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Certified Six Sigma Black Belt

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The following information is provided by the American Society for Quality (ASQ):

 

        

Certification Requirements

Eligibility

CSSBB participants must register with ASQ headquarters.  Eligibility requires two completed projects with signed affidavits or one completed project with signed affidavit and three years work experience within the Six Sigma Body of Knowledge.  No education waiver is given. 

Examination

Each certification candidate is required to pass a written examination that consists of multiple-choice questions that measure comprehension of the Body of Knowledge. The CSSBB examination is a one-part, 150-question, four hour exam and is offered in the English language only.

The Application Process

How do I apply for certification?

Complete and submit to ASQ headquarters along with supporting documentation for all qualifying work history (resume, job description, etc.) and the correct fee.

Applications must be submitted on or before the deadline date.

What if my application isn't approved?

If you do not meet the minimum work or education experience, you may obtain a partial refund of the application fee by contacting the Certification Department at ASQ headquarters. ASQ will not waive the examination requirements. $50.00 of your fee is an application fee and is not refundable.

Once the exam has been held, or you have taken the examination, no refunds will be given. Approval of a certification application guarantees only the right to take the examination and does not guarantee certification.

Where may I take the exam?

Examinations are conducted twice a year, March and October. Examination sites are hosted by local ASQ sections and by international organizations (contact the ASQ Certification Department for international locations). You will be notified approximately two weeks before the examination date of your assigned testing location. Please allow extra time for international mail.

The Exam

How do I prepare for the exam?

Preparation time for the exam is dependent upon your level of experience. Review the Body of Knowledge to focus your studies on the areas in which you need the most review.

What is the content of the examination?

The Body of Knowledge lists the subject areas from which the examination questions are drawn. Keep in mind that any single examination represents only a sample of the Body of Knowledge and will not cover all the topics listed.

 

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Body of Knowledge

 

The topics in this Body of Knowledge include additional detail in the form of subtext explanations and the cognitive level at which the questions will be written. This information will provide useful guidance for both the Examination Development Committee and the candidates preparing to take the exam. The subtext is not intended to limit the subject matter or be all-inclusive of what might be covered in an exam. It is meant to clarify the type of content to be included in the exam. The descriptor in parentheses at the end of each entry refers to the maximum cognitive level at which the topic will be tested. A more complete description of cognitive levels is provided at the end of this document.

  1. Enterprise-Wide Deployment [9 Questions]
    1. Enterprise-wide view
      1. History of continuous improvement
        Describe the origins of continuous improvement and its impact on other improvement models. (Remember)
      2. Value and foundations of Six Sigma
        Describe the value of Six Sigma, its philosophy, history and goals. (Understand)
      3. Value and foundations of Lean
        Describe the value of Lean, its philosophy, history and goals. (Understand)
      4. Integration of Lean and Six Sigma
        Describe the relationship between Lean and Six Sigma. (Understand)
      5. Business processes and systems
        Describe the relationship among various business processes (design, production, purchasing, accounting, sales, etc.) and the impact these relationships can have on business systems. (Understand)
      6. Six sigma and Lean applications
        Describe how these tools are applied to processes in all types of enterprises: manufacturing, service, transactional, product and process design, innovation, etc. (Understand)
    2. Leadership
      1. Enterprise leadership responsibilities
        Describe the responsibilities of executive leaders and how they affect the deployment of Six Sigma in terms of providing resources, managing change, communicating ideas, etc. (Understand)
      2. Organizational roadblocks
        Describe the impact an organization’s culture and inherent structure can have on the success of Six Sigma, and how deployment failure can result from the lack of resources, management support, etc.; identify and apply various techniques to overcome these barriers. (Apply)
      3. Change management
        Describe and use various techniques for facilitating and managing organizational change. (Apply)
      4. Six Sigma projects and kaizen events
        Describe how projects and kaizen events are selected, when to use Six Sigma instead of other problem-solving approaches, and the importance of aligning their objectives with organizational goals. (Apply)
      5. Six Sigma roles and responsibilities
        Describe the roles and responsibilities of Six Sigma participants: black belt, master black belt, green belt, champion, process owners and project sponsors. (Understand)

       

