Showing posts with label Six Sigma. Show all posts
Showing posts with label Six Sigma. Show all posts

Sunday, November 30, 2008

Statistical Process Control (SPC)

Statistical process control (SPC) is a method for achieving quality control in manufacturing processes. It is a set of methods using statistical tools such as mean, variance and others, to detect whether the process observed is under control.
History
Statistical process control was pioneered by Walter A. Shewhart and taken up by W. Edwards Deming with significant effect by the Americans during the World War II to improve aircraft production. Deming was also instrumental in introducing SPC techniques into Japanese industry after that war.
General
Classical Quality Control was achieved by observing important properties of the finished product and accept/reject the finished product. As opposed to this statistical process control uses statistical tools to observe the performance of the production line to predict significant deviations that may result in reject products.
The underlying assumption in the SPC method is that any production process will produce products whose properties vary slightly from their designed values, even when the production line is running normally, and these variances can be analyzed statistically to control the process.
For example, a breakfast cereal packaging line may be designed to fill each cereal box with 500 grams of product, but some boxes will have slightly more than 500 grams, and some will have slightly less, producing a distribution of net weights. If the production process itself changes (for example, the machines doing the manufacture begin to wear) this distribution can shift or spread out. For example, as its cams and pulleys wear out, the cereal filling machine may start putting more cereal into each box than it was designed to. If this change is allowed to continue unchecked, product may be produced that fall outside the tolerances of the manufacturer or consumer, causing product to be rejected.
By using statistical tools, the operator of the production line can discover that a significant change has been made to the production line, by wear and tear or other means, and correct the problem - or even stop production - before producing product outside specifications. An example of such a statistical tool would be the Shewhart control chart, and the operator in the aforementioned example plotting the net weight in the Shewhart chart.
QA , QC & Quality tools
Quality Assurance , Quality Control & Quality tools
Just In Time (JIT) is an inventory strategy implemented to improve the return on investment of a business by reducing in-process inventory and its associated costs. The process is driven by a series of signals, or Kanban that tell production processes to make the next part. Kanban are usually simple visual signals, such as the presence or absence of a part on a shelf. JIT can lead to dramatic improvements in a manufacturing organization's return on investment, quality, and efficiency when implemented correctly.
New stock is ordered when stock reaches the re-order level. This saves warehouse space and costs. However, one drawback of the JIT system is that the re-order level is determined by historical demand. If demand rises above the historical average planning duration demand, the firm could deplete inventory and cause customer service issues. To meet a 95% service rate a firm must carry about 2 standard deviations of demand in safety stock. Forecasted shifts in demand should be planned for around the Kanban until trends can be established to reset the appropriate Kanban level. In recent years manufacturers have touted a trailing 13 week average is a better predictor than most forecastors could provide.For More info referhttp://en.wikipedia.org/wiki/Just_In_Time
Kaizen ( Japanese for "change for the better" or "improvement") is an approach to productivity improvement originating in applications of the work of American experts such as Frederick Winslow Taylor, Frank Bunker Gilbreth, Walter Shewhart,and of the War Department's Training Within Industry program by post-WWII Japanese manufacturers. The development of Kaizen went hand-in-hand with that of Quality control circles, but it was not limited to quality assurance.
The goals of kaizen include the elimination of waste (defined as "activities that add cost but do not add value"), just-in-time delivery, production load leveling of amount and types, standardized work, paced moving lines, right-sized equipment, and others. A closer definition of the Japanese usage of Kaizen is "to take it apart and put back together in a better way." What is taken apart is usually a process, system, product, or service.
Kaizen is a daily activity whose purpose goes beyond improvement. It is also a process that when done correctly humanizes the workplace, eliminates hard work (both mental and physical), teaches people how to do rapid experiments using the scientific method, and how to learn to see and eliminate waste in business processes.
"Kaizen" is the correct usage. "Kaizen event" or "kaizen blitz" are incorrect usage. Kaizen is often misunderstood and applied incorrectly, resulting in bad outcomes including, for example, layoffs. This is called "kaiaku" - literally, "change for the worse." Layoffs are not the intent of kaizen. Instead, kaizen must be practiced in tandem with the "Respect for People" principle. Without "Respect for People," there can be no continuous improvement. Instead, the usual result is one-time gains that quickly fade.
Importantly, kaizen must operate with three principles in place: process and results (not results-only); systemic thinking (i.e. big picture, not solely the narrow view); and non judgmental, non-blaming (because blaming is wasteful).
Everyone participates in kaizen; people of all levels in an organization, CEO on down, as well as external stakeholders if needed. The format for kaizen can be individual, suggestion system, small group, or large group.
The only way to truly understand the intent, meaning, and power of kaizen is through direct participation - many, many times. Lean accounting and just in time producton are related concepts.
Process Models
A decades-long goal has been to find repeatable, predictable processes or methodologies (software engineering) that improve productivity and quality. Some try to systematize or formalize the seemingly unruly task of writing software. Others apply project management techniques to writing software. Without project management, software projects can easily be delivered late or over budget. With large numbers of software projects not meeting their expectations in terms of functionality, cost, or delivery schedule, effective project management is proving difficult.
Waterfall processes
