Clint Steele
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Everything posted by Clint Steele
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Interesting question. There is actually a whole community that focuses on the application of all design tools to business and other areas. Try looking up design thinking to see what you find. However, if I were to select a basic tool, then it would be FMEA. In business I think you need to think of all the things that could go wrong and be ready for them. FMEA hekp you do that. If you need help comming up with more ideas, then HAZOPs.
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Few people realise that how, with a little mathematical modelling, easy it is to robustify a system (some would say perform DFSS). In the following an example of the simplest form of analytical robustification will be given. This example demonstrates the process with enough clarity that you will be able to expand and apply it to any situation that you can mathematically model. However, mathematical modelling is another issue. Consider a situation someone wants to get measurements from a specific location on a volcano. Because the volcano is so hot, it is not possible to get all of the entire research crew to that point without very expensive equipment. Therefore, the plan is to launch a very well insulated probe from some distance. The probe will land at the desired position, take the desired readings and then transmit them back before being consumed by the magma. These probes are expendable, but not cheap; therefore, they must be launched and landed with sufficient precision. This means a repeatable range R. There is randomness in both the launch velocity v and the launch angle q. Given this randomness, what is the best combination of v and q to maximise the repeatability of the range (this means minimise the standard deviation of R sr). Start with the expression for the range: R = ½ v2Sin2q Now recall the first order approximations for calculating the mean my and the standard deviation sy of an output variable y that is a function f of x1, x,2 .... xn: my = f(mx1, mx2, ....mxn) sy2= (df(mx1, mx2,....mxn)/dx1)2 sx12 + (df(mx1, mx2,....mxn)/dx2)2 sx22 + ... (df(mx1, mx2,....mxn)/dxn)2 sxn2 Note: These are first order approximations, and thus at times they will be limited in their accuracy. Usually, they are very good though. The fist step of this approach to analytical robustification is to find an expression for the mean of the output (in this case it is R). mR= ½ mv2 Sin 2mq The second step is to fine the expression for the standard deviation of the output. sR2 = (mv Sin2mq)2 sv2 + (mv2Sin 2mq)2 sq2 At this stage the desire is to minimise the value of sR2. However, it is also important that mR be equal to the desired range or target range TR. Thus, the next step is to create and expression for mean of one of the inputs that is a function of TR. In this case v will be chosen simply because it is the easiest. mR = TR = ½ mv2 Sin 2mq => mv = (2 TR / Sin 2mq)1/2 Insert the above into the expression for sR2 sR2 = ((2 TR / Sin 2mq)1/2 Sin2mq)2sv2 + ((2 TR / Sin 2mq) Sin 2mq)2sq2=> sR = (2 TR Sin 2mq sv2 + 4 TR2sq2)1/2 This is an expression for the standard deviation of R given that the mean of R is kept at the desired target value TR. Because the above expression is a function of only one input mq (mv was removed when it was substituted for the expression that included TR), it is possible to find the minimum value of sR by simply plotting the expression. It is also possible to use observation. It can be seen that the smaller the value of mq the smaller sR will be. However, according to the expression for TR this implicitly means that the velocity will need to approach infinity: most unlikely. Therefore, it is clear that the most robust design has a maximised velocity. Two points to note: 1. The standard deviation of each input could be a function of the respective mean. If this were the case, then the expression for sR and the findings would be very different. 2. In this case there was only remaining input variable, which made it easy to analyse and optimise. In other, probably more realistic, cases, the option of plotting will not be present. However, many optimisation tools exist in various spreadsheet and mathematical applications that can be used to minimise the expression. Application of the above method can require some mental effort. However, the time and resources saved by reducing the experimental investigations make it truly worth the effort. Additionally, if you're on of the few people in the company who can do this, then you can be truly valuable. If you want to improve your skills so that you can master techniques like that above, then take a look here.
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Most of us are wrongly taught that robust design (of DFSS) can only be achieved through experimental methods like DOE and Taguchi. It's a time consuming approach and it's been known for a while that it's very limited. What's more, robust design is significantly easier to understand visually and can also be done easily and quickly mathematically by simply looking at an equation. Let's see how. Consider the formula below. It is for the stiffness of a simple helical spring. We want a certain spring rate k. The question we are now faced with is: what values should we select for each of the input variables to minimise the effects of randomness (or have a robust design)? Consider the graph below. Note how when we have a smaller gradient (blue) the variability is compressed, but with a larger gradient (red) it is expanded? Well that's basically robustification: finding the smaller gradient. So now back to the spring. Let's consider each variable and it's gradient: The spring diameter D Increasing the value will quickly reduce the gradient; it is inverse and cubed The wire diameter d Decreasing it will reduce the gradient very quickly because it is quatic The modulus of rigidity G The gradient doesn't change because it is linear The number of coils n Increasing the value decreases the gradient fairly quickly; it is reciprocated Therefore, the easiest way to robustify this design is to: minimise d, maximise D, maximise n and then adjust G to provide the desired k value. Now obviously this is a simple example, and you will probably have something more sophisticated. Nevertheless, what I have explained to you here is enough so that you can now understand the mathematics of how a system is easily robustified. Without costly experiments. Remember, it is all about the gradient. So why don't we know more about these simple and easy probabilistic methods? probably because the quality industry is still dominated by by statistitians who are basically experimentalists. They key is to become familiar with principles of probabilistic design methods and robustification. Once you have, you can intuitively apply these principles. And produce quality designs with ease. If you want to improve your understanding of how probability and mathematics can help you easily improve quality and achieve six sigma, then you can learn more here. You can sign up to a free theory update about probabilistic design, download some free software and get a free sample of of an e-book on probabilistic design. Please let me know if you have any questions about this. I think a lot of people are let down by not being taught this stuff, and I really want to rectify this situation.
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