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Variables Search: A Great Experimental Design for Troubleshooting Complex Systems

• Dec 8, 2011
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A number of experimental designs have been developed to help scientists understand cause-and-effect relationships between parameters in complex systems. Variables Search is a very effective troubleshooting technique developed by Dorian Shainin , recipient of four major ASQ awards. Keki Bhote describes Variables Search and other Shainin problem-solving methods in World Class Quality: Using Design of Experiments to Make It Happen . Variables Search has several benefits compared to other experimental designs:

• Much easier to learn and use
• You quickly find out whether key parameters have been accounted for or overlooked
• Relatively few experiments are required to pinpoint the critical variables. This is extremely important because experimentation is costly and time-consuming.
• "Confounded" variables, where a scientist cannot determine whether a given response is due to a multivariable interaction or a single variable, is an issue with many Design of Experiment ( DOE ) techniques, e.g., fractional factorials, Taguchi orthogonal arrays, Plackett-Burman designs. Variables Search clearly dissociates the main and interaction effects from each other.
• Some conditions are replicated, which helps assess experimental error

Variables Search Phase 1 - Determine whether the critical variables have been uncovered

Referring to the Phase 1 flowchart, several guidelines should be kept in mind while creating a "Variables List":

• Selecting Variables: It's better to include seemingly irrelevant variables on the list, rather than omitting them, in case those variables turn out to be significant.
• Ranking Variables: While variables can be ranked arbitrarily, there's a benefit associated with placing the most influential variables highest on the list. Variables ranked highest will be examined first during Phase 2; consequently, the number of experiments will be reduced if this activity was done effectively.
• Choosing Settings: Each (+) value should be chosen with the belief that it will lead to the desired outcome , while each (-) value should be selected with the thought it will lead to an unwanted result .

When carrying out the six tests mentioned in the Phase 1 flowchart, randomize these experiments to ensure that uncontrolled variables do not bias the results. A test design example for six variables is displayed in the table below.

To verify you're on the right track, I recommend doing two experiments up front; one experiment with all variables set at their (+) values, the other with all variables set at their (-) levels. Did the (+) settings experiment achieve the desired effect, while the (-) settings lead to an adverse response? If not, then the Variables List must be revised. Either:

• Reexamine the Variables List. Should more variables be added to the list?
• It's possible the (+) and (-) levels of one or more variables were assigned incorrectly and they're canceling the influence of other variables. Should any (+) and (-) values be reassigned?

If necessary, repeat the initial set of experiments until the (+) settings lead to a good outcome and the (-) settings leads to a poor result. Once this occurs, carry out the four remaining Phase 1 experiments.

Examining the results, answer the two questions posed on the Phase 1 flowchart. To establish a 95% confidence level that the critical variables have indeed been uncovered, both questions must be answered "yes."

Variables Search Phase 2 - Pinpoint the critical variables

Phase 2 consists of a series of paired experiments to screen variables for their significance. This is done by swapping the (+) and (-) values of one variable at a time. By keeping all other variables at the conditions established during the Phase 1 experiments, the effect of the changed variable is highlighted. The order of these variable swapping experiments should be based upon the ranking done in Phase 1. The first set of paired experiments is depicted in the table below.

These paired experiments have three possible outcomes:

• The response variable is not affected at all when the variable under study is switched. This indicates that particular variable is insignificant within the range of conditions tested.

• The outputs change somewhat. This means the variable being studied is significant and it is interacting with other variables.

• There is a complete reversal of outputs. This means the switched variable is the one and only critical variable.

Continue with the paired experiments per the Phase 2 flowchart until one or more significant variables have been identified.

Variables Search Phase 3 - Confirm that every interacting variable has been identified

Once two interacting variables have been identified during Phase 2, a pair of experiments must be completed to confirm that only those variables are interacting. The (+) and (-) settings of these two variables must both be switched from conditions established during Phase 1. In the table below, Variables B and D are switched. If, as indicated, the results reverse completely, all interacting variables have been identified and no further experimentation is necessary. If this is not the case, return to Phase 2 to identify another key parameter and then repeat the Phase 3 confirmation experiments.

