Locked lesson.
About this lesson
Exercise files
Download this lesson’s related exercise files.
DOE in Design Optimization.docx88.6 KB DOE in Design Optimization - Solution.docx
61.5 KB
Quick reference
DOE in Design Optimization
DOEs are often used to optimize the design of a product, process or system. The fractional factorial DOE is especially well suited to this analysis as it progresses from the screening phase to refining phase to optimizing phase.
When to use
When a product, process, or system is either totally new or is a major upgrade to an existing one, a DOE is very helpful for optimizing the design around the parameters the business has chosen as the critical ones for design success. This is usually done prior to design freeze so the results can be incorporated into the design with minimal effort.
Instructions
The fractional factorial DOE methodology is ideally suited for design optimization. It provides empirical data for analysis – not intuition or gut feel. In addition, its iterative nature aligns well with many design and development processes that build several generations of prototypes, with each adding sophistication and building on the lessons from the previous phase.
Screening
The screening phase identifies the significant factors that require further study. The values for the factors that are insignificant can be set following the screening phase. These are normally set at the value that is in the best interest of the business – low cost, high reliability, preferred supplier, etc. These factors will not impact the performance that is studied as part of the DOE and can therefore have wide tolerances, at least as far as this factor is concerned. The screening study will also identify the best value for any significant qualitative control factors. If the performance results were not adequate during the screening study, consider using the path of steepest ascent or descent to shift the control factors to a point with better performance.
Refining
The refining phase is crucial for the design optimization process. This phase is normally run with only quantitative factors and often these factors are multi-level. Main effects plots and interaction plots are used to identify the best settings for these factors. The design space equation generated in this phase can be solved for various initial conditions or operating conditions to identify the best possible performance. Since this phase is to refine the understanding, it is quite appropriate to change the levels of the high and low settings for the factor to a zone of preferred performance or a zone of intersection on an interaction plot. If there are only a few factors that are being studied in this phase, consider doing a full factorial design for these factors in order to learn as much as you can about them.
One of the more useful analysis provided by Minitab during this phase is the main effects plot. It will show what setting will provide the best performance in the response factor. It also indicates the sensitivity of the factor based upon the steepness of the slope of the line in the plot. A steep slope indicates a sensitive factor. If that factor can be made available to the operator or user of the product, process, or system it can become the primary control for the system. If it is not easily accessible by the operator or user, then the factor must be highly controlled to prevent small changes from occurring. For if small changes occur in this factor, you could be seeing large changes in the response factor. Another plot that may be helpful is a main effects for variance. If the factor has a steep slope in this chart, it indicates that the variance changes over the span of the factor and reduces its usefulness as a product, process, or system control.
Optimizing
This is the final phase of the fractional factorial DOE study and it normally has only a few runs. If the optimal point was adequately tested in the refining phase, you may not need any runs in this phase, although I still recommend a confirmatory run. It is also possible that based upon the interaction plots of the refining phase or a point of interest in the design space equation, you may find it beneficial to conduct several tests of just one factor. These tests should be to verify an optimal setting for that factor.
Hints & tips
- Replicates improve the statistical accuracy of your refining phase but require many more runs, However, if the number of runs are set due to cost or schedule, I would prefer to do a full factorial DOE rather than a fractions factorial with replicates in the refining phase.
- If the refining phase results don’t seem to make sense, remember that you probably did the screening phase in a fractional factorial manner and you have confounded a control factor with an interaction effect. If so, take the control factor that shows the least significance in the refining phase and compare its Yates values from the screening phase with the Yates values for interaction effects to determine which effect was confounded.
- Your design space equation may require higher math than algebra to solve. If possible set ranges for factors to establish relationships between them to simplify the analysis.
- 00:04 Hi, I'm Ray Sheen.
- 00:06 Well, in the last lesson we looked at using DOE for
- 00:08 creating brand new designs or working with new technology.
- 00:12 And now in this lesson we want to consider how do we use it to
- 00:15 optimize an existing design.
- 00:19 In my experience, this was the primary focus of DOE's.
- 00:23 Now part of the reason for that may have been due to the fact that I've worked for
- 00:26 years in product development, not in basic research.
- 00:29 We would often take an old design or a prototype that came from the lab and
- 00:34 do a major design upgrade using data from a DOE.
- 00:38 Now the different types of DOE's that we have been exposed to in this course,
- 00:42 the one best suited to design optimization is the fractional factorial DOE.
- 00:47 The whole structure is an iterative approach to improving the design.
- 00:51 First in the screening phase, the critical significant factors are identified.
- 00:55 These factors continue on further in the analysis and the other minor factors
- 01:00 are optimized based upon the business' goals for the system optimization.
- 01:04 For a cost reduction effort, just set up the lowest cost.
- 01:07 If it was a performance upgrade,
- 01:08 they're set at whatever setting would contribute to the best performance.
- 01:13 Next we go to the refining phase with the significant factors.
- 01:16 As we mentioned at the time, these are usually quantitative factors.