  2. Organizational Process Management and Measures [9 Questions]
    1. Impact on stakeholders
      Describe the impact Six Sigma projects can have on customers, suppliers and other stakeholders. (Understand)
    2. Critical to x (CTx) requirements
      Define and describe various CTx requirements (critical to quality (CTQ), cost (CTC), process (CTP), safety (CTS), delivery (CTD), etc.) and the importance of aligning projects with those requirements. (Apply)
    3. Benchmarking
      Define and distinguish between various types of benchmarking, including best practices, competitive, collaborative, etc. (Apply)
    4. Business performance measures
      Define and describe various business performance measures, including balanced scorecard, key performance indicators (KPIs), the financial impact of customer loyalty, etc. (Understand)
    5. Financial measures
      Define and use financial measures, including revenue growth, market share, margin, cost of quality (COQ), net present value (NPV), return on investment (ROI), cost-benefit analysis, etc. (Apply)

     

  3. Team Management [16 Questions]
    1. Team formation
      1. Team types and constraints
        Define and describe various types of teams (e.g., formal, informal, virtual, cross-functional, self-directed, etc.), and determine what team model will work best for a given situation. Identify constraining factors including geography, technology, schedules, etc. (Apply)
      2. Team roles
        Define and describe various team roles and responsibilities, including leader, facilitator, coach, individual member, etc. (Understand)
      3. Team member selection
        Define and describe various factors that influence the selection of team members, including required skills sets, subject matter expertise, availability, etc. (Apply)
      4. Launching teams
        Identify and describe the elements required for launching a team, including having management support, establishing clear goals, ground rules and timelines, and how these elements can affect the team’s success. (Apply)
    2. Team facilitation
      1. Team motivation
        Describe and apply techniques that motivate team members and support and sustain their participation and commitment. (Apply)
      2. Team stages
        Facilitate the team through the classic stages of development: forming, storming, norming, performing and adjourning. (Apply)
      3. Team communication      
        Identify and use appropriate communication methods (both within the team and from the team to various stakeholders) to report progress, conduct milestone reviews and support the overall success of the project. (Apply)
    3. Team dynamics
      Identify and use various techniques (e.g., coaching, mentoring, intervention, etc.) to overcome various group dynamic challenges, including overbearing/dominant or reluctant participants, feuding and other forms of unproductive disagreement, unquestioned acceptance of opinions as facts, groupthink, floundering, rushing to accomplish or finish, digressions, tangents, etc. (Evaluate)
    4. Time management for teams
      Select and use various time management techniques including publishing agendas with time limits on each entry, adhering to the agenda, requiring pre-work by attendees, ensuring that the right people and resources are available, etc. (Apply)
    5. Team decision-making tools
      Define, select and use tools such as brainstorming, nominal group technique, multi-voting, etc. (Apply)
    6. Management and planning tools
      Define, select and apply the following tools: affinity diagrams, tree diagrams, process decision program charts (PDPC), matrix diagrams, interrelationship digraphs, prioritization matrices and activity network diagrams. (Apply)
    7. Team performance evaluation and reward
      Measure team progress in relation to goals, objectives and other metrics that support team success and reward and recognize the team for its accomplishments. (Analyze)
  4.   Define [15 Questions]
    1. Voice of the customer
      1. Customer identification
        Segment customers for each project and show how the project will impact both internal and external customers. (Apply)
      2. Customer feedback
        Identify and select the appropriate data collection method (surveys, focus groups, interviews, observation, etc.) to gather customer feedback to better understand customer needs, expectations and requirements. Ensure that the instruments used are reviewed for validity and reliability to avoid introducing bias or ambiguity in the responses. (Apply)
      3. Customer requirements  
        Define, select and use appropriate tools to determine customer requirements, such as CTQ flow-down, quality function deployment (QFD) and the Kano model. (Apply)
    2. Project charter
      1. Problem statement
        Develop and evaluate the problem statement in relation to the project’s baseline performance and improvement goals. (Create)
      2. Project scope
        Develop and review project boundaries to ensure that the project has value to the customer. (Analyze)
      3. Goals and objectives
        Develop the goals and objectives for the project on the basis of the problem statement and scope. (Apply)
      4. Project performance measures
        Identify and evaluate performance measurements (e.g., cost, revenue, schedule, etc.) that connect critical elements of the process to key outputs. (Analyze)
    3. Project tracking
      Identify, develop and use project management tools, such as schedules, Gantt charts, toll-gate reviews, etc., to track project progress. (Create)