To quantify the influences of individual variables in a multi-variable interaction, experimental results can be analyzed by various software programs that perform Analysis of Variance (ANOVA) calculations, or the Yates algorithm can be employed to manually calculate each variable's effects.

How can you can use the variables search method in your work or research?

Image of puzzled via flickr user andy.brandon50 under creative commons license..

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Six Sigma vs. Shainin - Content of problems that can be solved by Shainin

• Thread starter Caydinli
• Start date Sep 20, 2004
• Sep 20, 2004

Claes Gefvenberg

Prophet of Profit

Caydinli said: I'll be trained for Shainin Apprentice and then Journeyman? I'd like to understand the content of problems that can be solved by Shainin. And also understand the practical advantages of Six Sigma and Shainin to each other. Do they fit to all problems faced in manufacturing area Thanks { "lightbox_close": "Close", "lightbox_next": "Next", "lightbox_previous": "Previous", "lightbox_error": "The requested content cannot be loaded. Please try again later.", "lightbox_start_slideshow": "Start slideshow", "lightbox_stop_slideshow": "Stop slideshow", "lightbox_full_screen": "Full screen", "lightbox_thumbnails": "Thumbnails", "lightbox_download": "Download", "lightbox_share": "Share", "lightbox_zoom": "Zoom", "lightbox_new_window": "New window", "lightbox_toggle_sidebar": "Toggle sidebar" } Click to expand...

The Shainin method consists of the following steps: 1. Determine if the method can solve the specific issue 2. 'To translate' the issue (the characteristic) to a measurable quantity 3. To reduce the search area ('Intelligent Searching') 4. To determine the cause(s) 5. To quantify the effect of the causes 6. To verify the suggested improvement 7. To determine process parameter borders 8. To control the process The following tools have been developed to apply this method: 1. Components Search 2. Multi vari chart 3. Paired Comparison 4. Variables Search 5. Full Factorials 6. Better vs current 7. Scatter Plots 8. Process Certification 9. Operator Certification Click to expand...

Tim Folkerts

Wes, Just out of curiousity, which do you consider "old hat" and which do you have no clue about? Let me present my take on Shainin. The Shainin techniques and training are proprietary, so it is hard to find much on the web (unlike six sigma, where any consultant can certify new black belts). If you can find an old copy of "World Class Qualty" by Keki R. Bhote, it describes many of these techniques. And yes, many of them are "old hat". The goal, as I understand it (I haven't been through the training), is to simplify calculations and present some standardized approaches to problem-solving so that you don't need an advanced degree in statistics or engineering to use the techniques. Statistical calculations are replaced by simple comparisons. * In B vs C, suppose you have some samples from your C urrent process and some samples from the (hopefully) B etter process. Any statistician could calculate and interpret a t-test, but suppose you don't have a statistican (or suppose the results are simply a rank order, rather than actual values). B vs C testing provides some simple rules where all you have to do is rank the samples. I don't have the rules handy, but they go something like "if you test 3 C and 3 B, and 3 of the top 4 are C, then C is better." There are many variations depending on how many of each type you have to test. Just rank and check the chart with the rules. * In precontrol, you simply divide the spec limits into three ranges - the middle half is "green", the upper quarter and lower quarter are "yellow" and anything outside the spec limits is "red". Forget all the "two out of three at least 2 sigma from the center" type rules for traditional control charts. All you do is draw 2 samples. One "red" or 2 "yellows" means you have a problem. The statistical power will be reduced, but the point is that a floor worker can do the measurements, plot it on a chart, and immediately know what to do without any math. Similarly, the DOE-type techniques (full factorial, component search, etc) tend to be straightforward to implement and to interpret. They may not be the best techniques if you are an expert, but they are usually easy to use. Tim F  

