Prof. Rob Leachman IEOR130 Fall, 2018courses.ieor.berkeley.edu/ieor130/3_Introduction to Six...A Six Sigma project typically has specific financial goals for cost reduction or profit

Prof. Rob LeachmanIEOR130Fall, 2018

9/6/2018 1Rob Leachman Intro to Six Sigma

Six Sigma is an engineering management paradigm originally developed at Motorola. Its application has spread from hi-tech manufacturing to general business processes in many industries.

Six Sigma seeks to improve the quality of process outputs by identifying and removing the causes of defects (errors) and variability. It involves statistical methods and usually relies on a

special infrastructure of people within the organization who are experts in these methods.

A Six Sigma project typically has specific financial goals for cost reduction or profit gain.9/6/2018 2Rob Leachman Intro to Six Sigma

First written formulation by Bill Smith of Motorola in 1986.

BUT, Six Sigma draws heavily on the previously published quality paradigms and methodologies (statistical quality control, TQM, Zero Defects, etc.) developed by Shewhart, Deming, Juran, Ishikawa, Taguchi and others from the 1930s up to the 1980s.

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A defect is anything that could lead to customer dissatisfaction. Defects are very costly.

There must be continuous effort to achieve stable and predictable process results (i.e., to reduce process variation and hence defects).

Processes have characteristics that can be measured, analyzed, improved and controlled.

Achieving sustained quality improvement requires commitment from the entire organization.

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Consider a process generating an on-going stream of output.

If on an on-going basis we plot the averages of parameter measurements for groups of five or more output units of the process, then by the Central Limit Theorem of statistics, we should see a normal distribution .

PROVIDED THAT the process is stable, i.e., provided that consecutive measurements are independent and identically distributed (IID) random variables. If not IID, then the process is not in statistical control and is

said to be out-of-control (OOC).

9/6/2018 5Rob Leachman Intro to Six Sigma

For a normal distribution, 99.9% of the mass lies between [µ-3σ, µ+3σ], where µ denotes the mean and σ denotes the standard deviation. Thus, a spread of 6σ contains virtually all the output of the process:

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We assume for each important process parameter that the engineers define specification limits, whereby if the parameter falls below the lower specification limit (LSL) or above the upper specification limit (USL), then the output unit is defective and no good for the customer.

How many defects we experience can be characterized by comparing the spec limits to the 6σspread of the normal distribution for the process…

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A very well-controlled process. The distribution is well-centered between the spec limits, and the 6σ spread is half the 12σ spread of the spec limits.

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Process capability concerns the ability of the process to generate output within the spec limits. Motorola developed some metrics for this purpose:

Cp = {USL – LSL}/6σ is termed the process capability index, where USL denotes the upper specification limit and LSL denotes the lower specification limit. Cp >> 1 means good process capability. Cp < 1 means bad

process capability, i.e., lots of scrap is being generated.

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Cp = 1 might seem like there would be little scrap. But that would only be the case if the process was perfectly centered (i.e., the mean lies exactly halfway between LSL and USL).

To allow for the fact that a process might not be well-centered, a new metric was developed:

Cpk = Min { (µ-LSL)/3σ, (USL-µ)/3σ } is called the process performance index.

Cpk > 1 indicates the mean is more than 3σ away from the nearest spec limit, i.e., there is little or no scrap.

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It is found in practice that the process mean is often not stationary but tends to drift over time.

Thus Cpk = 1 does not imply quality is really great, because if the process drifts unfavorably we will start getting scrap.

A common industry goal is to raise Cpk for all important process parameters to at least 1.5, i.e., the nearest spec limit should be at least 4.5σaway from the process mean.

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Identify the occurrences of process variation and establish containment measures Add inspections or measurements (e.g., SPC charts) to

detect out-of-control “excursions” Engineer fixes to eliminate root causes of excursions,

OR: Re-engineer the product so that the spec limits can be

wider yet the customer will be just as happy

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DMAIC (for existing processes) Define high-level goals and define the existing process. Measure key aspects of the process and set up data

collection systems. Analyze the data to verify cause-and-effect

relationships. Determine those relationships. Improve or optimize the process based on application

of techniques like design of experiments. Control to ensure that any deviations from targets are

corrected before they result in defects.