  5. Measure [26 Questions]
    1. Process characteristics
      1. Input and output variables
        Identify these process variables and evaluate their relationships using SIPOC and other tools. (Evaluate)
      2. Process flow metrics
        Evaluate process flow and utilization to identify waste and constraints by analyzing work in progress (WIP), work in queue (WIQ), touch time, takt time, cycle time, throughput, etc. (Evaluate)
      3. Process analysis tools
        Analyze processes by developing and using value stream maps, process maps, flowcharts, procedures, work instructions, spaghetti diagrams, circle diagrams, etc. (Analyze)
    2. Data collection
      1. Types of data
        Define, classify and evaluate qualitative and quantitative data, continuous (variables) and discrete (attributes) data and convert attributes data to variables measures when appropriate. (Evaluate)
      2. Measurement scales
        Define and apply nominal, ordinal, interval and ratio measurement scales. (Apply)
      3. Sampling methods
        Define and apply the concepts related to sampling (e.g., representative selection, homogeneity, bias, etc.). Select and use appropriate sampling methods (e.g., random sampling, stratified sampling, systematic sampling, etc.) that ensure the integrity of data. (Evaluate)
      4. Collecting data
        Develop data collection plans, including consideration of how the data will be collected (e.g., check sheets, data coding techniques, automated data collection, etc.) and how it will be used. (Apply)
    3. Measurement systems
      1. Measurement methods
        Define and describe measurement methods for both continuous and discrete data. (Understand)
      2. Measurement systems analysis
        Use various analytical methods (e.g., repeatability and reproducibility (R&R), correlation, bias, linearity, precision to tolerance, percent agreement, etc.) to analyze and interpret measurement system capability for variables and attributes measurement systems. (Evaluate)
      3. Measurement systems in the enterprise
        Identify how measurement systems can be applied in marketing, sales, engineering, research and development (R&D), supply chain management, customer satisfaction and other functional areas. (Understand)
      4. Metrology
        Define and describe elements of metrology, including calibration systems, traceability to reference standards, the control and integrity of standards and measurement devices, etc. (Understand)
    4. Basic statistics
      1. Basic terms
        Define and distinguish between population parameters and sample statistics (e.g., proportion, mean, standard deviation, etc.) (Apply)
      2. Central limit theorem
        Describe and use this theorem and apply the sampling distribution of the mean to inferential statistics for confidence intervals, control charts, etc. (Apply)
      3. Descriptive statistics
        Calculate and interpret measures of dispersion and central tendency and construct and interpret frequency distributions and cumulative frequency distributions. (Evaluate)
      4. Graphical methods
        Construct and interpret diagrams and charts, including box-and-whisker plots, run charts, scatter diagrams, histograms, normal probability plots, etc. (Evaluate)
      5. Valid statistical conclusions
        Define and distinguish between enumerative (descriptive) and analytic (inferential) statistical studies and evaluate their results to draw valid conclusions. (Evaluate)
    5. Probability
      1. Basic concepts
        Describe and apply probability concepts such as independence, mutually exclusive events, multiplication rules, complementary probability, joint occurrence of events, etc. (Apply)
      2. Commonly used distributions
        Describe, apply and interpret the following distributions: normal, Poisson, binomial, chi square, Student’s t and F distributions. (Evaluate)
      3. Other distributions
        Describe when and how to use the following distributions: hypergeometric, bivariate, exponential, lognormal and Weibull. (Apply)
    6. Process capability
      1. Process capability indices
        Define, select and calculate Cp and Cpk to assess process capability. (Evaluate)
      2. Process performance indices
        Define, select and calculate Pp, Ppk and Cpm to assess process performance. (Evaluate)
      3. Short-term and long-term capability
        Describe and use appropriate assumptions and conventions when only short-term data or attributes data are available and when long-term data are available. Interpret the relationship between long-term and short-term capability. (Evaluate)
      4. Process capability for non-normal data
        Identify non-normal data and determine when it is appropriate to use Box-Cox or other transformation techniques. (Apply)
      5. Process capability for attributes data
        Calculate the process capability and process sigma level for attributes data. (Apply)
      6. Process capability studies
        Describe and apply elements of designing and conducting process capability studies, including identifying characteristics and specifications, developing sampling plans and verifying stability and normality. (Evaluate)
      7. Process performance vs. specification
        Distinguish between natural process limits and specification limits, and calculate process performance metrics such as percent defective, parts per million (PPM), defects per million opportunities (DPMO), defects per unit (DPU), process sigma, rolled throughput yield (RTY), etc. (Evaluate)