The best-known and oldest process is the waterfall model, where developers (roughly) follow these steps in order. They state requirements, analyze them, design a solution approach, architect a software framework for that solution, develop code, test (perhaps unit tests then system tests), deploy, and maintain. After each step is finished, the process proceeds to the next step, just as builders don't revise the foundation of a house after the framing has been erected. If iteration is not included in the planning, the process has no provision for correcting errors in early steps (for example, in the requirements), so the entire (expensive) engineering process may be executed to the end, resulting in unusable or unneeded software features.In old style (CMM) processes, architecture and design preceded coding, usually by separate people in a separate process step.
Iterative processes
Iterative development prescribes the construction of initially small but ever larger portions of a software project to help all those involved to uncover important issues early before problems or faulty assumptions can lead to disaster. Iterative processes are preferred by commercial developers because it allows a potential of reaching the design goals of a customer who does not know how to define what he wants.
Agile software development processes are built on the foundation of iterative development. To that foundation they add a lighter, more people-centric viewpoint than traditional approaches. Agile processes use feedback, rather than planning, as their primary control mechanism. The feedback is driven by regular tests and releases of the evolving software.Agile processes seem to be more efficient than older methodologies, using less programmer time to produce more functional, higher quality software, but have the drawback from a business perspective that they do not provide long-term planning capability. In essence, they say that they will provide the most bang for the buck, but won't say exactly when that bang will be.
Extreme Programming, XP, is the best-known agile process. In XP, the phases are carried out in extremely small (or "continuous") steps compared to the older, "batch" processes. The (intentionally incomplete) first pass through the steps might take a day or a week, rather than the months or years of each complete step in the Waterfall model. First, one writes automated tests, to provide concrete goals for development. Next is coding (by a pair of programmers), which is complete when all the tests pass, and the programmers can't think of any more tests that are needed. Design and architecture emerge out of refactoring, and come after coding. Design is done by the same people who do the coding. (Only the last feature - merging design and code - is common to all the other agile processes.) The incomplete but functional system is deployed or demonstrated for (some subset of) the users (at least one of which is on the development team). At this point, the practitioners start again on writing tests for the next most important part of the system.
While Iterative development approaches have their advantages, software architects are still faced with the challenge of creating a reliable foundation upon which to develop. Such a foundation often requires a fair amount of upfront analysis and prototyping to build a development model. The development model often relies upon specific design patterns and entity relationship diagrams (ERD). Without this upfront foundation, Iterative development can create long term challenges that are significant in terms of cost and quality.
Critics of iterative development approaches point out that these processes place what may be an unreasonable expectation upon the recipient of the software: that they must possess the skills and experience of a seasoned software developer. The approach can also be very expensive, akin to... "If you don't know what kind of house you want, let me build you one and see if you like it. If you don't, we'll tear it all down and start over." A large pile of building-materials, which are now scrap, can be the final result of such a lack of up-front discipline.
Formal methods
Formal methods are mathematical approaches to solving software (and hardware) problems at the requirements, specification and design levels. Examples of formal methods include the B-Method, Petri nets, RAISE and VDM. Various formal specification notations are available, such as the Z notation. More generally, automata theory can be used to build up and validate application behaviour by designing a system of finite state machines.
Finite state machine (FSM) based methodologies allow executable software specification and by-passing of conventional coding (see virtual finite state machine or event driven finite state machine).
Recent approaches try to merge the specification and code into one activity to ensure the specification and code match. While Agile methods propagate specification of all requirements in code, methods such as VFSM develop executable specifications, trying to avoid the coding activity entirely
Quality control tools
The following are the mostwidely used Quality control tools
Run Chart : Run charts are used to analyze processes according to time or order. Run charts are useful in discovering patterns that occur over time. Detailed tutorial
Pareto Chart : Pareto charts are extremely useful because they can be used to identify those factors that have the greatest cumulative effect on the system, and thus screen out the less significant factors in an analysis. Ideally, this allows the user to focus attention on a few important factors in a process.
Flow Chart : Flowcharts are pictorial representations of a process. By breaking the process down into its constituent steps, flowcharts can be useful in identifying where errors are likely to be found in the system. Detailed tutorial
Cause and Effect Diagram :This diagram, also called an Ishikawa diagram (or fish bone diagram), is used to associate multiple possible causes with a single effect. Thus, given a particular effect, the diagram is constructed to identify and organize possible causes for it. Detailed tutorial
Histogram : Histograms provide a simple, graphical view of accumulated data, including its dispersionand central tendancy. In addition to the ease with which they can beconstructed, histograms provide the easiest way to evaluate the distribution ofdata. Detailed tutorialScatter diagrams : Scatter diagramsare graphical tools that attempt to depict the influence that one variable has on another. A common diagram of this type usually displays points representing the observed value of one variable corresponding to the value of another variable. Detailed tutorial
Control Chart : The control chart is the fundamental tool of statistical process control, as it indicates the range of variability that is built into a system (known as common cause variation). Thus, it helps determine whether or not a process is operating consistently or if a special cause has occurred to change the process mean or variance.