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DMADV (for new products or processes) Define design goals consistent with customer desires and

enterprise strategy. Measure and identify CTQs (critical-to-quality

characteristics), product capabilities, production process capability, and risks.

Analyze to develop and design alternatives, create a high-level design and evaluate design capability to select best design.

Design details, optimize the design, and plan for design verification. (May require simulation.)

Verify the design, set up pilot runs, implement the production process, hand over to process owners.9/6/2018 14Rob Leachman Intro to Six Sigma

Statistical process control charts (AKA Shewhartcontrol charts, SPC charts)

Ishikawa diagrams (AKA Fishbone diagrams) Design of experiments (DOE) Failure modes and effects analysis (FMEA) Fault detection and classification (FDC) Regression analysis, Analysis of variance Taguchi methods, Taguchi Loss Function Many others

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Continuous process parameter X-bar chart – track mean of fixed-size samples LCL = , UCL = µ is process mean, σ is process standard deviation, n is

sample size

R chart – track range of five-unit samples LCL = d3R, UCL = d4R, R is average range of sample, d3

and d4 are constants from statistical tables σ = R/d2, d2 is constant from statistical table (can use

this in X-bar chart)

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n/3σµ − n/3σµ +

Countable parameter (e.g., particles on wafer) C chart LCL = , UCL = c is the average count for a fixed-size sample

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cc 3− cc 3+

nppp /)1(3 −− nppp /)1(3 −+

• Binary parameter (e.g., good or not good)• P chart

• LCL = , UCL =• p is the average fraction bad , n is the sample size

1920s and 1930s – Shewhart invents control charts at Bell Labs and implements them in Western Electric (AT&T’s manufacturing arm)

1940s – Western Electric and a few others make good use of SPC, but most companies resist it

1950s – Deming goes to Japan; SPC is embraced there

1970s & 1980s – Many American industries are decimated by Japanese competition

1980s & 1990s – TQM and 6-σ movements in USA9/6/2018 Rob Leachman Intro to Six Sigma 18

Introduce quality management professionals that cut across traditional dept. boundaries Executive Leadership – define vision, empower role holders

with freedom and resources Champions – responsible for implementation, mentor the

Black Belts Master Black Belt – Full-time, in-house coaches, ensure

consistent application across functions and departments Black Belt – Full-time, apply methodology to specific

projects Green Belt – handle implementation under guidance of

Black Belts along with other job duties Yellow Belt – trained in basic application of tools, work with

Black Belts, closest to the work9/6/2018 19Rob Leachman Intro to Six Sigma

For the period 1986 – 2006, Motorola claims its Six Sigma programs achieved $17 billion in savings.

Starting in the 1990s, General Electric under Jack Welch became a strong disciple of Six Sigma, and GE claims major successes from it. Subsequently, Six Sigma became a management craze. Success

at other companies has been mixed.

Six Sigma is not a panacea. It is no substitute for inventing and marketing great products. It is an incremental improvement on previous quality theories.

On the other hand, there is no substitute for great quality, and the methodologies embraced by Six Sigma embody the best knowledge we have on the subject.

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Introduction to �Six SigmaSix Sigma – What is it?Six Sigma HistorySix Sigma DoctrineWhere does the “Six Sigma” term come from?Where does “Six Sigma” come from? (cont.)Where does “Six Sigma” come from? (cont.)Process distribution vs. Spec limitsProcess CapabilityProcess Performance IndexProcess driftProcess improvement strategiesImprovement methodologiesImprovement MethodologiesQuality management toolsTypes of SPC ChartsTypes of SPC Control ChartsSPC HistorySix Sigma OrganizationSix Sigma Evaluation