis, Lorraine had many unanswered questions. She asked management to delay any decision until she could explore these questions with a Six Sigma consultant. That’s where things stood when I entered the picture.

Table 1: Old vs.
New Closing Rates

Lorraine viewed the analysis as important because it would demonstrate that the Six Sigma approach could be applied in this service company, something that skeptical managers didn’t believe. In a meeting with the sales team leader, I was presented with the data shown in Table 1. As often happens, this summary data was all that was available; for a variety of reasons (but chiefly due to a time constraint) the number of sales calls used to compute these rates could not be obtained.

If you are a black belt or master black belt, or just statistically inclined, please take a couple of minutes before reading the remainder of this column to think about the data and jot down how you’d proceed from here.

When dealing with the data in Table 1, it’s tempting to apply a statistical technique such as a paired t-test to it. Using Microsoft Excel, it’s a simple matter to compute the t-statistic, which is 4.55, a highly significant result. Statistical purists would ask if the data are approximately normal and an endless variety of other technical questions about the data. I would argue, however, that all of this is premature and, ultimately, beside the point. The first order of business is to determine if we are comparing apples to apples.

Table 2: Apples-to-Apples Comparison

Further discussion revealed that the company had not two but nine sales teams, all of the same size. A further complication was that the teams sold different products. More probing uncovered the fact that four of the eight other teams sold a product mix similar to that of the team using the new closing method. At this point it appeared that, to make an apples-to-apples comparison, you would assess the results of these five teams for the 16-week project. Descriptive statistics are shown in Table 2.

Table 3: Data Groups

Further analysis using nonparametric methods indicated that there are three distinct groups in these data (see Table 3).

Table 3 presents a decidedly different picture than was originally given to management. The new closing method now appears to be no better than normal. Still, there are bright spots. Assuming that teams 5 and 8 aren’t oranges being compared to apples, potential gains should be possible from discovering why team 5 performs under the norm, and why team 8 outperforms the norm. More information might also be obtained by plotting the 16 weeks over time to identify trends and other patterns. Using the Six Sigma approach, the information can be converted to knowledge, the knowledge to action, and the action to an improved bottom line. It’s more work than the old standby, the bar chart, but it’s worth it.

The complete data file used in this article is posted at www.pyzdek.com/2000-05.xls . The challenge is to analyze the data in a number of different ways to determine how the different analyses would affect management decisions. Send your results to me for inclusion in a future column.
]]> http://www.sixsigmatraining.org/statistical-tools-for-six-sigma/jumping-to-statistical-conclusions.html/feed 0 What is a Black Belt? http://www.sixsigmatraining.org/introduction-to-six-sigma/what-is-a-black-belt-2.html?source=rss http://www.sixsigmatraining.org/introduction-to-six-sigma/what-is-a-black-belt-2.html#comments Mon, 17 Aug 2009 07:00:23 +0000 Thomas Pyzdek http://www.sixsigmatraining.org/?p=1634 Who are they and what do they do?

I‘m often asked about the term “black belt” as it relates to six sigma. What, precisely, is a black belt? Where did the term originate? For that matter, where did the term “six sigma” originate? And, while we’re on the subject, what’s a green belt or master black belt?

Let’s start with the term “six sigma.” In a conversation with Ed Bales of Motorola University, I learned that Motorola coined the term in 1986. As those who have worked in quality for a while know, this term has statistical roots in the technique known as process capability analysis. Prior to the Japanese industrial invasion of U.S. markets, quality practitioners were happy with three sigma quality, which translates to about three errors or defects per 1,000 items for processes in a state of statistical control. Motorola discovered that its processes weren’t in statistical control–estimates based on field failure data indicated that Motorola’s processes apparently drifted by an average of 1.5 standard deviations. In a conversation with ex-Motorola trainer Mikel Harry, I learned that he considers the Cpk index–which measures short-term process variability under statistical control–worthless. Harry prefers the Ppk index, which measures actual performance rather than process capability. (Note that many experts, including me, disagree strongly with Harry on this issue.) In any case, before computing expected process failures, Motorola adds this 1.5 standard deviation. Thus, when we hear that a six sigma process will produce 3.4 parts-per-million (PPM) failures, we find that this PPM corresponds to the area in the tail beyond 4.5 standard deviations above the mean for a normal distribution.

