Six Sigma: DMAIC and Statistics

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The DMAIC roadmap phase by phase with the statistics behind it: measurement systems, capability indices, control charts, hypothesis tests, and the lean tools a Green Belt is expected to apply.

What does the term Six Sigma mean as a performance level?
A process whose specification limits sit six standard deviations from the mean, which with the conventional 1.5 sigma long-term shift corresponds to 3.4 defects per million opportunities (DPMO).
Where and when did Six Sigma originate, and who popularised it?
Motorola developed it in 1986 (engineer Bill Smith is credited with the concept, Mikel Harry with the deployment model), and General Electric under Jack Welch made it famous from 1995 onward.
What are the five phases of DMAIC?
Define, Measure, Analyze, Improve, Control. It is the roadmap for improving an existing process.
DMAIC vs DMADV: when is each used?
DMAIC improves an existing process. DMADV (Define, Measure, Analyze, Design, Verify), a Design for Six Sigma approach, creates a new process or product, or redesigns one that cannot meet requirements by incremental improvement.
What are the Six Sigma belt levels and what does each do?
White and Yellow Belts have awareness-level training and support projects; Green Belts lead smaller projects part time; Black Belts lead complex projects full time and coach Green Belts; Master Black Belts train and mentor Black Belts and steer the program.
What does a Six Sigma Champion do?
A senior manager who selects and sponsors projects, removes organisational barriers, allocates resources and holds tollgate reviews. The Champion owns the business result, not the analysis.
What is a process owner in a Six Sigma project?
The manager responsible for the process being improved, who supplies knowledge during the project and takes over the control plan and sustained results at closure.
What is the equation Y = f(x) in Six Sigma thinking?
The output Y is a function of the process inputs (the Xs). Six Sigma finds the vital few Xs that drive Y and controls them, rather than inspecting Y after the fact.
What is a tollgate review?
A checkpoint at the end of each DMAIC phase where the Champion and stakeholders review deliverables and decide whether the project proceeds, reworks the phase, or stops.
What is the cost of poor quality (COPQ)?
The total cost of failing to meet requirements: scrap, rework, warranty, returns, lost customers and the hidden factory of inspection and expediting. Six Sigma projects are justified largely by COPQ reduction.
What is the hidden factory?
The unmeasured rework, re-inspection and workarounds that make a process appear to have a good final yield while consuming capacity and cost.
What belongs in a Six Sigma project charter?
Problem statement, goal statement, business case, scope (in and out), team and roles, milestones for each phase, and the primary metric (with a baseline and target).
How should a problem statement be written?
As a factual description of the gap: what is wrong, where, when, how big it is and what it costs, with no cause and no solution.
What is SIPOC?
A high-level process map listing Suppliers, Inputs, Process (in five to seven steps), Outputs and Customers, used in Define to agree the scope and boundaries.
What is voice of the customer (VOC), and how is it turned into a CTQ?
VOC is what customers say they need, gathered by interviews, surveys, complaints and observation. A critical-to-quality (CTQ) characteristic is that need translated into a measurable requirement with a target and limits.
What is a CTQ tree?
A diagram that breaks a broad customer need into drivers and then into specific, measurable requirements, ensuring every CTQ traces back to a need.
What are the categories of the Kano model?
Must-be (basic, expected; absence causes dissatisfaction), one-dimensional (performance; more is better), attractive (delighters; unexpected, create satisfaction), plus indifferent and reverse attributes. Proposed by Noriaki Kano in 1984.
What is an affinity diagram?
A tool that groups many brainstormed ideas or VOC statements into natural themes by sorting them silently, then labelling each cluster.
What are the elements of a stakeholder analysis in a Six Sigma project?
A list of stakeholders with their level of influence, their current and required support, their concerns and an action plan to move them, often shown as a grid of influence against support.
What is an operational definition?
A precise, agreed description of what is being measured, how it is measured, and what counts as a defect, so that two people measuring the same thing get the same result.
Attribute data vs variable data.
Attribute (discrete) data counts or classifies: pass or fail, number of defects. Variable (continuous) data measures on a scale: length, time, weight. Variable data carries more information per observation and needs smaller samples.
What is a data collection plan?
A plan stating what will be measured, the operational definition, the data type, the sampling method and size, who collects it, when, how it is recorded and how the measurement system is validated.
What does measurement system analysis (MSA) evaluate?
Whether the measurement system is good enough to see the process variation: accuracy (bias), linearity, stability, and precision, which is split into repeatability and reproducibility.
Repeatability vs reproducibility in a Gage R&R study.
Repeatability is variation when one operator measures the same part repeatedly with the same gauge (equipment variation). Reproducibility is variation between different operators measuring the same parts (appraiser variation).
What are the acceptance guidelines for a Gage R&R study?
Gauge R&R under 10 percent of the tolerance or total variation is acceptable, 10 to 30 percent may be acceptable depending on the application and cost, over 30 percent is unacceptable. The number of distinct categories should be at least 5.
What is an attribute agreement analysis?
The MSA for pass/fail or categorical judgments: several appraisers rate the same items several times, and the study reports agreement within appraisers, between appraisers, and against a known standard.
What is the 10 to 1 rule of gauge resolution?
The measurement instrument should be able to resolve at least one tenth of the tolerance (or of the process variation) being measured.
How is DPMO calculated?
Defects per million opportunities: the number of defects divided by the number of units times the opportunities for a defect per unit, multiplied by one million.
Defects vs defectives.
A defect is a single nonconformance; a defective is a unit that has one or more defects. A unit can have several defects but is counted as one defective.
What is DPU, and how does it relate to yield?
Defects per unit is total defects divided by units. Under a Poisson model, the probability of a defect-free unit (first-time yield) is e to the minus DPU.