Understanding ASQ-CQA -Knowing the Ways

Knowing ASQ CQA The Quality Auditor Certification My Pre-exam Self Study Notes 4th September 2018

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Aeronautical Quality Assurance

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Aeronautical Quality Assurance

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SR-71

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SR-71

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SR-71

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SR-71A

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闭门练功

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http://independent.academia.edu/CharlieChong1 http://www.yumpu.com/zh/browse/user/charliechong http://issuu.com/charlieccchong

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http://greekhouseoffonts.com/

The Magical Book of Tank Inspection ICP

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闭门练功

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闭门练功

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Fion Zhang at Shanghai 4th September 2018

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Content: 1. ASQ BOK 2. Pre-read: Six Sigma 6σ-The Wikipedia

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ASQ Mission: The American Society for Quality advances individual, organizational, and community excellence worldwide through learning, quality improvement, and knowledge exchange.

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ASQ Mission: The American Society for Quality advances individual, organizational, and community excellence worldwide through learning, quality improvement, and knowledge exchange.

excellence • •

learning knowledge exchange

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https://asq.org/about-asq/asq-awards/deming

The Certified Quality Auditor (CQA) is a professional who understands：  the standards and  the principles of auditing and  the auditing techniques of ;  examining,  questioning,  evaluating, and  reporting to determine a quality system’s adequacy and deficiencies. The Certified Quality Auditor analyzes all elements of a quality system and judges its degree of adherence to the criteria of industrial management and quality evaluation and control systems.

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 the auditing techniques of ;  examining,  questioning,  evaluating, and  reporting

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…appropriate techniques to gather, identify, and classify objective evidence.

The Auditing Techniques: Examining

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The Auditing Techniques: Questioning

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The Auditing Techniques: Evaluating & Reporting

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CQA Computer Delivered – The CQA examination is a one-part,165-multiplechoice-question,five-and-a-half-hour exam and is offered in English only.

One hundred and fifty questions are scored and 15 are unscored. Paper and Pencil – The CQA examination is a one-part,150-multiple-choice-question,five-hour exam and is offered in English only.

165 – 15 Questions 5 hours. minus

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Minimum Expectations  Must possess the knowledge and ability to effectively conduct different types of audits, as appropriate for the method, relationship, or purpose of the audit, and must recognize the effect those audit types will have on the audit scope and outcomes.  Must be able to audit in a professional, ethical, and objective manner using and interpreting applicable standards or requirements, with an awareness of potential legal and financial ramifications 财务影响.  Must be able to effectively plan, communicate, and execute an audit within its defined scope, including scheduling resources, conducting necessary meetings in performance of the audit, and using appropriate techniques to gather, identify, and classify objective evidence.

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 Must be able to verify, document, and communicate audit results, develop an audit report, and evaluate the effectiveness of corrective action and follow up.  Must possess interpersonal skills to resolve conflict, conduct interviews, and make presentations while participating as an audit team member, and must possess knowledge of the unique responsibilities of the lead auditor and team facilitator.  Must understand the value that quality auditing adds to the organization and how auditing can reveal interrelationships between business processes that can influence outcomes and organizational risk.  Must be able to select appropriate quality and auditing tools and techniques, and use them effectively in a variety of practical applications.

Must possess interpersonal skills to resolve conflict.

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BOK Examinations will continue to present a number of case studies. Each case study will include a brief scenario outlining critical details about an audit situation. In addition, each case study will be supported by related audit documents. The documents will be contained in a separate booklet “Confidential Audit Documents – CQA Case Studies� that will be part of the test materials distributed at the examination. Approximately 15-20 percent (25-30 questions) of the test will be devoted to these case studies.

Although the questions related to these cases will use the same four-choice answer format as the rest of the test, the use of scenario details and sample documents will allow the candidates to apply their critical thinking skills in evaluating realistic situations and accompanying documents, memos, etc.

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BOK Knowledge

Percentage Score

I. Auditing Fundamentals (27 Questions)

18%

II. Audit Process (42 Questions)

28%

III. Auditor Competencies (25 Questions)

17%

IV. Audit Program Management and Business Applications (30 Questions)

20%

V. Quality Tools and Techniques (26 Questions)

17%

150 Questions

100%

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BOK Approximately 15-20 percent (25-30 questions) of the test will be devoted to these case studies.

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BOK I. Auditing Fundamentals (27 Questions) A. Types of Quality Audits 1. Method Define, differentiate, and analyze various audit types by method: product, process, desk, department, function, element, system, management. (Analyze)

4. Common elements with other audits Identify elements such as audit purpose, data gathering techniques, tracing, etc., that quality audits have in common with environmental, safety, financial, and other types of audits.

(Apply)

2. Auditor-auditee relationship Define, differentiate, and analyze various audit types by auditor-auditee relationship: first-party, second-party, third-party, internal and external.

(Analyze)

B. Purpose and Scope of Audits 1. Elements of purpose and scope Describe and determine how the purpose of an audit can affect its scope. (Apply)

3. Purpose Define, differentiate, and analyze various audit types by purpose: verification of corrective action (follow-up) audits, risk audits, accreditation (registration) and compliance audits, surveillance and for-cause audits.

(Analyze)

2. Benefits of audits Analyze how audits can be used to provide an independent assessment of system effectiveness and efficiency, risks to the bottom line, and other organizational measures.

(Analyze)

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I. Auditing Fundamentals (27 Questions) C. Criteria to Audit Against Define and distinguish between various audit criteria, such as external (industry, national, international) standards, contracts, specifications, quality awards, policies, internal quality management system (QMS), sustainability, social responsibility, etc. (Analyze)

2. Legal consequences Identify potential legal and financial ramifications of improper auditor actions (carelessness, negligence, etc.) in various situations, and anticipate the effect that certain audit results can have on an auditee‘s liability.

(Apply)

D. Roles and Responsibilities of Audit Participants Define and describe the functions and responsibilities of various audit participants, including audit team members, lead auditor, client, auditee, etc. (Apply)

3. Audit credibility Identify and apply various factors that influence audit credibility, such as auditor independence, objectivity, and qualifications. (Apply)

E. Professional Conduct and Consequences for Auditors 1. Professional conduct and responsibilities Define and apply the ASQ Code of Conduct, concepts of due diligence and due care with respect to confidentiality and conflict of interest, and appropriate actions in response to the discovery of illegal activities or unsafe conditions. (Apply)

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II. Audit Process (42 Questions) A. Audit Preparation and Planning 1. Elements of the audit planning process Evaluate and implement the basic steps in audit preparation and planning: Who? • verify audit authority; (?)