OK - Here's what I understand about items in the list: Also bear in mind that I no longer have the patience or the math skills to do Analysis of Variation (ANOVA) on my own - I need software to do this for me. Shainins Seven Diagnostic Tools Multi Vary Charts These are fundamentally a stratified experiment directed at identifying Red x and Pink x. (Causes of variation). They look like but should not be confused with control charts. OK - this is always a good starting point for a DOE - find the causes of variation Components Search This is a tool used where a product can be disassembled and re assembled and is used to find poor quality or failing components Doh! If you can do this, you can probably spot the choke points and stumbling blocks as you look at the components. Paired Comparisons This tool uses the above tools to further home in on the family of Red x and Pink x using binary queues. It attempts to use high and low factors to reduce the number of experiments. OK. So? Better vs current After a series of tests have been carried out to determine causes of variation B v's C issued to compare 3 current methods of production with 3 better methods with 5 possible outcomes ranging from the possibility that current methods give results at least as good as the better ones through to the option where even the worst results from the 'better' options are better that the best current methods. This was news to me. I'm still not clear where multiple "current methods" came from or how they derive the "better methods" in the first place - it may be simple if you take the course, but mystifies me now. In many industries, it is EXPENSIVE to actually run an alternate process side by side with a current process to make the comparison. Scatter Plots This is a graphical representation of results from experiments. It aims to look at the tolerance limits of data in order to determine the true cause of variation. Yep! Old hat, but very worthwhile. Full Factorials Shainin recommends the use of the full factorials, as they are not likely to miss important data, which he believes is possible with Orthogonal Arrays. Most of the things I've dealt with had too many variables and possible ways to go to take the time and effort to do "Full Factorials." So this is old hat, but not meaningful in my experience because the cost of doing the DOE using this offsets any savings in process. Staff and process certification leave me a little mystified - exactly how is this different from determining ANY area for improvement? Certainly, you want to make sure of the capability and capacity of personnel and machinery. Is this stuff for a chapter for any but raw greenhorns? Raw greenhorns are not usually in charge of designing experiments for process improvement. I respect the math and statistical skills of many here in the Cove who are able to do stuff routinely in manipulating numbers when I have to check a cheat sheet for formulas, simply because I don't use them often enough to retain them in memory. Ultimately, though, a Design of Experiments is supposed to point the way to methods where the process operators do NOT have to use "brute force" by testing every possible modification of a product or process to attain the most cost-effective method of manufacture. A good DOE often involves a team [of experts on materials, machines, function of finished product, market competition, new product designs in the pipeline, etc.] to make the determination when continuing effort to improve a process will not generate sufficient efficiencies to justify the cost of experimenting. In my opinion, DOE by Shainin or Taguchi, or anyone else needs to keep the "big picture" in focus all the time to avoid "analysis paralysis" where the DOE becomes more important than selling product. I have no axe to grind against Shainin or any of the other DOE systems. I try to keep in mind DOE is merely one of the tools in my kit. I also have visions of Red Beads and Funnels dancing in my head all the time and always worry about bad processes or "tampering."  

• Dec 14, 2004

Tim Folkerts said: Wes, Just out of curiousity, which do you consider "old hat" and which do you have no clue about? Click to expand...

Caydinli said: I'll be trained for Shainin Apprentice and then Journeyman? I'd like to understand the content of problems that can be solved by Shainin. And also understand the practical advantages of Six Sigma and Shainin to each other. Do they fit to all problems faced in manufacturing area Thanks Click to expand...

alfawei said: I dont think Shainin & Sixsigma ,even PDCA can solve all problem in manufacturing area. Click to expand...

Quite Involved in Discussions

• Dec 15, 2004

alfawei said: I dont think Shainin & Sixsigma ,even PDCA can solve all problem in manufacturing area. These are just tools of solving problems. The environment is changing quickly ! The method and it's user must change too. Click to expand...

• Jan 21, 2005

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A high order generalized finite difference method for solving the anisotropic elliptic interface problem in static and moving systems

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Bibliometrics & citations, view options, recommendations, an immersed raviart–thomas mixed finite element method for elliptic interface problems on unfitted meshes.

This paper presents a lowest-order immersed Raviart–Thomas mixed triangular finite element method for solving elliptic interface problems on unfitted meshes independent of the interface. In order to achieve the optimal convergence rates on ...

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We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements. Three of these unfitted finite element methods, known from the literature, are studied. Two of these are suitable only for small ...

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