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Saturday, November 15, 2008

Root Cause Analysis

Root cause analysis (RCA) is a class of problem solving methods aimed at identifying the root causes of problems or events. The practice of RCA is predicated on the belief that problems are best solved by attempting to correct or eliminate root causes, as opposed to merely addressing the immediately obvious symptoms. By directing corrective measures at root causes, it is hoped that the likelihood of problem recurrence will be minimized. However, it is recognized that complete prevention of recurrence by a single intervention is not always possible. Thus, RCA is often considered to be an iterative process, and is frequently viewed as a tool of continuous improvement.

Root cause analysis is not a single, sharply defined methodology; there are many different tools, processes, and philosophies of RCA in existence. However, most of these can be classed into five, very-broadly defined "schools" that are named here by their basic fields of origin: safety-based, production-based, process-based, failure-based, and systems-based.

Despite the seeming disparity in purpose and definition among the various schools of root cause analysis, there are some general principles that could be considered as universal. Similarly, it is possible to define a general process for performing RCA.

General principles of root cause analysis

  1. Aiming corrective measures at root causes is more effective than merely treating the symptoms of a problem.
  2. To be effective, RCA must be performed systematically, and conclusions must be backed up by evidence.
  3. There is usually more than one root cause for any given problem.

General process for performing and documenting an RCA-based Corrective Action

Notice that RCA (in steps 3, 4 and 5) forms the most critical part of successful corrective action, because it directs the corrective action at the root of the problem.

  1. Define the problem.
  2. Gather data/evidence.
  3. Identify issues that contributed to the problem.
  4. Find root causes.
  5. Develop solution recommendations.
  6. Implement the recommendations.
  7. Observe the recommended solutions to ensure effectiveness.