• determine the (1) purpose, (2) scope, and (3) type of audit; • identify the requirements to audit against and the resources necessary, including the size and number of audit teams. (Evaluate) 2. Auditor selection Identify and examine various auditor selection criteria, such as education, experience, industry background, and subject matter or technical expertise. (Analyze) 3. Audit-related documentation Identify the sources of pre-audit information and examine audit related documentation, such as audit criteria references and results from prior audits. (Analyze)

4. Logistics Identify and organize audit-related logistics, including travel, safety and security considerations, the need for escorts, translators, confidentiality agreements, clear right of access, etc. (Analyze) 5. Auditing tools and working papers Identify the sampling plan or method and procedural guidelines to be used for the specific audit. Select and prepare working papers (checklists, log sheets, etc.) to document the audit. (Create) 6. Auditing strategies Identify and use various tactical methods for conducting an audit, such as forward and backward tracing (?), discovery, etc. (Apply) I found a good explanation of the difference between forward and backward traceability here: • Checking forward traceability: taking a batch of materials/components and tracing them through the process, including work in process, all the way to the finished products that were made with those materials/components.

• Checking backward traceability – this is taking a finished product batch and tracing it, starting from the customer, back through the process including work in process, all the way to the batches of materials/components received from suppliers. https://qualityinspection.org/forward-backward-traceability/ Charlie Chong/ Fion Zhang

II. Audit Process (42 Questions) B. Audit Performance 1. On-site audit management Interpret situations throughout the performance of the audit to determine whether time is being managed well and when changes need to be made, such as revising planned audit team activities, reallocating resources, adjusting the audit plan, etc., and communicate with the auditee about any changes or other events related to the audit.

(Analyze) 2. Opening meeting Manage the opening meeting of an audit by identifying the audit‘s purpose and scope, describing any scoring or rating criteria that will be used during the audit, creating a record of the attendees, reviewing the audit schedule, and answering questions as needed. (Apply)

Risk= Probability x Consequences (Risk= frequency x severity?)

(Risk ≡ Significant?)

3. Audit data collection and analysis Use various data collection methods to capture information: • Conducting interviews, • observing work activities, methods • taking physical measurements, • examining documents, etc.

Evaluate the results to determine their importance for providing audit evidence. (Evaluate) 4. Establishment of objective evidence Identify and differentiate characteristics of objective evidence, such as observed, measured, confirmed or corroborated (Confirm/证实), and documented.

(Analyze) 5. Organization of objective evidence Classify evidence in terms of significance, severity, frequency, and level of risk. Evaluate the evidence for its potential impact on product, process, system, cost of quality, etc., and determine whether additional investigation is required to meet the scope of the audit.

(Evaluate)

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5. Organization of objective evidence Classify evidence in terms of :  significance,  severity, level of risk  frequency, and  level of risk.

Severity x frequency

Evaluate the evidence for its potential impact on  product,  process,  system,  cost of quality, etc., and determine whether additional investigation is required to meet the scope of the audit. (Evaluate)

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Evaluate the evidence for its potential impact on  product,  process,  system,  cost of quality, etc., The etc.;  Tarnishing the Company Image.  Others?

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Evaluate the evidence for its potential impact on  product,  process,  system,  cost of quality, etc., The etc.;  Tarnishing the Company Image.  Others?

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Evaluate the evidence for its potential impact on  product,  process,  system,  cost of quality, etc., The etc.;  Tarnishing the Company Image,  Environmental,  Others?

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II. Audit Process (42 Questions) 6. Exit and closing meetings Formally manage these meetings: reiterate the audit‘s purpose, scope, and scoring or rating criteria, and create a record of the attendees. Present the audit results and obtain concurrence on evidence that could lead to an adverse conclusion. Discuss the next steps in the process (follow-up audit, additional evidence-gathering, etc.), and clarify who is responsible for performing those steps. (Apply)

2. Effective reports Develop and evaluate components of effective audit reports, including background information, executive summary, prioritized results (observations, findings, opportunities for improvement, etc.). Use graphical tools or other means of emphasizing conclusions, and develop a timeline for auditee response and/or corrections. (Create)

3. Final audit report steps C. Audit Reporting Obtain necessary approvals for the audit report 1. Report development and content and distribute it according to established Group observations into actionable findings of procedures. Identify the contents of the audit file significance, and identify the severity and risk to and retain the file in accordance with the client and the auditee. Use appropriate steps established policies and procedures. (Apply) to generate the audit report: organize and summarize details, review and finalize results, emphasize critical issues, establish unique identifiers or codes for critical issues to facilitate tracking and monitoring, etc. (Create)

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II. Audit Process (42 Questions) D. Audit Follow-Up and Closure 1. Elements of the corrective action process Identify and evaluate various elements: assignment of responsibility for problem identification; the performance of root cause analysis and recurrence prevention. (Evaluate)

4. Follow-up on ineffective corrective action Develop strategies to use when corrective actions are not implemented or are not effective, such as communicating to the next level of management, reissuing the corrective action request, and re-auditing. (Create)

2. Review of corrective action plan 5. Audit closure Evaluate the acceptability of proposed corrective Identify and apply various elements of, and actions and schedule for completion. Identify criteria for, audit closure (Apply) and apply strategies for negotiating changes to unacceptable plans. (Evaluate)

3. Verification of corrective action Determine the adequacy of corrective actions taken by verifying and evaluating new or updated procedures, observing revised processes, conducting follow-up audits, etc.

(Evaluate)

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D. Audit Follow-Up and Closure 1. Elements of the corrective action process Identify and evaluate various elements:  assignment of responsibility for problem identification;  the performance of root cause analysis and  recurrence prevention. (Evaluate)

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RCA Kaoru Ishikawa Diagram

D. Audit Follow-Up and Closure 1. Elements of the corrective action process Identify and evaluate various elements: assignment of responsibility for problem identification; the performance of root cause analysis and recurrence prevention. (Evaluate) 2. Review of corrective action plan Evaluate the acceptability of proposed corrective actions and schedule for completion. Identify and apply strategies for negotiating changes to unacceptable plans. (Evaluate) Assignment of responsibility for problem identificationAeronautical‘s SME in turbine.

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Recurrence Prevention & RCA D. Audit Follow-Up and Closure 1. Elements of the corrective action process Identify and evaluate various elements: assignment of responsibility for problem identification; the performance of root cause analysis and recurrence prevention. (Evaluate)

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III. Auditor Competencies (25 Questions) A. Auditor Characteristics Identify characteristics that make auditors effective: interpersonal skills, problem-solving skills, attention to detail, cultural awareness and sensitivity, ability to work independently as well as in a group or on a team, etc.