Motorola also adopted the terms “black belt” and “green belt.” For my book The Six Sigma Handbook, I did extensive research into what employers expect of people with these titles. Here is a summary of these various responsibilities:

  • Master black belt–This is the highest level of technical and organizational proficiency. Because master black belts train black belts, they must know everything the black belts know, as well as understand the mathematical theory on which the statistical methods are based. Masters must be able to assist black belts in applying the methods correctly in unusual situations. Whenever possible, statistical training should be conducted only by master black belts. If it’s necessary for black belts and green belts to provide training, they should only do so under the guidance of master black belts. Because of the nature of the master’s duties, communications and teaching skills should be judged as important as technical competence in selecting candidates.
  • Black belt–Candidates for technical leader (black belt) status are technically oriented individuals held in high regard by their peers. They should be actively involved in the organizational change and development process. Candidates may come from a wide range of disciplines and need not be formally trained statisticians or engineers. However, because they are expected to master a wide variety of technical tools in a relatively short period of time, technical leader candidates will probably possess a background in college-level mathematics, the basic tool of quantitative analysis. College-level course work in statistical methods should be a prerequisite.

Six sigma technical leaders work to extract actionable knowledge from an organization’s information warehouse. Successful candidates should understand one or more operating systems, spreadsheets, database managers, presentation programs and word processors. As part of their training they will be required to become proficient in the use of one or more advanced statistical analysis software packages.

  • Green belt –Green belts are six sigma team leaders capable of forming and facilitating six sigma teams and managing six sigma projects from concept to completion. Typically, green-belt training consists of five days of classroom training and is conducted in conjunction with six sigma team projects. Training covers facilitation techniques and meeting management, project management, quality management tools, quality control tools, problem solving, and exploratory data analysis. Usually, six sigma black belts help green belts choose their projects prior to the training, attend training with their green belts and assist them with their projects after the training.

Although the martial arts terms described above are common, they are by no means universal. Companies and consulting firms often create their own titles to describe the work done by these technical leaders.

]]> http://www.sixsigmatraining.org/introduction-to-six-sigma/what-is-a-black-belt-2.html/feed 0 Six Sigma Cures the Common Cold! http://www.sixsigmatraining.org/introduction-to-six-sigma/six-sigma-cures-the-common-cold.html?source=rss http://www.sixsigmatraining.org/introduction-to-six-sigma/six-sigma-cures-the-common-cold.html#comments Wed, 06 May 2009 15:32:56 +0000 Thomas Pyzdek http://www.sixsigmatraining.org/?p=1166 For some reason that I can’t fathom, Six Sigma gets dissed not for what it can do, but for what it doesn’t do well. For example, there are many articles that knock Six Sigma because a company that uses the approach sees its stock price decline. Another common knock is that some companies that use Six Sigma are perceived as less innovative, a debatable perception in any event, but why should Six Sigma take the rap for this?

I once had a Black Belt student who had difficulty with the concept of mistake proofing, or poka yoke. When given an assignment to identify the type of mistake proofing exemplified by the cord which keeps the gas cap fastened to the vehicle he just couldn’t see that this was a prevention mechanism. “It doesn’t prevent the person from not putting the gas cap back on.” He argued. “And it doesn’t keep them from over-filling the tank either.” True, I conceded. It also doesn’t prevent bad breath. But it does prevent the person from leaving the gas cap on the pump or the top of the vehicle and driving off without it. That’s what it is supposed to do, and it does it quite well. Six Sigma also has its place, but it’s not the only thing a company needs to do to be successful. That doesn’t make it any less valuable when used properly.