[edit] Root cause analysis techniques

  • 5 Whys
  • Failure mode and effects analysis
  • Pareto analysis
  • Fault tree analysis
  • Bayesian inference
  • Ishikawa diagram, also known as the fishbone diagram or cause and effect diagram
  • Barrier analysis - a technique often used in particularly in process industries. It is based on tracing energy flows, with a focus on barriers to those flows, to identify how and why the barriers did not prevent the energy flows from causing harm.
  • Change analysis - an investigation technique often used for problems or accidents. It is based on comparing a situation that does not exhibit the problem to one that does, in order to identify the changes or differences that might explain why the problem occurred.
  • Causal factor tree analysis - a technique based on displaying causal factors in a tree-structure such that cause-effect dependencies are clearly identified.

Basic Elements of Root Cause

  • Materials

- Defective Raw Material

- Wrong type for job

- Lack of raw material

  • Machine/Equipment

- Incorrect tool selection

- Poor maintenance or design

- Poor equipment or tool placement

- Defective Equipment or tool

  • Environment

- Orderly workplace

- job design or layout of work

- Surfaces poorly maintained

- Physical demands of the task

- Forces of Nature

  • Management

- No or poor management involvement

- Inattention to task

- Task hazards not guarded properly

- Other (horseplay, inattention....)

- Stress demands

  • Methods

- No or poor procedures

- Practices are not the same as written procedures

- Poor communication

  • Management System

- Training or education lacking

- Poor employee involvement

- Poor recognition of hazard

- Previously identified hazards were not eliminated

Here Some Scheme matrix of RCA Download it HERE


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Thursday, August 21, 2008

Quality-Process-Software-CMMI-ISO-SixSigma

Differences between Continuous and Staged Representations in CMMI
http://www.sei.cmu.edu/cmmi/presentations/sepg05.presentations/cepeda-cmmi.pdf

CMMI 1.2 for Development online - browser version
http://www.wibas.de/presentation/site/cmmi_1.2_browser.html.en

This is the link to see online version of CMMI 1.2 for development
http://chrguibert.free.fr/cmmi12/text/index.php

What is not CMMI Level 4 and 5
http://www.sei.cmu.edu/appraisal-program/presentations/hi-matmis.pdf

Causal Analysis and Resolution: A Business Driver at All Levels http://www.dtic.mil/ndia/2002cmmi/norausky3a1.pdf

Quality Glossary
http://www.isixsigma.com/dictionary/glossary.asp

Quality Methodologies
http://www.isixsigma.com/me/

Statistics in Quality
http://www.isixsigma.com/st/

Quality Tools
http://www.isixsigma.com/tt/-

5Whys http://www.protoolkits.com/Analysisandrequirements/Analysistechniques/fivewhys.html-

Fishbone Diagrams
http://www.protoolkits.com/Analysisandrequirements/Analysistechniques/fishbonediagrams.html

Manage Changes
http://www.protoolkits.com/Analysisandrequirements/managechangerequests.html-

Process Maps
http://www.protoolkits.com/Analysisandrequirements/Analysistechniques/processmaps.html

One who wants to know about CMMI and related stuff, become a member in https://seir.sei.cmu.edu/seir
[Site will ask you about the work you do and why you want to become a member.]

Some Project Management Literature Templates and Checklists can be found athttp://www.brookes.ac.uk/services/hr/project/templates/index.html

Project Management Reference Site
http://www.managementhelp.org/plan_dec/project/project.htmhttp://www.method123.com/free-project-management-book.php

Some Suggested Readings
www.processimpact.com/PMBP/Module_8/data/downloads/metrics_traps.pdf http://www.processimpact.com/pubs.shtml#requirements http://www.processimpact.com/articles/metrics_primer.html

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Wednesday, August 13, 2008

Relation Between CMMi and Six SIgma

Successfully implementing CMMI and Six Sigma together requires an understanding of the relationships between the two.

This report contains a brief summary of each initiative and then outlines the connections between frameworks commonly used in Six Sigma and the CMMI process areas. Coupling this knowledge with a conscious strategy enables an organization to create tactical plans and specific mappings to support implementation.