(Apply)

D. Communication and Presentation Techniques Select and use written, oral, and electronic communication techniques for presentations made during audits for opening, closing, ad-hoc meetings, etc. Use technical and managerial reporting techniques, including graphs, charts, diagrams, multimedia aids, etc., in various situations: domestic, global, in-person, virtual (e-audits), multiple sites simultaneously, etc. (Evaluate)

B. On-Site Audit Resource Management Identify and apply techniques for managing audit teams, scheduling audit meetings and activities, making E. Interviewing Techniques logistical adjustments, etc. (Apply) Select and use appropriate interviewing techniques and methodologies. (Apply) C. Conflict Resolution 1. Use open-ended or closed question types Identify typical conflict situations (mild to vehement 2. Use active listening, paraphrasing (另种表达方式), (intense) disagreements, auditee empathy (同情), etc. delaying tactics, interruptions, etc.) and determine 3. Recognize and respond to non-verbal cues (提示, appropriate techniques for resolving them: 暗示,表示): body language, the significance of  clarifying the question or request, pauses and their length, etc.  reiterating ground rules, 4. Determine when and how to prompt (促使) a  intervention by another authority, response: when supervisors are present, when  cool-down periods, etc. interviewing a group of workers, when using a (Analyze) translator, etc.

Paraphrasing Tool to paraphrase or rewrite full length essays and articles or to find new ways to express simple phrases, sentences or single words.

Empathy: the ability to understand and share the feelings of another.

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III. Auditor Competencies (25 Questions) F. Team Dynamics Define, describe, and apply various aspects of team dynamics. (Apply) 1. Team-building: clarifying roles and responsibilities for participants and leaders to ensure equitable treatment for all team members, providing clear direction for deliverables, identifying necessary resources and ensuring their availability, etc.

2.

Team facilitation: providing coaching and guidance, defusing clashes between members, eliciting (bring out) input from all, cultivating objectivity, overseeing progress, encouraging diverse views and consensus, etc.

3.

Stages of team development: forming, storming, norming, and performing (further reading)

Tuckman's stages of group development

https://en.wikipedia.org/wiki/Tuckman%27s_stages_of_group_de velopment

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IV. Audit Program Management and Business Applications (30 Questions) A. Audit Program Management 1. Senior management support Identify and explain management‘s role in creating and supporting the audit function.

(Understand) 2. Staffing and resource management Develop staffing budgets that provide adequate time for auditors to plan, conduct, and respond to scheduled audits, including time and resources that internal auditees need to participate. Identify any special equipment resources needed and ensure their adequacy and availability. Consider the use of and requirements for special audits (outsourced or contracted audits, virtual or e-audits, shared audits, etc.) as driven by costs, geography, etc.

Evaluate results and adjust resources as needed on a regular basis. (Evaluate)

3. Auditor training and development Identify minimum audit knowledge and skill requirements for auditors.

Provide training on various aspects of the audit process such as relevant standards, regulatory influences, facilitation techniques, etc. Provide training on diversity and cultural influences (ethnicity, gender, age, organized labor, etc.) and how such factors can affect communications and other interactions among audit participants. (Create) 4. Audit program evaluation Select the correct metric to evaluate the audit program, including tracking its effect on the bottom line and the risk to the organization. (Evaluate)

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Special audits:  outsourced or contracted audits,  virtual or e-audits,  Shared audits, etc.

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Special audits:  outsourced or contracted audits,  virtual or e-audits,  Shared audits, etc.

virtual or e-audits Virtual Auditing With states facing more and more budget restrictions and travel being one area that is being cut from their budgets, state auditing departments need to come up with innovative constructive ways of continue to perform audits on Motor Fuel Accounts without the cost associated of traveling to the Taxpayers location. What are Virtual Audits? Virtual audits are paperless, electronic audits that are conducted without face to face interaction between government and industry. All data is exchanged in electronic formats such as MS Word, Excel, PDF files, text files and EDI files. https://old.taxadmin.org/fta/mf/unif_docs/ white/virtualaudits.pdf

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Special audits:  outsourced or contracted audits,  virtual or e-audits,  Shared audits, etc.

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IV. Audit Program Management and Business Applications (30 Questions) 5. Internal audit program management Develop procedures, policies, and schedules to support the organization‘s objectives. Review internal audit results to identify systemic trends. (Create) 6. External audit program management Develop procedures, policies, and schedules in support of the supplier management program, including: • supplier qualification surveys, • surveillance audits, • supplier improvement, etc.

7. Best practices Analyze audit results to: • Standardize best practices and • Lessons learned, across the organization. (Analyze) 8. Organizational risk management Analyze how the audit program affects an organization‘s risk level and how the risk level can influence the number and frequency of audits performed. (Analyze) [Note: Tools and techniques for managing risk are covered in BoK area V.H. (?) ]

(Create) There will be audit report to the Auditee and report to the management (as management review).

So there will be 2 minimum reports?

9. Management review input Examine and summarize audit program results, trends, and changes in risk to provide input to management reviews. (Evaluate) Charlie Chong/ Fion Zhang

9. Management review input Examine and summarize: ď Ž audit program results, ď Ž trends, and ď Ž changes in risk to provide input to management reviews. (Evaluate)

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9. Management review input Examine and summarize: ď Ž audit program results, ď Ž trends, and ď Ž changes in risk to provide input to management reviews. (Evaluate)

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9. Management review input Examine and summarize:  audit program results,  trends, and  changes in risk to provide input to management reviews. (Evaluate) KPI

KPI

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9. Management review input Examine and summarize:  audit program results,  trends, and  changes in risk to provide input to management reviews. (Evaluate)

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https://www.japantimes.co.jp/news/2016/05/10/business/five-million-new-takata-recalls-ordered-japan/#.W488FNwzaUk

9. Management review input Examine and summarize:  audit program results,  trends, and  changes in risk to provide input to management reviews. (Evaluate)

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https://www.theatlantic.com/photo/2011/07/the-history-of-the-space-shuttle/100097/

IV. Audit Program Management and Business Applications (30 Questions) B. Business and Financial Impact 1. Auditing as a management tool Use audit results to monitor: • continuous improvement, • Supplier management, • customer satisfaction, etc., and • to provide management with an independent view of the strategic plan‘s effectiveness and how well it is deployed.

3. Cost of quality (COQ) principles Identify, describe, and analyze the audit program‘s effect on the four COQ categories: • prevention, • Appraisal (assessment,评估-检验?), • internal failure, • External failure.

(Analyze)

(Analyze) 4. Emerging roles of the auditor 2. Interrelationships of business processes Recognize new roles and responsibilities for Identify how business units (receiving, product auditors, such as being process consultants and process design, production, engineering, and facilitators who can help resolve internal sales, marketing, field support, etc.) and multiple issues, improve processes, and add value to sites are interrelated, and recognize how their the organization. (Understand) unique metrics and goals can be in conflict with one another. (Understand)

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4. Emerging roles of the auditor Recognize new roles and responsibilities for auditors, such as being: • process consultants and • facilitators who can help resolve internal issues, improve processes, and add value to the organization.

(Understand) Charlie Chong/ Fion Zhang

4. Emerging roles of the auditor Recognize new roles and responsibilities for auditors, such as being: • process consultants and • facilitators who can help resolve internal issues, improve processes, and add value to the organization.