]]> http://www.sixsigmatraining.org/introduction-to-six-sigma/six-sigma-cures-the-common-cold.html/feed 1 21 Soft Skills All Six Sigma Belts Need http://www.sixsigmatraining.org/introduction-to-six-sigma/101-soft-skills-a-six-sigma-black-belt-needs.html?source=rss http://www.sixsigmatraining.org/introduction-to-six-sigma/101-soft-skills-a-six-sigma-black-belt-needs.html#comments Wed, 08 Apr 2009 18:21:12 +0000 Thomas Pyzdek http://www.sixsigmatraining.org/?p=987 One of my most popular articles is 101 Things a Six Sigma Black Belt Should Know. Of course, the list is primarily a list of technical tools and skills needed, but anyone who has worked as a change agent knows that there’s more to it than that. Soft skills are at least as important, if not more so. Some of the soft skills are people skills, others are intuition about a change project’s chances of success, and still others involve an understanding of the organization. When I teach Six Sigma classes I have several lessons and assignments around these topics. I thought it would be fun to see how long a list of soft skills I could come up with. Even more fun would be to see how many readers of this post could add to the list. So, here we go:

  1. The Six Sigma Black Belt should be able to excite leadership about the need for change
  2. The Six Sigma Black Belt should have an intuitive sense for which projects are right for their organization
  3. The Six Sigma Black Belt should know how to assess a project’s likelihood for success
  4. The Six Sigma Black Belt should be able to recruit sponsors for their change activities
  5. The Six Sigma Black Belt should know who to turn for when they need a mentor
  6. The Six Sigma Black Belt should understand the mix of personality attributes needed to make a team successful
  7. The Six Sigma Black Belt should understand the team development stages and how to guide a team through these stages
  8. The Six Sigma Black Belt should be able to resolve conflicts between team members
  9. The Six Sigma Black Belt should know when to exercise control and when to release control in a team situation
  10. The Six Sigma Black Belt should know how to plan and facilitate effective meetings
  11. The Six Sigma Black Belt should be an effective public speaker
  12. The Six Sigma Black Belt should be able to facilitate brainstorming sessions
  13. The Six Sigma Black Belt Should know how to achieve consensus
  14. The Six Sigma Black Belt should know what to do when consensus isn’t possible (e.g., nominal group technique.)
  15. The Six Sigma Black Belt should be able to create a stakeholder communication plan
  16. The Six Sigma Black Belt should know how to gain the cooperation of cross-functional stakeholders
  17. The Six Sigma Black Belt should know how to assess restrainers and drivers relative to a goal
  18. The Six Sigma Black Belt should know how to obtain the voice of the customer
  19. The Six Sigma Black Belt should know how to learn about customer needs that customers may not be able to vocalize (e.g., Gemba, Follow-Me-Home)
  20. The Six Sigma Black Belt should know how to determine the relative importance of different customer demands
  21. The Six Sigma Black Belt should understand Kano analysis

This is all I have time for at the moment. I’m sure there are many other skills not on this list. Can we come up with a full 101 things? Your input is required!

]]> http://www.sixsigmatraining.org/introduction-to-six-sigma/101-soft-skills-a-six-sigma-black-belt-needs.html/feed 5 101 Things a Black Belt Should Know http://www.sixsigmatraining.org/introduction-to-six-sigma/101-things-a-black-belt-should-know.html?source=rss http://www.sixsigmatraining.org/introduction-to-six-sigma/101-things-a-black-belt-should-know.html#comments Fri, 06 Mar 2009 15:27:53 +0000 Thomas Pyzdek http://www.sixsigmatraining.org.php5-10.websitetestlink.com/?p=295 In general, a Six Sigma Black Belt should be quantitatively oriented.

With minimal guidance, the Six Sigma Black Belt should be able to use data to convert broad generalizations into actionable goals.

The Six Sigma Black Belt should be able to make the business case for attempting to accomplish

these goals.]]> Copyright © 2003
by Thomas Pyzdek, all rights reserved

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  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.
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