Posts Tagged ‘sigma black belt’

Design of Experiments and Baseball

Monday, August 31st, 2009

A Black Belt steps up to the plate with Six Sigma confidence.

Bill had a problem. His company’s baseball team wasn’t doing that well, and he was part of the reason. Bill was in a long slump. Frankly, he stunk at the plate.

But Bill is a Six Sigma Black Belt. He decided to approach his batting problem just like he would approach any process problem at work–by conducting a designed experiment. First, Bill determined which factors are important. He wrote up a lengthy list and then winnowed it down to four experimental variables (see Table 1).

Table 1: Experimental Variables for Hitting

Bill decided to spend a few evenings and weekends on the practice field swinging at 100 pitches for each of the 16 combinations of the four variables needed to conduct a full-factorial experiment. The field was equipped with a pitching machine that could be programmed to throw pitches at either 60 mph or 80 mph. Bill decided to count any ball that went past the infield in fair territory as a hit. Over a two-week period Bill was able to complete the experiment, producing the results shown in Table 2.

Table 2: Bill’s Batting Experiment

The analysis indicates that factors B and D, and especially the C-D interaction, make big differences in Bill’s performance. Factors A and C do not have a significant effect on Bill’s batting average. The analysis in Table 3 shows the details.

Table 3: Significant Factor Effects

The 95-percent confidence interval for C (position in the batter’s box) includes zero, meaning that C is not statistically significant as a main effect. (C is included because the significant C-D interaction term requires it for statistical reasons.) However, the other factors in the table–B (choke on the bat) and D (speed of the pitch)–are statistically significant. The most important factor is the C-D interaction, which has an impressive effect of more than 9 percent. The coefficient estimate tells us what happens to Bill’s batting average as we go from one level of the variable to another. For example, when B is at the high level (choke up on the bat two inches), Bill’s batting average improves by about four percentage points.

The analysis indicates that when Bill is facing a pitcher with real heat (80 mph isn’t too bad for an amateur pitcher), he can improve his batting average from 8 percent to 28.75 percent by standing near the back of the batter’s box (see Table 4). Conversely, when Bill is up against a 60-mph hurler, he’s better off in the front of the batter’s box (38.75 percent in front hits vs. 15 percent in back). Combining all of these results, Bill’s strategy is to always choke up on the bat and position himself in the batter’s box depending on the expected speed of the pitch.

Table 4: Bill’s Results

Bill may not be ready for the majors with this strategy, but he’s hitting a lot better than the .206 (20.6%) he’d been getting without a strategy. In the meantime, Bill, work on hitting that fast ball!

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What is a Black Belt?

Monday, August 17th, 2009

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.

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How Six Sigma Can Help With Marketing

Monday, August 17th, 2009

Marketing is a process. Six Sigma is an approach for achieving process excellence. It will help you improve the marketing process by providing tools & techniques for identifying what the marketing process is, including suppliers, inputs, process steps, outputs, and customers. Six Sigma helps you understand the need to determine who owns the process and helps the process owner determine how to improve it. It provides a framework for improving all aspects of this process. It does much more as well. I recommend you enroll and take a week to look around the training site. If it looks like a good value to you, stay in the course and become a Certified Six Sigma Black Belt or Green Belt.

The converse is also true, marketing can help Six Sigma. Both marketing and Six Sigma focus on customers. Marketing is a management discipline dedicated to understanding customer demands, how to design products meet them, and how to let potential customers know what’s available. In Six Sigma training for Black Belts and Green Belts we teach a number of tools that are borrowed directly from marketing, such as the analytic hierarchical process, quality function deployment and Pugh matrices. Master Blacks use conjoint analysis, a quasi-designed experiment approach to measuring customer importance weights. Design for Six Sigma is all about integrating the design process across marketing, engineering, and production to better meet implicit and explicit customer demands.

Beyond the technical tools, when Six Sigma or Lean Six Sigma is well done it begins with understanding what customers are solving for, then helping them achieve their goals by improving the processes you use to provide them with service. This is truly an integration of marketing and Six Sigma.

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A Change Agent’s Most Important Personal Attribute

Thursday, July 30th, 2009

Today I received a call from a person interested in becoming a Certified Six Sigma Black Belt. Of course, we value him as a customer and he will learn a great deal if he decides to enroll in our Six Sigma training. Among the things he’ll learn are both “hard skills” involving statistics and data analysis techniques, and “soft skills” such as conflict management, team dynamics, and stakeholder analysis. Still, I have my doubts about his chances of becoming a successful Six Sigma Black Belt. He has what I call a “Can’t Do” personality. This is the diametric opposite of the Can Do person. This type of individual looks for reasons why a particular thing can’t be done. How about a project in the sales department? No way, sales people won’t go for it, sales isn’t a process anyway, management won’t let us touch the sales area, etc. etc. etc.