(Understand) Auditor as well as SME

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V. Quality Tools and Techniques (26 Questions) A. Basic Quality and Problem-solving Tools Identify, interpret, and analyze: 1) Pareto charts, 2) cause and effect diagrams, 3) flowcharts, 4) statistical process control (SPC) charts, 5) check sheets, 6) scatter diagrams, 7) histograms, 8) root cause analysis, 9) plan-do-check-act (PDCA). (Analyze) B. Process Improvement Techniques 1. Six Sigma Identify, interpret, and apply the Six Sigma DMAIC phases: define, measure, analyze, improve, control. (Apply)

C. Basic Statistics 1. Measures of central tendency Identify, interpret, and use mean, median, and mode. (Apply) 2. Measures of dispersion Identify, interpret, and use standard deviation and frequency distribution. (Apply) 3. Qualitative and quantitative analysis Describe qualitative data in terms of the nature, type, or attribute of an observation or condition.

Describe how quantitative data is used to detect patterns or trends and how such analysis can indicate whether a problem is systemic or isolated. (Understand)

2. Lean Identify, interpret, and apply lean Tools (?) : 5S, standard operations, kanban (pull), error-proofing, value stream mapping, etc. (Apply)

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V. Quality Tools and Techniques (26 Questions) D. Process Variation 1. Common and special cause Identify and distinguish between common and special cause variation. (Apply) 2. Process performance metrics Describe elements of Cp and Cpk process capability studies (process centering and stability, specification limits, underlying distribution, etc.), and how these studies and other performance metrics are used in relation to established goals. (Understand)

E. Sampling Methods 1. Acceptance sampling plans Identify and interpret these plans for attributes and variables data.

(Understand) 2. Types of sampling Describe and distinguish between: • random, • stratified, and • cluster sampling, and identify the uses and potential problems of non-statistical sampling. (Understand)

3. Outliers Describe their significance and impact.

(Understand)

3. Sampling terms Define related terms including consumer and producer risk, confidence level, etc. (Understand)

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V. Quality Tools and Techniques (26 Questions) F. Change Control and Configuration Management Identify the principles of change control and configuration management systems as used in various applications: hardware, software (including security considerations), product, process, and service. (Understand) G. Verification and Validation Define, distinguish between, and use various methods of verifying and validating processes. (Analyze)

H. Risk Management Tools Identify methods for managing risk, including: • risk avoidance, • mitigation, • tradeoffs, etc., and describe tools and methods for estimating and controlling risk: • failure mode and effects analysis (FMEA), • hazard analysis and critical control points (HACCP), • critical to quality (CTQ) analysis, • health hazard analysis (HHA), etc.

(Understand) [Note: Organizational risk management is covered in BoK area IV.A.8.]

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LEVELS OF COGNITION (awareness) Based on Bloom‘s Taxonomy—Revised (2001)

In addition to content specifics, the subtext for each topic in this BoK also indicates the intended complexity level of the test questions for that topic. These levels are based on ―Levels of Cognition‖ (from Bloom‘s Taxonomy- Revised, 2001) and are presented below 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 (conspicuous/prominent) 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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CQA- Open Book Exam!

FREQUENTLY ASKED QUESTIONS Is the exam open-book?

With the exception of the constructed-response portion of the Manager of Quality/Organizational Excellence exam, exams are open-book.

All reference materials (i.e. including all forms of notes) must be bound and remain bound during the exam. Bound refers to material permanently bound by stitching or glue and materials fastened securely in its cover by fasteners, which penetrate all papers (i.e. ring binders, spiral binders, plastic snap binders, brads, or screw posts). Manually or hand stapled documents that are not securely fastened in their covers are not allowed. The size of workspace area at Prometric test centers is limited. The approximate desk dimensions are 48" in length and 24" in width.

Before you enter the exam room, the Test Center Administrator (TCA) will inspect all references.

"Post-Its" will be permitted as book tabs only (must be attached prior to entering the test center).

Items strictly prohibited in the exam area: hand stapled or paper-clipped materials, blank writing tablets or tablets containing blank pages, unbound tablets, unbound notes, slide charts and/or wheel charts (hand-held cardboard or plastic calculating devices with rotating or sliding pieces).

Absolutely no collections of questions and answers or weekly refresher-course quizzes are permitted. Reference sources that contain such copy are not allowed unless the questions are removed.

Examinees are responsible for abiding by applicable copyright laws. https://asq.org/cert/faq/open-book-exam

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CQA More to read • • • • • • • • •

Six Sigma DMAIC phases: define, measure, analyze, improve, control.

Process capability Cp and Cpk Lean Tools (?) : 5S, standard operations, kanban (pull), error-proofing, value stream mapping, etc.

Risk Management Tools failure mode and effects analysis (FMEA), hazard analysis and critical control points (HACCP), critical to quality (CTQ) analysis, health hazard analysis (HHA), etc.

Sampling methods

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CQA Star War Dead Star

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CQA- Reading II Pre-Handbook Reading, the WIKI ways.

Six Sigma DMAIC phases: define, measure, analyze, improve, control.

https://en.wikipedia.org/wiki/Six_Sigma

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https://en.wikipedia.org/wiki/Six_Sigma

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Six Sigma (6Ďƒ) is a set of techniques and tools for process improvement. It was introduced by engineer Bill Smith while working at Motorola in 1986. Jack Welch made it central to his business strategy at General Electric in 1995.

Six Sigma strategies seek to improve the quality of the output of a process by identifying and removing the causes of defects and minimizing variability in manufacturing and business processes. It uses a set of quality management methods, mainly empirical, statistical methods, and creates a special infrastructure of people within the organization who are experts in these methods. Each Six Sigma project carried out within an organization follows a defined sequence of steps and has specific value targets, for example: reduce process cycle time, reduce pollution, reduce costs, increase customer satisfaction, and increase profits.

The term Six Sigma (capitalized because it was written that way when registered as a Motorola trademark on December 28, 1993) originated from terminology associated with statistical modeling of manufacturing processes. The maturity of a manufacturing process can be described by a sigma rating indicating its yield or the percentage of defect-free products it creates. A six sigma process is one in which 99.99966% (?) of all opportunities to produce some feature of a part are statistically expected to be free of defects (3.4 defective features per million opportunities). Motorola set a goal of "six sigma" for all of its manufacturing. https://en.wikipedia.org/wiki/Six_Sigma

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Six Sigma doctrine asserts: Continuous efforts to achieve stable and predictable process results (e.g. by reducing process variation) are of vital importance to business success.

Manufacturing and business processes have characteristics that can be DMAIC ―defined, measured, analyzed, improved, and controlled.‖ Achieving sustained quality improvement requires commitment from the entire organization, particularly from top-level management.

Features that set Six Sigma apart from previous quality-improvement initiatives include:  A clear focus on achieving measurable and quantifiable financial returns from any Six Sigma project.  An increased emphasis on strong and passionate (enthusiastic) management leadership and support.  A clear commitment to making decisions on the basis of verifiable data and statistical methods, rather than assumptions and guesswork.