       

  6. Analyze [24 Questions]
    1. Measuring and modeling relationships between variables
      1. Correlation coefficient
        Calculate and interpret the correlation coefficient and its confidence interval, and describe the difference between correlation and causation. (Analyze)
        NOTE: Serial correlation will not be tested.
      2. Regression
        Calculate and interpret regression analysis, and apply and interpret hypothesis tests for regression statistics. Use the regression model for estimation and prediction, analyze the uncertainty in the estimate, and perform a residuals analysis to validate the model. (Evaluate)
        NOTE: Models that have non-linear parameters will not be tested.
      3. Multivariate tools
        Use and interpret multivariate tools such as principal components, factor analysis, discriminant analysis, multiple analysis of variance (MANOVA), etc., to investigate sources of variation. (Analyze)
      4. Multi-vari studies
        Use and interpret charts of these studies and determine the difference between positional, cyclical and temporal variation. (Analyze)
      5. Attributes data analysis
        Analyze attributes data using logit, probit, logistic regression, etc., to investigate sources of variation. (Analyze)
    2. Hypothesis testing
      1. Terminology
        Define and interpret the significance level, power, type I and type II errors of statistical tests. (Evaluate)
      2. Statistical vs. practical significance
        Define, compare and interpret statistical and practical significance. (Evaluate)
      3. Sample size
        Calculate sample size for common hypothesis tests (e.g., equality of means, equality of proportions, etc.). (Apply)
      4. Point and interval estimates
        Define and distinguish between confidence and prediction intervals. Define and interpret the efficiency and bias of estimators. Calculate tolerance and confidence intervals. (Evaluate)
      5. Tests for means, variances and proportions
        Use and interpret the results of hypothesis tests for means, variances and proportions. (Evaluate)
      6. Analysis of variance (ANOVA)
        Select, calculate and interpret the results of ANOVAs. (Evaluate)
      7. Goodness-of-fit (chi square) tests
        Define, select and interpret the results of these tests. (Evaluate)
      8. Contingency tables
        Select, develop and use contingency tables to determine statistical significance. (Evaluate)
      9. Non-parametric tests
        Select, develop and use various non-parametric tests, including Mood’s Median, Levene’s test, Kruskal-Wallis, Mann-Whitney, etc. (Evaluate)
    3. Failure mode and effects analysis (FMEA)
      Describe the purpose and elements of FMEA, including risk priority number (RPN), and evaluate FMEA results for processes, products and services. Distinguish between design FMEA (DFMEA) and process FMEA (PFMEA), and interpret results from each. (Evaluate)
    4. Additional analysis methods
      1. Gap analysis
        Use various tools and techniques (gap analysis, scenario planning, etc.) to compare the current and future state in terms of pre-defined metrics. (Analyze)
      2. Root cause analysis
        Define and describe the purpose of root cause analysis, recognize the issues involved in identifying a root cause, and use various tools (e.g., the 5 whys, Pareto charts, fault tree analysis, cause and effect diagrams, etc.) for resolving chronic problems. (Evaluate)
      3. Waste analysis
        Identify and interpret the 7 classic wastes (overproduction, inventory, defects, over-processing, waiting, motion and transportation) and other forms of waste such as resource under-utilization, etc. (Analyze)

       