Successful change agents are invariably Can Do people. To be sure they spend a lot of time planning to avoid obstacles, but when they encounter the inevitable obstacle, they don’t shrink from the challenge. They found ways over, under, around, or through the obstacle. They are not to be stopped. They are relentless pursuers of change.

I once had the opportunity to work with a major aerospace client to study the success factors for their Six Sigma Black Belts. We reviewed the histories of a number of Black Belts who had success levels that varied from poor to excellent. After coming up with a list of the factors that seemed to have an impact on success we went through an exercise to determine the importance weights. Using the Analytic Hierarchical Process (AHP) the Six Sigma Champion, Master Black Belts, and me came up with the weights shown in Figure 1.

Figure 1-Black Belt Success Factor Weights

Figure 1-Black Belt Success Factor Weights

The weights are, of course, subjective and only approximate. You may feel free to modify them if you feel strongly that they’re incorrect. Better yet, you may want to identify your own set of criteria and weights. The important thing is to determine the criteria and then develop a method of evaluating candidates on each criterion. The sum of the candidate’s criterion score times the criterion weight will give you an overall numerical assessment that can be useful in sorting out those candidates with high potential from those less likely to succeed as Black Belts. Of course, the numerical assessment is not the only input into the selection decision, but it is a very useful one.

You may be surprised to see the low weight given to math skills. The rationale is that Black Belts will receive 200 hours of training, much of it focused on the practical application of statistical techniques using computer software and requiring very little actual mathematics. Software automates the analysis, making math skills less necessary. The mathematical theory underlying a technique is not discussed beyond the level necessary to help the Black Belt properly apply the tool. Black Belts who need help with a particular tool have access to Master Black Belts, other Black Belts, consultants, professors, and a wealth of other resources. Most statistical techniques used in Six Sigma are relatively straightforward and often graphical; spotting obvious errors is usually not too difficult for trained Black Belts. Projects seldom fail due to a lack of mathematical expertise. In contrast, the Black Belt will often have to rely on his or her own abilities to deal with the obstacles to change they will inevitably encounter. Failure to overcome the obstacle will often spell failure of the entire project.

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101 Soft Skills a Six Sigma Black Belt Needs

Wednesday, April 8th, 2009

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!

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An Overview of Six Sigma Black Belt Training

Monday, April 6th, 2009

July 5, 2008

Tom presents the audio track of the first lesson of his online Black Belt training. His approach is unique because it presents the various tools in the context of how they are applied. If you are not yet a Six Sigma Black Belt, you will discover what is taught in Black Belt training. If you’re already a Black Belt, this podcast will help you understand when and how each tool is applied. You may want to listen to this podcast in several listenings. 22:49.

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Modeling with Regression

Monday, April 6th, 2009

July 1, 2008

One important Black Belt activity is to use the organization’s data warehouse to explore cause and effect relationships by building models using multiple linear regression. This isn’t as easy as just throwing all of the candidate Xs into a software package and crunching away. This podcast describes the technique Tom teaches in Six Sigma Black Belt training. 5:32.

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Six Sigma Black Belt How To Guide I

Monday, April 6th, 2009

October 21, 2007

What does it take to be an effective Six Sigma Black Belt? This two-part podcast tackles this question. In Part I Tom discusses the role of the Black Belt, motivating others, working with teams as a Black Belt, management’s responsibilities to teams, proper team structure, how to get the voice of the process, and problem solving. 10:09.

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101 Things a Black Belt Should Know

Friday, March 6th, 2009

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.
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Good books on Six Sigma and other topics

What is Six Sigma?

By Thomas Pyzdek, Author of The Six Sigma Handbook

For Motorola, the originator of Six Sigma, the answer to the question "Why Six Sigma?" was simple: survival. Motorola came to Six Sigma because it was being consistently beaten in the competitive marketplace by foreign firms that were able to produce higher quality products at a lower cost. When a Japanese firm took over a Motorola factory that manufactured Quasar television sets in the United States in the 1970s, they promptly set about making drastic changes in the way the factory operated. Under Japanese management, the factory was soon producing TV sets with 1/20th the number of defects they had produced under Motorola management. They did this using the same workforce, technology, and designs, making it clear that the problem was Motorola's management. Eventually, even Motorola's own executives had to admit "our quality stinks." Read More...