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The term ―six sigma‖ comes from statistics and is used in statistical quality control, which evaluates process capability. Originally, it referred to the ability of manufacturing processes to produce a very high proportion of output within specification. Processes that operate with ―six sigma quality‖ over the short term are assumed to produce longterm defect levels below 3.4 defects per million opportunities (DPMO). The 3.4 dpmo is based on a ―shift‖ of +/- 1.5 sigma created by the psychologist Dr Mikel Harry. He created this figure based on the tolerance in the height of a stack of discs. Six Sigma‗s implicit goal is to improve all processes, but not to the 3.4 DPMO level necessarily.

Organizations need to determine an appropriate sigma level for each of their most important processes and strive to achieve these. As a result of this goal, it is incumbent (有义务的) on management of the organization to prioritize areas of improvement.

"Six Sigma" was registered June 11, 1991 as U.S. Service Mark 1,647,704. In 2005 Motorola attributed over US$17 billion in savings to Six Sigma.[5] Other early adopters of Six Sigma include Honeywell and General Electric, where Jack Welch introduced the method. By the late 1990s, about two-thirds of the Fortune 500 organizations had begun Six Sigma initiatives with the aim of reducing costs and improving quality.

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In recent years, some practitioners have combined Six Sigma ideas with lean manufacturing to create a methodology named Lean Six Sigma. The Lean Six Sigma methodology views lean manufacturing, which addresses process flow and waste issues, and Six Sigma, with its focus on variation and design, as complementary disciplines aimed at promoting "business and operational excellence". Companies such as GE, Accenture, Verizon, GENPACT, and IBM use Lean Six Sigma to focus transformation efforts not just on efficiency but also on growth. It serves as a foundation for innovation throughout the organization, from manufacturing and software development to sales and service delivery functions.

The International Organization for Standardization (ISO) has published in 2011 the first standard "ISO 13053:2011" defining a Six Sigma process. Other "standards" are created mostly by universities or companies that have so-called first-party certification programs for Six Sigma.

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is a set of techniques and tools for process improvement. It was introduced by engineer

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Six Sigma Difference from lean management Lean management and Six Sigma are two concepts which share similar methodologies and tools. Both programs are Japanese-influenced, but they are two different programs: ď Ž Lean management is focused on eliminating waste and ensuring efficiency while ď Ž Six Sigma's focus is on eliminating defects and reducing variability.

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Methodologies Six Sigma projects follow two project methodologies inspired by Deming's Plan-DoStudy-Act Cycle. These methodologies, composed of five phases each, bear the acronyms DMAIC and DMADV. ď Ž DMAIC is used for projects aimed at improving an existing business process. ď Ž DMADV is used for projects aimed at creating new product or process designs.

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DMAIC The DMAIC project methodology has five phases: 1. Define the system, the voice of the customer and their requirements, and the project goals, specifically.

2. Measure key aspects of the current process and collect relevant data; calculate the 'as-is' Process Capability.

3. Analyze the data to investigate and verify cause-and-effect relationships.

Determine what the relationships are, and attempt to ensure that all factors have been considered. Seek out root cause of the defect under investigation.

4. Improve or optimize the current process based upon data analysis using techniques such as design of experiments, poka yoke or mistake proofing, and standard work to create a new, future state process. Set up pilot runs to establish process capability.

5. Control the future state process to ensure that any deviations from the target are corrected before they result in defects. Implement control systems such as statistical process control, production boards, visual workplaces, and continuously monitor the process. This process is repeated until the desired quality level is obtained.

Some organizations add a Recognize step at the beginning, which is to recognize the right problem to work on, thus yielding an RDMAIC methodology.

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Poka-yoke or Mistake Proofing

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DMADV or DFSS The five steps of DMADV The DMADV project methodology, known as DFSS ("Design For Six Sigma"), features five phases: 1. Define design goals that are consistent with customer demands and the enterprise strategy.

2. Measure and identify CTQs (characteristics that are Critical To Quality), measure product capabilities, production process capability, and measure risks.

3. Analyze to develop and design alternatives 4. Design an improved alternative, best suited per analysis in the previous step 5. Verify the design, set up pilot runs, implement the production process and hand it over to the process owner(s).

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DMAIC- Define, Measure, Analuze, Improve, Control

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DMADV (DFSS)- Define, Measure, Analyze, Design, Verify

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Quality management tools and methods Within the individual phases of a DMAIC or DMADV project, Six Sigma utilizes many established quality-management tools that are also used outside Six Sigma. The following table shows an overview of the main methods used.

• • • • • • • • • • •

5 Whys Statistical and fitting tools Analysis of variance General linear model ANOVA Gauge R&R Regression analysis Correlation Scatter diagram Chi-squared test Axiomatic design Business Process Mapping/Check sheet

• • • • • • •

Cause & effects diagram (also known as fishbone or Ishikawa diagram) Control chart/Control plan (also known as a swimlane map)/Run charts Cost-benefit analysis CTQ tree Design of experiments/Stratification Histograms/Pareto analysis/Pareto chart Pick chart/Process capability/Rolled throughput yield

• •

• • • • •

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Quality Function Deployment (QFD) Quantitative marketing research through use of Enterprise Feedback Management (EFM) systems Root cause analysis SIPOC analysis (Suppliers, Inputs, Process, Outputs, Customers) COPIS analysis (Customer centric version/perspective of SIPOC) Taguchi methods/Taguchi Loss Function Value stream mapping

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Implementation roles One key innovation of Six Sigma involves the absolute "professionalizing" of quality management functions. Prior to Six Sigma, quality management in practice was largely relegated to the production floor and to statisticians in a separate quality department. Formal Six Sigma programs adopt a kind of elite ranking terminology (similar to some martial arts systems, like judo) to define a hierarchy (and special career path) that includes all business functions and levels. Six Sigma identifies several key roles for its successful implementation.

1.

2.

3.

4.

5.

Executive Leadership includes the CEO and other members of top management. They are responsible for setting up a vision for Six Sigma implementation. They also empower the other role holders with the freedom and resources to explore new ideas for breakthrough improvements by transcending departmental barriers and overcoming inherent resistance to change.

Champions take responsibility for Six Sigma implementation across the organization in an integrated manner. The Executive Leadership draws them from upper management. Champions also act as mentors to Black Belts.

Master Black Belts, identified by Champions, act as in-house coaches on Six Sigma. They devote 100% of their time to Six Sigma. They assist Champions and guide Black Belts and Green Belts. Apart from statistical tasks, they spend their time on ensuring consistent application of Six Sigma across various functions and departments.

Black Belts operate under Master Black Belts to apply Six Sigma methodology to specific projects. They devote 100% of their valued time to Six Sigma. They primarily focus on Six Sigma project execution and special leadership with special tasks, whereas Champions and Master Black Belts focus on identifying projects/functions for Six Sigma.

Green Belts are the employees who take up Six Sigma implementation along with their other job responsibilities, operating under the guidance of Black Belts.