Example strategies and tactics that organizations have used to integrate these initiatives are also provided.

http://www.sei.cmu.edu/pub/documents/05.reports/pdf/05tn005.pdf

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Friday, March 14, 2008

Six Sigma for Leaders

by Pete Pande

The nature of the debate surrounding Six Sigma presents an opportunity to better understand how value can be offered to improve the caliber of leadership in an organization.

It’s been more than 10 years since GE’s aggressive adoption of Six Sigma launched a renaissance of quality methods, and some 20 years since Motorola first began minting Black Belts and concentrating on defects. And yet, despite hundreds of documented successes and thousands of committed Six Sigma practitioners, criticism of and skepticism about Six Sigma remains as strong, and probably stronger, than ever.

One recent, visible example: when Bob Nardelli departed as head of Home Depot, anti-Sigma voices quickly proclaimed that his downfall showed the failure of Six Sigma. On a daily basis, you can find dozens of articles and blogs proclaiming that rather than promoting improvement Six Sigma serves to squelch innovation and creativity.

Even if one shares in the skepticism about Six Sigma, it could be suggested that the arguments pro and con warrant attention from those in the quality field. And that the nature of the debate presents an opportunity to better understand how value can be offered not just to improve processes and products, but to improve the caliber of leadership in an organization.

How the Real World Hears the Argument

It is important not to over-simplify the message of Six Sigma concepts. Even if management and executives buy into and have enthusiasm for many ideas of Six Sigma, the door is often left open for some legitimate doubts. Here are examples of a few Six Sigma sacred cows and how they often come across to those who spend their days running businesses and departments:

Measurement and Management by Fact

Most managers and leaders agree that they need more—or at least better—metrics, and would be better off using data more consistently in their diagnosis and decision-making. But for plenty of critical decisions, most leaders recognize that the uncertainties they have to cope with are not likely to be eliminated, at least in the short-term, by improved measures. This is especially true of the strategic choices that most influence the future of a business. Management can be improved by better measures, but always requires some element of “gut.”

Focus on the Customer

Six Sigma has helped many organizations (re)connect with customers and better align products and services to their needs. At the same time, smart businesspeople know when to, in a sense, ignore the customer. A laser-like attention to satisfying today’s customers can, in fact, lead a company into trouble—an oft-cited example being Motorola’s focus on high-quality analog cell phones.

It’s All About Process

Many have said: “It’s not the people, it’s the process.” But sometimes it is the people.

One of the best ways to show that Six Sigma does not work (or any other approach, for that matter) is to define it narrowly—for example, “it’s only about defect reduction”—and then provide examples where it does not apply. That’s what happens when an organization fails to account for the diversity of challenges that face businesses and leaders. Six Sigma principles and methods can be applied to a broader array of issues, and can have real relevance to leaders facing an increasingly complex environment. But first, the real nature of why simple answers do not work has to be understood.

The Paradoxes of Business Success

If one listens carefully to the arguments for and against Six Sigma or, more broadly, to debates over how to achieve success in business, it will be found that there is no single right answer. In fact, there are usually at least two—often seemingly contradictory—right answers. These can be called paradoxes, perhaps not technically correct, but pretty close.

Some of these paradoxes have already been touched on: facts and intuition are critical; processes and people count; love the customer, but beware of the customer. There are others: speed should be balanced with deliberateness; teamwork is key, but individual initiative is an essential catalyst; asking for buy-in works for many people, but a smart leader knows when to enforce compliance. Each is right, and wrong, depending on the circumstance.

Another critical paradox involves change itself. Proactive organizations and leaders are continually trying to improve their performance and stay ahead in the race to compete. But ironically the push for change can be self-defeating. Here’s the classic problem described by a key manager: “The tendency right now is to do everything. Leadership is getting frustrated because they’ve been trying to fix things for five years or so and instead of getting better, things seem to be getting worse.” One of the most valuable steps to achieving greater change return on investment is to stop changing so much.