- 01:20 I often use multi-level factor settings, and
- 01:23 we use the results of this phase to identify zones of best performance.
- 01:27 Also, we need to watch closely for interaction effects.
- 01:31 Understanding these can sometimes boost the system performance.
- 01:35 Finally, we go to the optimizing phase.
- 01:38 This part of the study will normally use the predicted
- 01:40 ideal settings to validate the expected performance.
- 01:44 Sometimes I will also use this study to vary one factor
- 01:47 in order to find its sensitivity for tolerancing purposes.
- 01:51 It's almost like doing an OFAT with that factor, but
- 01:53 only after we have already put all the other factors at their optimal settings.
- 01:59 Let's take a minute to discuss each phase in further detail.
- 02:02 First, the screening phase.
- 02:04 The results of the screening phase are the list of significant factors and
- 02:08 Minitab gives those to us in both the table and
- 02:11 the much easier to read horizontal bar graph.
- 02:14 Within the table,
- 02:16 the factors with a p-value that is below 0.05 are significant.
- 02:21 For the quantitative major factors, they get to go on to the refining phase for
- 02:26 further analysis.
- 02:27 The qualitative major factors don't need refinement, they are what they are.
- 02:31 So use the best case selection of that factor in all the remaining studies.
- 02:36 If the DOE results are not up to the desired level of the new design,
- 02:41 consider using the path of steepest ascent or descent to move your input
- 02:45 factors to a region where you will get the improved performance.
- 02:50 With the minor factors, you have a level of flexibility.
- 02:53 You can change those without it making much difference to the system product or
- 02:58 process.
- 02:59 So set them at a value that helps to meet the overall optimization objective,
- 03:04 cost, quality, reliability, whatever.
- 03:07 Another thing to remember with these is that you can set a wide tolerance with
- 03:10 little risk, and those tolerances will lower production costs and
- 03:14 often can improve quality.
- 03:17 Now let's recap how a refining study leads to design optimization.
- 03:22 Of course, the purpose of this phase is to find the optimal settings for the design.
- 03:27 Feel free to change the levels for high and
- 03:29 low on the factors between the screening study and this study.
- 03:33 At the screening study indicates that a factor should be
- 03:36 at the high end to get optimal performance.
- 03:38 Then in the refining study, use several high factor settings
- 03:42 to see if there is a sensitivity issue in that range.
- 03:46 A good place to start is with the tolerance band around the target value for
- 03:50 the control factor.
- 03:52 And whenever I have enough runs in my DOE budget,
- 03:55 I will use multi-level factors at this phase.
- 03:58 That is so
- 03:59 I can get a sharper understanding of factor effects on performance.
- 04:04 If there was a significant interaction effect and
- 04:06 some of the factors being studied,
- 04:08 use multi-level factors and if possible focus them on the interaction point.
- 04:12 Again, to gain better understanding of that sensitivity.
- 04:17 If you only have a few factors, my cut off is usually three,
- 04:20 use a full factorial design instead of a fractional factorial at this phase.
- 04:25 This will get you the most data from that phase.
- 04:30 The last thing I want to discuss in this area of design optimization is the use of
- 04:35 the main effect plots in Minitab.
- 04:37 The main effect plots we discussed in Minitab lesson were ones that
- 04:40 are using the mean value for that data.
- 04:43 These are shown as linear, the steeper the slope of the line,
- 04:46 the more significant the factor.
- 04:49 Depending upon whether the goal is to maximize or
- 04:51 minimize the output, the high end or
- 04:54 the low end of the main effect plot would be considered the optimal design point.
- 04:58 In this diagram factors 1, 2, and 4 provides strong impact on the performance.
- 05:05 With 1 and 2 being a positive impact,
- 05:08 meaning the higher the factor, the higher the performance.
- 05:11 And factor 4 is a strong negative impact, meaning the higher the factor,
- 05:16 the lower the performance.
- 05:19 Factor 3 is almost horizontal, so it does not affect performance.
- 05:24 Another type of main effects plot is based upon the standard deviation
- 05:28 instead of the mean value.
- 05:30 I didn't show you how to create this because quite frankly,
- 05:33 there are a number of additional steps needed and it's seldom used.
- 05:37 If you want to know how to create it, the wizard in Minitab will explain.
- 05:41 But let's look at what it is telling us.
- 05:43 What we see here is variance, and that means the variability or
- 05:47 sensitivity of the factor.
- 05:48 Factors 1 and 2 have consistent variants throughout the factor range.
- 05:54 Factor 3 is a strong positive,
- 05:57 meaning that the variability is much higher when the factor is high.
- 06:01 So avoid that if you can.
- 06:03 And factor 4 has a negative slope.
- 06:05 So the variability in performance is much higher when the factor is low.
- 06:10 And if you want tight predictable performance,
- 06:13 avoid the zones with high variance.
- 06:16 DOE is a very powerful tool for design optimization.
- 06:20 With each phase we learn more about the design and get better performance.
Lesson notes are only available for subscribers.
PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.