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According to proponents (坺莎者) of the system, special training is needed for all of these practitioners to ensure that they follow the methodology and use the data-driven approach correctly. Some organizations use additional belt colours, such as Yellow Belts, for employees that have basic training in Six Sigma tools and generally participate in projects and "White belts" for those locally trained in the concepts but do not participate in the project team. "Orange belts" are also mentioned to be used for special cases.

Defining roles and responsibilities for: Top management, Champion, Master Black Belt, Black Belt and Green Belt.

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Formal Six Sigma programs adopt a kind of elite ranking terminology (Key to define each roles and responsibilities)

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Certification General Electric and Motorola developed certification programs as part of their Six Sigma implementation, verifying individuals' command of the Six Sigma methods at the relevant skill level (Green Belt, Black Belt etc.). Following this approach, many organizations in the 1990s started offering Six Sigma certifications to their employees.

Criteria for Green Belt and Black Belt certification vary; some companies simply require participation in a course and a Six Sigma project. There is no standard certification body, and different certification services are offered by various quality associations and other providers against a fee. The American Society for Quality for example requires Black Belt applicants to pass a written exam and to provide a signed affidavit stating that they have completed two projects or one project combined with three years' practical experience in the body of knowledge https://en.wikipedia.org/wiki/Six_Sigma

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Etymology*of "six sigma process" The term "six sigma process" comes from the notion that if one has six standard deviations between the process mean and the nearest specification limit, as shown in the graph, practically items will fail to meet specifications. This is based on the calculation method employed in process capability studies. * Etymology- a study of origin of a word

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Graph of the normal distribution, which underlies the statistical assumptions of the Six Sigma model. In the centre at 0, the Greek letter µ (mu) marks the mean, with the horizontal axis showing distance from the mean, marked in standard deviations and given the letter σ (sigma).

The greater the standard deviation, the greater is the spread of values encountered. For the green curve shown above, µ = 0 and σ = 1. The upper and lower specification limits (marked USL and LSL) are at a distance of 6σ from the mean. Because of the properties of the normal distribution, values lying that far away from the mean are extremely unlikely: approximately 1 in a billion too low, and the same too high. Even if the mean were to move right or left by 1.5σ at some point in the future (1.5 sigma shift, coloured red and blue), there is still a good safety cushion. This is why Six Sigma aims to have processes where the mean is at least 6σ away from the nearest specification limit. https://en.wikipedia.org/wiki/Six_Sigma

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Graph of the normal distribution, which underlies the statistical assumptions of the Six Sigma model. In the centre at 0, the Greek letter µ (mu) marks the mean, with the horizontal axis showing distance from the mean, marked in standard deviations and given the letter σ (sigma).

The greater the standard deviation, the greater is the spread of values encountered. For the green curve shown above, µ = 0 and σ = 1. The upper and lower specification limits (marked USL and LSL) are at a distance of 6σ from the mean. Because of the properties of the normal distribution, values lying that far away from the mean are extremely unlikely: approximately 1 in a billion too low, and the same too high.

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Even if the mean were to move right or left by 1.5Ďƒ at some point in the future (1.5 sigma shift, coloured red and blue), there is still a good safety cushion. This is why Six Sigma aims to have processes where the mean is at least 6Ďƒ away from the nearest specification limit.

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Even if the mean were to move right or left by 1.5Ďƒ at some point in the future (1.5 sigma shift, coloured red and blue), there is still a good safety cushion. This is why Six Sigma aims to have processes where the mean is at least 6Ďƒ away from the nearest specification limit.

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Exercise: Calculate area under the curves: 2σ ±2σ 3σ ±3σ

= 0.0.4772 = 0.9545 = 0.4987 = 0.9973 http://onlinestatbook.com/2/calculators/normal_dist.html

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Exercise: Calculate area under the normal curves between LSL/USL at ±3σ, for, USL-ũ= 1.5σ Areas under the curve = 0.933 http://onlinestatbook.com/2/calculators/normal_dist.html

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Exercise: Calculate area under the normal curves between LSL/USL at ±3σ, for, USL-ũ= 1.5σ Areas under the curve = 0.933

http://onlinestatbook.com/2/calculators/normal_dist.html 3 sigma process: Note due to the limitation of online statistical calculator 3σ process was used to illustrate the scenario

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Knowing: Process capability index Definitions ď Ž Cp= Process Capability. A simple and straightforward indicator of process capability.

Cp= USL−LSL 6Ďƒ

(Estimates what the process is capable of producing if the process mean were to be centered between the specification limits. Assumes process output is approximately normally distributed.)

ď Ž Cp, lower= ĹŠâˆ’LSL 3Ďƒ

(Estimates process capability for specifications that consist of a lower limit only (for example, concentration). Assumes process output is approximately normally distributed.)

ď Ž Cp, upper= USLâˆ’ĹŠ 3Ďƒ

(Estimates process capability for specifications that consist of a upper limit only (for example, strength). Assumes process output is approximately normally distributed.)

ď Ž Cpk= Process Capability Index. Adjustment of Cp for the effect of non-centered distribution. ĹŠâˆ’LSL Cpk= min[ USLâˆ’ĹŠ , ] 3Ďƒ 3Ďƒ

(Estimates what the process is capable of producing, considering that the process mean may not be centered between the specification limits. (If the process mean is not centered, Cp overestimates process capability.) Cpk<0, if the process mean falls outside of the specification limits. Assumes process output is approximately normally distributed.)

ď Ž Cpm = Taguchi Capability Index Cpm= â&#x2C6;&#x161;[1+(đ??śĹŠâ&#x2C6;&#x2019;T)2] đ?&#x2018;?

Ď&#x192;

(The process capability indices Cp and Cpk are widely used to provide unitless measures of process potential and performance. These indices do no adequately address the issue of process centering. An alternative definition of Cp advocated by Taguchi addresses this issue directly. Later authors introduced the name C pm for the Taguchi index and examined statistical properties of an inefficient estimator under the assumption that the process mean coincides with the target value. http://asq.org/qic/display-item/?item=11328 )

ď Ž Cpkm = Taguchi Capability Index Cpkm= â&#x2C6;&#x161;[1+(đ??ś ĹŠâ&#x2C6;&#x2019;T)2] đ?&#x2018;?đ?&#x2018;&#x2DC;

Ď&#x192;

(Estimates process capability around a target, T, and accounts for an off-center process mean. Assumes process output is approximately normally distributed.. http://asq.org/qic/displayitem/?item=11328 )

ď Ž Pp= Process Performance. A simple and straightforward indicator of process performance. ď Ž Ppk= Process Performance Index. Adjustment of Pp for the effect of non-centered distribution.

The target process mean is T, the estimated mean of the process is ĹŠ and the estimated variability of the process (expressed as a standard deviation) Ď&#x192;.