Applying Six Sigma to Leadership

Like anyone, leaders fall victim to their own habits and preferences—when what they need is the ability to adapt to each new situation and embrace the reality of the paradoxes. Particularly as the pace of change accelerates, leaders need to work even smarter than ever—and cannot rely on past experience or charisma to ensure future success.

With that in mind, Six Sigma approaches can best support effective leadership by emphasizing the themes of balance and flexibility. In other words, the benefit of Six Sigma discipline should not be limited to, for example, better data, but rather to helping leaders gain a clearer understanding of when more data is critical. Or when a decision by necessity is based more on intuition than facts, they need help to manage risks and/or more effectively test their hypotheses by applying facts after the decision.

This means changing the game and broadening the scope of many Six Sigma initiatives—though for some of the most successful efforts the gap will be much narrower. It may be necessary to adjust an organization’s working definition of Six Sigma—or even rebrand its efforts. But first, if one is up to the challenge, leaders will have to be engaged with differently to demonstrate how one’s support can help them beyond the confines of the Six Sigma program.

Some tips on where to start:

Position change as an investment

Rather than just picking the next DMAIC (define, measure, analyze, improve and control), lean or Design for Six Sigma projects, leaders should be engaged in a discussion around how the broader portfolio of change initiatives are selected and managed. They should be encourage to do less and establish guidelines to ensure a more balanced set of investments, for example,, a conscious mix of quick hits, mid-range and long-range initiatives.

Acknowledge/market the paradoxes

A more credible view of how Six Sigma can help a business should acknowledge both where the core principles fit, and where they don’t. As an example, if a project team had to forge ahead without solid Voice of the Customer (VOC) input, one should not be too quick to see that as a failure, but rather a business choice—the validity of which can be assessed over time. Getting comfortable with the boundaries and trade offs does not mean excusing laziness or lack of discipline. Instead, it puts an organization in a position to better understand where and when to push harder— for example, invest time and money to get more VOC data—and when to manage the risks on the back end.

Encourage Hypotheses

One of the biggest complaints about Six Sigma—particularly from leaders—is that, “we already know (or knew) the answer.” In reality, however, no answer or solution is a 100% certainty. One can actually help leaders—without telling them they are wrong—by reminding them that their answers are really educated guesses. Just that subtle shift in perspective opens the door to greater discipline and flexibility. Reticent leaders can feel encouraged to act as long as they can manage the unknowns. Confident ones may be willing to apply more care rather than simply assume their answers are correct.

Love it or hate it, Six Sigma is the closest we’ve come to bringing quality thinking into the realm of leadership since Deming’s challenging 14 points. Naysayers can continue to marginalize and undermine the gains made so far. It is much better to recognize the aspects of Six Sigma that can be applied to the real challenges of leadership—and build on the successes achieved during the past 20 years.

Tech Tips

# Awareness of the paradoxes of business can help leaders work smarter.

# Six Sigma approaches can best support effective leadership by emphasizing the themes of balance and flexibility.

# An organization may need to broaden the scope of its Six Sigma initiative to see positive results.



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Monday, March 3, 2008

Lean Manufacturing or Six Sigma - which method is best?

by Carl Wright


Lean Manufacturing or Six Sigma?

Lean Manufacturing and Six Sigma are two of the most popular improvement initiatives utilized by major corporations. Many companies employ both methodologies combined under the name Lean Six Sigma.

Many companies are struggling to determine which initiative will bring the most impact for their organization.

It is critical for those individuals tasked with making the decision to understand the differences between lean manufacturing and six sigma.

First of all, they are both improvement initiatives. However, they are very different. Both are a collection of various "tools". For example, lean utilizes the tools of 5S, SMED, value stream mapping, takt time, standardized operations, error proofing, kaizen, line balancing, cellular manufacturing, and many others. Six sigma utilizes the tools of process mapping, FMEA, Cause and Effects Analysis, statistical analysis and process controls, regression analysis, design of experiments, and many others.

Lean manufacturing is a much less structured and is often viewed as the low hanging fruit of opportunities. Lean manufacturing initiatives often employ the Plan-Do-Check-Act (PDCA) model, while Six Sigma utilizes the Define-Measure-Analyze-Improve-Control (DMAIC) model.