  7.   Improve [23 Questions]
    1. Design of experiments (DOE)
      1. Terminology
        Define basic DOE terms, including independent and dependent variables, factors and levels, response, treatment, error, etc. (Understand)
      2. Design principles
        Define and apply DOE principles, including power and sample size, balance, repetition, replication, order, efficiency, randomization, blocking, interaction, confounding, resolution, etc. (Apply)
      3. Planning experiments
        Plan, organize and evaluate experiments by determining the objective, selecting factors, responses and measurement methods, choosing the appropriate design, etc. (Evaluate)
      4. One-factor experiments
        Design and conduct completely randomized, randomized block and Latin square designs and evaluate their results. (Evaluate)
      5. Two-level fractional factorial experiments
        Design, analyze and interpret these types of experiments and describe how confounding affects their use. (Evaluate)
      6. Full factorial experiments
        Design, conduct and analyze full factorial experiments. (Evaluate)
    2. Waste elimination
      Select and apply tools and techniques for eliminating or preventing waste, including pull systems, kanban, 5S, standard work, poka-yoke, etc. (Analyze)
    3. Cycle-time reduction
      Use various tools and techniques for reducing cycle time, including continuous flow, single-minute exchange of die (SMED), etc. (Analyze)
    4. Kaizen and kaizen blitz
      Define and distinguish between these two methods and apply them in various situations. (Apply)
    5. Theory of constraints (TOC)
      Define and describe this concept and its uses. (Understand)
    6. Implementation
      Develop plans for implementing the improved process (i.e., conduct pilot tests, simulations, etc.), and evaluate results to select the optimum solution. (Evaluate)
    7. Risk analysis and mitigation
      Use tools such as feasibility studies, SWOT analysis (strengths, weaknesses, opportunities and threats), PEST analysis (political, environmental, social and technological) and consequential metrics to analyze and mitigate risk. (Apply)

     

  8.   Control [21 Questions]
    1. Statistical process control (SPC)
      1. Objectives
        Define and describe the objectives of SPC, including monitoring and controlling process performance, tracking trends, runs, etc., and reducing variation in a process. (Understand)
      2. Selection of variables
        Identify and select critical characteristics for control chart monitoring. (Apply)
      3. Rational subgrouping
        Define and apply the principle of rational subgrouping. (Apply)
      4. Control chart selection
        Select and use the following control charts in various situations:
        XBAR - R, XBAR - s individual and moving range (ImR), p, np, c, u, short-run SPC and moving average. (Apply)
      5. Control chart analysis
        Interpret control charts and distinguish between common and special causes using rules for determining statistical control. (Analyze)
    2. Other control tools          
      1. Total productive maintenance (TPM)
        Define the elements of TPM and describe how it can be used to control the improved process. (Understand)
      2. Visual factory
        Define the elements of a visual factory and describe how they can help control the improved process. (Understand)
    3. Maintain controls
      1. Measurement system re-analysis
        Review and evaluate measurement system capability as process capability improves, and ensure that measurement capability is sufficient for its intended use. (Evaluate)
      2. Control plan
        Develop a control plan for ensuring the ongoing success of the improved process including the transfer of responsibility from the project team to the process owner. (Apply)
    4. Sustain improvements
      1. Lessons learned
        Document the lessons learned from all phases of a project and identify how improvements can be replicated and applied to other processes in the organization. (Apply)
      2. Training plan deployment
        Develop and implement training plans to ensure continued support of the improved process. (Apply)
      3. Documentation
        Develop or modify documents including standard operating procedures (SOPs), work instructions, etc., to ensure that the improvements are sustained over time. (Apply)
      4. Ongoing evaluation
        Identify and apply tools for ongoing evaluation of the improved process, including monitoring for new constraints, additional opportunities for improvement, etc. (Apply)

       

  9. Design for Six Sigma (DFSS) Frameworks and Methodologies [7 Questions]
    1. Common DFSS methodologies
      Identify and describe these methodologies. (Understand)
      1. DMADV (define, measure, analyze, design and validate)
      2. DMADOV (define, measure, analyze, design, optimize and validate)
    2. Design for X (DFX)
      Describe design constraints, including design for cost, design for manufacturability and producibility, design for test, design for maintainability, etc. (Understand)
    3. Robust design and process
      Describe the elements of robust product design, tolerance design and statistical tolerancing. (Apply)
    4. Special design tools
      1. Strategic
        Describe how Porter’s five forces analysis, portfolio architecting and other tools can be used in strategic design and planning. (Understand)
      2. Tactical
        Describe and use the theory of inventive problem-solving (TRIZ), systematic design, critical parameter management and Pugh analysis in designing products or processes. (Apply)

Levels of Cognitionbased on Bloom’s Taxonomy – Revised (2001)

In addition to content specifics, the subtext for each topic in this BOK also indicates the intended complexity levelof the test questions for that topic. These levels are from “Levels of Cognition” (from Bloom’s Taxonomy – Revised, 2001). They are in rank order - from least complex to most complex.

Remember
Recall or recognize terms, definitions, facts, ideas, materials, patterns, sequences, methods, principles, etc.