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Interpreting Cp, Cpk USL−ũ ũ−LSL

―Cpk , Cpk= min[ , ] is an index (a simple number) which measures how close a process 3σ 3σ is running to its specification limits, relative to the natural variability of the process. The larger the index, the less likely it is that any item will be outside the specs.‖

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Role of the 1.5 sigma shift Experience has shown that processes usually do not perform as well in the long term as they do in the short term. As a result, the number of sigmas that will fit between the process mean and the nearest specification limit may well drop over time, compared to an initial short-term study. To account for this real-life increase in process variation over time, an empirically based 1.5 sigma shift is introduced into the calculation. According to this idea, a process that fits 6 sigma between the process mean and the nearest specification limit in a short-term study will in the long term fit only 4.5 sigma – either because:   

the process mean will move over time, or because the long-term standard deviation of the process will be greater than that observed in the short term, or both.

Hence the widely accepted definition of a six sigma process is a process that produces 3.4 defective parts per million opportunities (DPMO). This is based on the fact that a process that is normally distributed will have 3.4 parts per million outside the limits, when the limits are six sigma from the "original" mean of zero and the process mean is then shifted by 1.5 sigma (and therefore, the six sigma limits are no longer symmetrical about the mean).

The former six sigma distribution, when under the effect of the 1.5 sigma shift, is commonly referred to as a 4.5 sigma process. The failure rate of a six sigma distribution with the mean shifted 1.5 sigma is not equivalent to the failure rate of a 4.5 sigma process with the mean centered on zero. This allows for the fact that special causes may result in a deterioration in process performance over time and is designed to prevent underestimation of the defect levels likely to be encountered in real-life operation.

3 sigma process

0

The role of the sigma shift is mainly academic. The purpose of six sigma is to generate organizational performance improvement. It is up to the organization to determine, based on customer expectations, what the appropriate sigma level of a process is. The purpose of the sigma value is as a comparative figure to determine whether a process is improving, deteriorating, stagnant or non-competitive with others in the same business. Six sigma (3.4 DPMO) is not the goal of all processes. http://onlinestatbook.com/2/calculators/normal_dist.html

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The failure rate of a six sigma distribution with the mean shifted 1.5 sigma is not equivalent to the failure rate of a 4.5 sigma process with the mean centered on zero. This allows for the fact that special causes may result in a deterioration in process performance over time and is designed to prevent underestimation of the defect levels likely to be encountered in real-life operation.

3 sigma process

3 sigma process mean shifted 1.5 sigma

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A control chart depicting a process that experienced a 1.5 sigma drift in the process mean toward the upper specification limit starting at midnight. Control charts are used to maintain 6 sigma quality by signaling when quality professionals should investigate a process to find and eliminate special-cause variation.

A control chart depicting a process that experienced a 1.5 sigma drift in the process mean toward the upper specification limit starting at midnight. Control charts are used to maintain 6 sigma quality by signaling when quality professionals should investigate a process to find and eliminate special-cause variation.

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Sigma levels The table below gives long-term DPMO values corresponding to various short-term sigma levels.

These figures assume that the process mean will shift by 1.5 sigma toward the side with the critical specification limit. In other words, they assume that after the initial USL−ũ ũ−LSL study determining the short-term sigma level, the long-term Cpk, Cpk= min[ , ] 3σ 3σ USL−ũ ũ−LSL or Cpk= min[ , ] ? value will turn out to be 0.5 less than the short-term Cpk 6σ 6σ value.

So, now for example, the DPMO figure given for 1 sigma assumes that the long-term process mean will be 0.5 sigma beyond the specification limit σ  (Cpk = –0.17) [Cpk= -0.5], rather than 1 sigma within it, 3σ σ  (Cpk = 0.33) [Cpk= ] as it was in the short-term study.

3σ Sigma levels The table below gives long-term DPMO values corresponding to various short-term sigma levels.

These figures assume that the process mean will shift by 1.5 sigma toward the side with the critical specification limit. In other words, they assume that after the initial study determining the short-term sigma USL−ũ ũ−LSL USL−ũ ũ−LSL level, the long-term Cpk, Cpk= min[ , ] or Cpk= min[ , ] ? value will turn out to be 0.5 less 3σ 3σ 6σ 6σ than the short-term Cpk value.

So, now for example, the DPMO figure given for 1 sigma assumes that the long-term process mean will be 0.5 sigma beyond the specification limit σ  (Cpk = –0.17) [Cpk= -0.5], rather than 1 sigma within it, 3σ σ  (Cpk = 0.33) [Cpk= ] as it was in the short-term study.

3σ Note that the defect percentages indicate only defects exceeding the specification limit to which the process mean is nearest. Defects beyond the far specification limit are not included in the percentages. The formula used here to calculate the DPMO is thus: DPMO = 1000000 x (1-Φ(level-1.5))

Note that the defect percentages indicate only defects exceeding the specification limit to which the process mean is nearest. Defects beyond the far specification limit are not included in the percentages. The formula used here to calculate the DPMO is thus: DPMO = 1000000 x (1-Φ(level-1.5))

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Six Sigma (6σ) is a set of techniques and tools for process improvement. It was introduced by engineer

Sigma level

Sigma (with 1.5σ shift)

Short-term Cpk

Long-term Cpk

1

−0.5

691,462

69%

31%

0.33

−0.17

2

0.5

308,538

31%

69%

0.67

0.17

3

1.5

66,807

6.7%

93.3%

1.00

0.5

4

2.5

6,210

0.62%

99.38%

1.33

0.83

5

3.5

233

0.023%

99.977%

1.67

1.17

6

4.5

3.4

0.00034%

99.99966%

2.00

1.5

7

5.5

0.019

0.0000019%

99.9999981%

2.33

1.83

DPMO

https://en.wikipedia.org/wiki/Six_Sigma

Percent defective

Percentage yield

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Application Six Sigma mostly finds application in large organizations. An important factor in the spread of Six Sigma was GE's 1998 announcement of $350 million in savings thanks to Six Sigma, a figure that later grew to more than $1 billion. According to industry consultants like Thomas Pyzdek and John Kullmann, companies with fewer than 500 employees are less suited to Six Sigma implementation or need to adapt the standard approach to make it work for them. Six Sigma however contains a large number of tools and techniques that work well in small to mid-size organizations. The fact that an organization is not big enough to be able to afford Black Belts does not diminish its abilities to make improvements using this set of tools and techniques. The infrastructure described as necessary to support Six Sigma is a result of the size of the organization rather than a requirement of Six Sigma itself.

Although the scope of Six Sigma differs depending on where it is implemented, it can successfully deliver its benefits to different applications.

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Recommended values Process capability indices are constructed to express more desirable capability with increasingly higher values.

Values near or below zero indicate processes operating off target (ũ far from T) or with high variation.