When companies combine the methodologies into a "Lean Six Sigma" initiative, most will utilize the DMAIC model and utilize lean tools where applicable. For example, when the six sigma project is at the Improve phase, a line balancing exercise could be used.

The PDCA model utilized with lean is often a quick process compared to the DMAIC model. Lean projects are often completed in hours or days, whereas most six sigma projects will take weeks or months to complete.

The lean manufacturing method is more of a "just do it" approach. The project might be planned, conducted, checked, and acted upon in the same day. For example, a manufacturing line might be changed to a U shaped cell in the morning, and fine tuned in the afternoon.

Maximum improvements are obtained when the tools are not forced into use. The business problem, challenge, or opportunities should point to which tools should be used.

For example, if a business wants to cut cycle time, it could be a six sigma, lean manufacturing, or combined project, depending on the complexity of the issues. If the setup time is the majority of the cycle time, a SMED project or simple kaizen event may obtain the improvement. If the entire supply chain is complex and the problems (opportunities) are not obvious, a six sigma project might be necessary.

The key is to determine the business problem first, and then decide which tools are necessary to solve it.

Most companies employing six sigma conduct the DMAIC phase model. Most of these projects range from a few weeks to several months. However, there is an emerging trend of utilizing the DMAIC model even if the project will only entail the use of lean tools. Proponents of this method believe the DMAIC model adds structure to lean projects, even when used in a quick manner.

Regardless of which methodology a company chooses to use, lean tools should be part of it. Utilizing six sigma tools without lean tools would limit the improvement potential of many projects. Also, lean tools alone will not solve all business problems, and six sigma increases the probability of success.

The bottom line is a company will benefit most to have both lean manufacturing and six sigma expertise. Although it may be difficult to have people with expertise in both disciplines, any expert in lean or six sigma should have a good understanding of the other

If possible, individuals should continue training until expertise is gained in both methods. When there is no bias toward one discipline, it is easier to keep an open mind as well as an understanding of which tools are best to solve a problem.

In summary, let the business problem determine the tools to use, rather than try to fit a tool to a problem.

A free lean manufacturing training primer of all major lean concepts in included at www.1stcourses.com


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Tuesday, January 29, 2008

ANOVA by any other name

Elegance rules
by Steven Ouellette

By the time you are reading this, you will have made your New Year’s resolutions, and I will have already broken mine. But I have an idea for a resolution that you might be interested in keeping, and one that could make your New Year happy and profitable. It is something that most Black Belts I talk to have never heard of. Before we get there, we need to talk about another powerful tool, with which you may be familiar.

Analysis of variance (ANOVA) is an elegant procedure—simple, economical, and powerful.We have this research question:

“Which of the four materials being considered for making a gear has the best wear characteristic?”

This will lead to the statistical question, “Which of the five materials has the highest average wear?” (I’ll discuss another statistical question—about the dispersion—in next month’s column.)

We make up eight gears out of each of the five materials and run them on our wear tester (on which, of course, we have performed our measurement system analysis and determined acceptability). You can get the data here.

We might be tempted to do multiple t-tests, but we would have to do 10 different t-tests (which is annoying). Even worse, when we do that we increase the chance of making an α error. If αFW is the chance of making a Type I error during all the tests, αPC is the Type I error for each test and c is the total number of tests:

So if our αPC for each t-test is 0.05, our actual αFW is inflated to about 40.13 percent.

Holy leftover fruit cake, Batman! That’s a serious chance of concluding that a significant difference exists in the materials when in fact they don’t.

Luckily, there’s a way to test for equality of all group averages in one test. ANOVA works because we have two potential sources of variation: variation within each group and variation between the averages of each group. If all the groups have the same average wear, then the variation between and within the groups is due only to random chance, and the different materials have no effect on wear. On the other hand, if the different materials do have different averages, the total variation we see will be higher than we would have guessed from the variability within each group.