Understand
Read and understand descriptions, communications, reports, tables, diagrams, directions, regulations, etc.

Apply
Know when and how to use ideas, procedures, methods, formulas, principles, theories, etc.
 
Analyze
Break down information into its constituent parts and recognize their relationship to one another and how they are organized; identify sublevel factors or salient data from a complex scenario.

Evaluate
Make judgments about the value of proposed ideas, solutions, etc., by comparing the proposal to specific criteria or standards.

Create
Put parts or elements together in such a way as to reveal a pattern or structure not clearly there before; identify which data or information from a complex set is appropriate to examine further or from which supported conclusions can be drawn

.

 

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Sample Questions

 

1. From an upper management perspective, what has been the principal motivating factor in embracing six sigma?

a. Bottom line results
b. Market share growth
c. Defect reductions
d. Customer focus

2. The SIPOC business model provides all of the following benefits, EXCEPT:

a. Providing a framework applicable to processes of all sizes
b. Identifying the few key business customers
c. Displaying cross-function activities in simple terms
d. Helping maintain the big business picture

3. In most cases, an improvement team receives the least control and direction during which of the following stages?

a. Forming
b. Storming
c. Performing
d. Norming

4. Which of the new quality management tools is used to organize facts and data about an unfamiliar subject or problem?

a. The affinity diagram
b. The header technique
c. The AND diagram
d. Matrix diagram

5. The purpose of "rolled throughput yield" in the six sigma define step would include all of the following, EXCEPT:

a. Spotting significant differences in yield
b. Providing a baseline metric
c. Using the calculation for customer analysis
d. Analyzing a process flow for improvement ideas

6. Flowcharting of activities and systems is most helpful in detecting:

a. Inappropriate use of resources
b. Deficiencies in the organizational structure
c. FMEA risk areas
d. Improper use of statistical methods

7. A null hypothesis requires several assumptions, a basic one of which is:

a. That the variables are significant
b. The variables are independent
c. That the sample size is adequate
d. That the confidence interval is ± 2 standard deviations

8. Which three of the following four techniques could easily be used to display the same data?

I. Stem and leaf plots
II. Boxplots
III. Scatter diagrams
IV. Histograms

a. I, II, and III only
b. I, II, and IV only
c. I, III, and IV only
d. II, III, and IV only

9. In the regression equation y = mx + b, y increases with x in all cases: 

a. If b is positive
b. If b is negative
c. If m is positive
d. If m is negative

10. If a sample size of 16 yields an average of 12 and standard deviation of 3, estimate the 95% confidence interval for the population (assume a normal distribution).

a. 10.40  <  m <   13.60
b. 10.45  <  m <13.55
c. 10.53  <  m <13.47
d. 10.77  <  m <13.23

11. A technique used to measure the degree of interdependence between two random variables is: 

a. Regression analysis
b. Hypothesis testing
c. Correlation analysis
d. Sampling

12. In a full factorial experimental design, factors A and B are both tested at 4 levels. How many experiments are conducted?

a. 8
b. 9
c. 12
d. 16

13. The smallest run number possible to examine the main effects of 22 factors at 2 levels is:

a. 23
b. 24
c. 44
d. 56

14. The main difference between traditional kaizen and the kaizen blitz approach is:

a. The number of people involved
b. The pace of the change effort
c. The amount of floor space saved
d. The commitment level of management

15. In a hypothetical situation, if all within time, piece to piece, and measurement variation were removed from a process, what would be left?

a. Nothing it would all be eliminated
b. Inherent process variation
c. Product spread
d. Time to time variation

16. Overproduction, scrap, waiting, and excess motion are all forms of:

a. TPM
b. Muda
c. Kanban
d. CFM

17. Consider the following definition: "The best combination of machines and people working together to produce a product or service at a particular point in time." What lean concept is being described?

a. Standard work
b. A future state map
c. The value stream
d. Ultimate cycle time

18. Which of the following is NOT a widely recognized topic area for DFX?

a. Design for profit
b. Design for assembly
c. Design for reliability
d. Design for appearance

 

1. a,   2. b,   3. c,   4. a,   5. c,    6. a,   7. b,   8. b,   9. c


10. a,   11. c,   12. d,   13. b,   14. b,    15. b,   16. b,   17. a,   18. a

 

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