Theory of Design of Experiments

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About this lesson

This lesson provides a high level description of the DOE process that applies to any type of DOE. It also answers the questions of when to do a DOE and why to do a DOE.

Quick reference

Theory of Design of Experiments

The theory behind Design of Experiments is that a mathematical model can be created by statistically analysing the values of the output factors (response) based upon controlled set of input factors.  This statistical model generates high confidence in the ability to design the system and optimize the performance.

When to use

The DOE analysis should be used when there is a need to understand how multiple factors can impact the performance of product, process, or system.

Instructions

An understanding of the basic theory behind DOE can be helpful when design the study and analysing the data.  DOE develops a mathematical model of the effect of each of the control factors on the output or response factors.  This model can be used to optimize performance, design process settings and tolerances, and identify critical factors for problem solving.

 

The DOE method uses all the data, unlike Trial and Error or OFAAT which may include tests that do not contribute to the design or the solution of the problem.  The analysis is a statistical analysis that can provide confidence levels for the model that is created.  The analysis can also be used to determine appropriate tolerance levels for the control or input factors to ensure the output or response is always acceptable.

The DOE model is different from a physical model.  A physical model will often include chemical and biological effects and interactions.  It is usually much more complex than the DOE mathematical model.  Because the DOE mathematical model is based upon an analysis of the factors within a certain region (low level to high level) it is only valid when factors are within that region.  Since the DOE model is a mathematical model, it can normally be solved mathematically to determine an optimum set of input factors for best performance.

The DOE method is used in design analysis whenever there is a new product or technology that is not well characterized.  This may be due to new factors that are being controlled, or new capabilities that are required.  This analysis defines the design space of the product, process or system.

The DOE is also an excellent analysis for understanding how to control a product, process, or system to eliminate or minimize a quality defect or problem.  The DOE model can be manipulated to minimize cost, cycle time, or quality defects.