I can therefore estimate the population variance in two ways. I can take the average of the variances within each group and I can find the variance between the means and divide by the sample size. Both ought to give me the same answer, within sampling error, if the true means of the groups are all the same. Here’s the genius part—if I make a ratio of these two estimates, I can use the good old F-statistic to test to see if they’re equal. If they’re different by an amount that could be due to sampling error, then as far as I can tell, the groups are all the same average and I calculate an F close to one. If the averages really are different, then the between estimate of the variance contains sample error and a variance component due to the differences in group averages.

Clearly, this F is going to be larger than one. Another cool thing is that it’s a one-tail test (see why?), which gives us additional power for the same α.

OK, fine, you knew all that. But sometimes it’s fun to just sit back and appreciate elegance when you find it.

Our null hypothesis for this ANOVA is:

H0: μ1 = μ2 = μ3 = μ4 = μ5

The alternative hypothesis is that the null statement is not true somehow.

First I check for normality, because that’s one of the assumptions in ANOVA.

Material

n

(A-D)A²*

p

(S-W)W

p

(L-M)r

p

Skew.

p

Kurt.

p

1.00

8

0.463

0.266

0.902

0.301

0.166

0.796

0.190

0.798

-1.301

>.10

2.00

8

0.654

0.089

0.859

0.117

0.701

0.161

-0.820

0.271

-0.924

>.10

3.00

8

0.392

0.396

0.897

0.274

0.000

1.000

0.000

1.000

-1.456

>.10

4.00

8

0.337

0.530

0.933

0.542

0.034

0.958

0.083

0.911

-0.438

>.10

5.00

8

0.777

0.043*

0.809

0.036*

0.750

0.111

-1.113

0.137

0.291

>.10

There’s one material that might not be normally distributed, as indicated by the Anderson-Darling and Shapiro-Wilk tests. ANOVA is fairly robust to departures from normality when n is large, but is highly affected by outliers. I reviewed a histogram of the data and found that, while it might be skewed, there are no outliers, therefore we are probably safe with ANOVA. Just to be sure, I ran a Kruskall-Wallace nonparametric test, which confirmed the results.

So we perform an ANOVA on our gear data, and generate something like this:

ONEWAY ANOVA

wear by material [1 to 5]

Source df SS MS F p
Between 4 700.1500 175.0375 46.324 0.000*
Within 35 132.2500 3.7786
Total 39 832.4000

Fixed Effects Analysis:
ω² = 81.92%

I’m going to talk about dispersion analysis in March, so for now let’s assume we have equal variances within the five materials. The p-value on the end of the ANOVA table is the probability of getting an F-statistic of 46.324 (or more extreme) from an F-distribution with 4, 35 degrees of freedom and an average of 1, which is pretty dang unlikely. So we reject the hypothesis that all the averages are equal, and conclude that the different materials do in fact influence the gear wear. The ω2 number is an estimate of the percentage of the total variation explained by differences in material, so clearly those differences are large compared to the sampling error.

But now what? We’ve found a significant difference, and if you refer to the alternative hypothesis, you’ll notice that ANOVA doesn’t tell you where the differences are. Now we enter the world of post-hoc analysis. (Post-hoc just means “after the fact.” Ham hock is something else entirely, so stop drooling.) We will delve into this realm next month, when our managers intrude their reality on our nice antiseptic ANOVA. Then I will show you something that you might not have seen before that could save you oodles of money.

Then again, I could be wrong.

Thanks to Mike Petrovich, for his program MVPstats, which makes these types of analyses fast and easy. Mike now has a shareware version of his flexible SPC program available for download.

About the author
Steven Ouellette is the founder of six-sigma-online.com, president of The ROI Alliance LLC, an instructor at the University of Colorado Engineering Management Program and Director of the Center for Statistical Solutions at the University. He has been in process design and improvement since 1992 as an engineer and later as a consultant working in many different industries. He has a Master Black Belt certification, a master’s degree in engineering management, and a bachelor’s degree in metallurgical and material science. He also acts as a board member on Orion Registrar’s Committee to Safeguard Impartiality.

(SOURCE QualityDigest.com)


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