(The target process mean is T, the estimated mean of the process is ũ and the estimated variability of the process (expressed as a standard deviation) σ. )

Fixing values for minimum "acceptable" process capability targets is a matter of personal opinion, and what consensus exists varies by industry, facility, and the process under consideration. For example, in the automotive industry, the Automotive Industry Action Group sets forth guidelines in the Production Part Approval USL−ũ ũ−LSL Process, 4th edition for recommended Cpk minimum values Cpk= min[ 3σ , 3σ ] for critical-to-quality CTQ process characteristics. However, these criteria are debatable and several processes may not be evaluated for capability just because they have not properly been assessed.

Since the process capability is a function of the specification, the Process Capability Index is only as good as the specification. For instance, if the specification came from an engineering guideline without considering the function and criticality of the part, a discussion around process capability is useless, and would have more benefits if focused on what are the real risks of having a part borderline out of specification. The loss function of Taguchi better illustrates this concept.

At least one academic expert recommends the following: (cont. ………)

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At least one academic expert recommends the following: ũ−LSL Cpk= min[ USL−ũ , ] 3σ 3σ

Situation

Recommended minimum process capability for twosided specifications

Recommended minimum process capability for onesided specification

Existing process

1.33

1.25

New process

1.50

1.45

Safety or critical parameter for existing process

1.50

1.45

Safety or critical parameter for new process

1.67

1.60

Six Sigma quality process

2.00

2.00

However where a process produces a characteristic with a capability index greater than 2.5, the unnecessary precision may be expensive.

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Relationship to measures of process fallout The mapping from process capability indices, such as Cpk, to measures of process fallout is straightforward.

Process fallout quantifies how many defects a process produces and is measured by DPMO or PPM. Process yield is the complement of process fallout and is approximately equal to the area under the probability density function, if the process output is approximately normally distributed. ÎŚ(Ď&#x192;) =

1 2Ď&#x20AC;

Ď&#x192; â&#x2C6;&#x2019;đ?&#x2018;Ą2/2 đ?&#x2018;&#x2019; â&#x2C6;&#x2019;Ď&#x192;

dt

In the short term ("short sigma"), the relationships are:

Cpk

Sigma level (Ď&#x192;)

Area under the probability density curve ÎŚ(Ď&#x192;)

Process yield

Process fallout(in terms of DPMO/PPM)

0.33

1

0.6826894921

68.27%

317311

0.67

2

0.9544997361

95.45%

45500

1.00

3

0.9973002039

99.73%

2700

1.33

4

0.9999366575

99.99%

63

1.67

5

0.9999994267

99.9999%

1

2.00

6

0.9999999980

99.9999998%

0.002

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Cpk

Sigma level (σ)

Area under the probability density curve Φ(σ)

Process yield

Process fallout(in terms of DPMO/PPM)

0.33

1

0.6826894921

68.27%

317311

0.67

2

0.9544997361

95.45%

45500

1.00

3

0.9973002039

99.73%

2700

1.33

4

0.9999366575

99.99%

63

1.67

5

0.9999994267

99.9999%

1

2.00

6

0.9999999980

99.9999998%

0.002

4 sigma σ level

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Cpk

Adjusted Sigma level (σ)

Area under the probability density curve Φ(σ)

Process yield

Process fallout(in terms of DPMO/PPM)

0.33

1

0.3085375387

30.85%

691462

0.67

2

0.6914624613

69.15%

308538

1.00

3

0.9331927987

93.32%

66807

1.33

4

0.9937903347

99.38%

6209

1.67

5

0.9997673709

99.9767%

232.6

2.00

6

0.9999966023

4 sigma σ level,3.40 99.99966% with 1.5σ shift

In the long term, processes can shift or drift significantly (most control charts are only sensitive to changes of 1.5σ or greater in process output). If there was a 1.5 sigma shift 1.5σ off of target in the processes (see Six Sigma), it would then produce the above relationships.

Because processes can shift or drift significantly long term, each process would have a unique sigma shift value, thus process capability indices are less applicable as they require statistical control.

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Example Consider a quality characteristic with target of 100.00 μm and upper and lower specification limits of (±4μm) 106.00μm and 94.00μm respectively. If, after carefully monitoring the process for a while, it appears that the process is in control and producing output predictably (as depicted in the run chart below), we can meaningfully estimate its mean and standard deviation.

If ũ and σ are estimated to be 98.94 μm and 1.03 μm, respectively, then

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If ĹŠ and Ď&#x192; are estimated to be 98.94 Îźm and 1.03 Îźm, respectively, then Index Cp=

USLâ&#x2C6;&#x2019;LSL

6Ď&#x192;

=

106.00â&#x2C6;&#x2019;94.00 = 6 đ?&#x2018;Ľ 1.03

Cpk= min[

USLâ&#x2C6;&#x2019;ĹŠ ĹŠâ&#x2C6;&#x2019;LSL

Cpm=

đ??śđ?&#x2018;?

3Ď&#x192;

â&#x2C6;&#x161;[1+(

Cpkm=

,

3Ď&#x192; =

ĹŠâ&#x2C6;&#x2019;T 2

Ď&#x192;)]

đ??śđ?&#x2018;?đ?&#x2018;&#x2DC;

ĹŠâ&#x2C6;&#x2019;T 2

â&#x2C6;&#x161;[1+(

Ď&#x192;)]

106.00â&#x2C6;&#x2019;98.94 98.94â&#x2C6;&#x2019;94.00 , ] 3 đ?&#x2018;Ľ 1.03 3 đ?&#x2018;Ľ 1.03 1.94

] = min[

â&#x2C6;&#x161;[1+(

=

1.94

= 1.35

98.94â&#x2C6;&#x2019;100.00 2

1.03

)]

1.6 98.94â&#x2C6;&#x2019;100.00 2

â&#x2C6;&#x161;[1+(

)]

1.03

= 1.6

= 1.11

The fact that the process is running off-center (about 1Ď&#x192; below its target) is reflected in the markedly different values for Cp, Cpk, Cpm, and Cpkm.

Cpk= min[ Cpkm=

USLâ&#x2C6;&#x2019;ĹŠ ĹŠâ&#x2C6;&#x2019;LSL

3Ď&#x192; đ??śđ?&#x2018;?đ?&#x2018;&#x2DC;

â&#x2C6;&#x161;[1+(

,

ĹŠâ&#x2C6;&#x2019;T 2

Ď&#x192;) ]

3Ď&#x192; =

] = min[

106.00â&#x2C6;&#x2019;98.94 98.94â&#x2C6;&#x2019;94.00 , 3 đ?&#x2018;Ľ 1.03 3 đ?&#x2018;Ľ 1.03

1.6 â&#x2C6;&#x161;[1+(

98.94â&#x2C6;&#x2019;100.00 2

1.03

)]

] = 1.6

= 1.11

Charlie Chong/ Fion Zhang

Charlie Chong/ Fion Zhang Charlie Chong/ Fion Zhang

Good Luck!

Charlie Chong/ Fion Zhang

Good Luck!

Charlie Chong/ Fion Zhang