Hints & tips

  • A DOE is only as good as the factors included in the analysis.  Later lessons will focus on factor selection, which is key to a good analysis.
  • The statistics used in creating a DOE model are straightforward.  Later lessons will show how to use statistical applications to do the analysis and how to conduct the analysis using a spreadsheet like Excel.
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  • 00:04 Hello, I'm Ray sheen.
  • 00:06 We've had several lessons introducing design of experiments, but
  • 00:09 we haven't really discussed how these different techniques work.
  • 00:13 So let's do that now.
  • 00:16 I call this the theory of DOE, but
  • 00:18 don't worry, I won't get into statistical proofs or anything like that.
  • 00:22 But I want to explain how it works.
  • 00:25 DOE is based upon the principle that the product system or
  • 00:28 service being analyzed can be thought of as a process.
  • 00:33 Now to control, guide, and direct this product or
  • 00:35 process, there are number of independent control factors.
  • 00:39 These may be discrete factors, such as an on-off switch, or these may be
  • 00:44 continuous or variable factors, like a dial or setting that the user can enter.
  • 00:49 In our study, we want to understand how we can use these control factors to get
  • 00:53 the best response from the product or process.
  • 00:57 Now there are often uncontrolled variable factors that
  • 01:00 may happen have an impact on the product or process performance.
  • 01:03 These are factors like ambient temperature or background noise.
  • 01:07 Hopefully, they have a very minor effect, but we need to allow for
  • 01:11 these in the study.
  • 01:14 They're also uncontrolled discrete factors.
  • 01:16 A discrete factor is one that has a limited or
  • 01:19 finite number of possible levels.
  • 01:21 This could be the work shift, its first shift or
  • 01:24 its second shift, or this could be a particular piece of equipment used.
  • 01:28 Again, we hope the impact is small, but we'll try to account for it.
  • 01:33 Finally, there's a response factor or factors.
  • 01:36 These are the product or
  • 01:37 process performance characteristics that are measured during the testing.
  • 01:42 You can have multiple performance measures with DOE, but it's critical that at least
  • 01:46 one of them be variable measurement, not all discrete measures.
  • 01:50 The DOE analysis of these measurements will create a formula or model of
  • 01:54 the product process or system performance based upon the controlled factor settings.
  • 02:01 Let's now consider why we would use the DOE instead of one of the other methods.
  • 02:05 DOE is a structured methodology.
  • 02:08 Every data point is important and contributes to the model.
  • 02:11 There are no wasted tests or tests without a useful result that can occur sometimes
  • 02:16 with trial and error or OFAAT.
  • 02:18 In addition, the structured approach means that I don't have to trust
  • 02:22 the 30 years of experience and insight to set up and run the tests.
  • 02:26 Second, the result is a robust model that will be used to analyze and
  • 02:31 predict performance.
  • 02:32 With trial and error, you only know if that one set of factor settings will work.
  • 02:38 You may be close to a failure point and not know it.
  • 02:40 With OFAAT, you know the performance along the path of the factor as you analyzed it,
  • 02:46 but if you had analyzed the factors in a different order,
  • 02:48 you would have followed a different path.
  • 02:51 So you see trial and error gives you a point, OFAAT gives you a path, but
  • 02:56 DOE defines the entire design space
  • 02:59 because it is using all the combinations of high and low settings.
  • 03:03 Also, you have a multivariate model, so
  • 03:05 you can understand what happens when multiple inputs are changing.
  • 03:10 Finally, the result is a statistical analysis
  • 03:13 with statistical confidence intervals, so you know how accurate the model is and
  • 03:18 if there is still uncertainty where that uncertainty exists.
  • 03:21 Again, this is not available with the other methods.
  • 03:24 By analyzing the model and the statistical confidence, you can operate your
  • 03:28 product processor system and a safe zone that provides the needed performance.
  • 03:34 While the DOE model is powerful, let's be clear,
  • 03:37 it's not the same as a physical model.
  • 03:40 A physical model is often much more complex and includes complex
  • 03:45 interactions and effects, such as chemical or biological interactions.
  • 03:49 Modeling these effects would require many variables, and
  • 03:52 it's beyond most DOE analyses.
  • 03:55 The DOE is a mathematical model not a physical model.
  • 03:59 Granted it is based upon the results of physical experiments.
  • 04:02 However, it is simpler than a physical model.
  • 04:05 Also the analysis will only be valid for
  • 04:08 the region in which the control factors were tested.
  • 04:11 The results should not be extrapolated beyond that point,
  • 04:15 since we do not have any physical results from the areas beyond that point.
  • 04:20 Well we will do physical experiments as part of a DOE.
  • 04:23 Our goal is to create a mathematical model.
  • 04:26 If our model is valid and accurate,
  • 04:28 it will greatly reduce analysis time required in the design phase.
  • 04:34 That's because we can mathematically solve the model for
  • 04:37 the point of optimal performance for whatever business goal or
  • 04:40 objectives we are working towards maximising.
  • 04:43 Rather than trial and
  • 04:43 error, we can predict this performance point from the model.
  • 04:47 But we've already hinted that it may not be the fastest,
  • 04:50 if you get a lucky guess and trial and error.
  • 04:53 So that begs the question, when should DOE be used?
  • 04:57 Well one condition is when you need to determine which factors are critical to
  • 05:01 achieving the desired product processor system performance.
  • 05:04 This is vital when trying to improve performance due to things like
  • 05:08 new technology or new factors, or
  • 05:10 if the design space is just not really well understood.
  • 05:14 One area particular with a DOE can deliver results that the others can't
  • 05:18 is to understand the interaction effects between control factors.
  • 05:23 Another time when I have found DOE to be helpful is when setting tolerances for
  • 05:28 new products, processes or systems.
  • 05:30 The DOE helps me to understand the sensitivity of each
  • 05:33 factor in addition to the optimal zone for performance.
  • 05:36 Sensitive factors will have tight tolerances, but insensitive factors can
  • 05:41 have broad tolerances, which will help to keep the cost down.
  • 05:45 On process improvement projects, like those associated with Lean Six Sigma,
  • 05:49 a DOE will sort through many factors to identify which factors are significant and
  • 05:54 which are not.
  • 05:55 In addition, the DOE model can be used
  • 05:58 to set the factors to levels that achieve the desired system performance.
  • 06:03 That performance could be lower costs,
  • 06:06 faster cycle times or reduction in scrap and rework.
  • 06:10 The statistical model that is a result of the DOE analysis is a powerful tool for
  • 06:16 design and process improvement.
  • 06:18 The theory of DOE allows for
  • 06:23 the creation of that model.

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