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Introduction to Robust Optimization

The automotive industry is very dynamic and the product is continuously changing. The competition is so cut-throat that it is becoming increasingly important to deliver quality products at all times. The customers are demanding the highest quality product at a cheaper price. Robust optimization is the mantra for automotive product development organizations both for original equipment manufacturers (OEMs) and their suppliers, especially in this competitive environment. Dr. Genichi Taguchi's Robust Optimization idea is simply revolutionary. To practice robust optimization correctly, product development and manufacturing organizations need to change the way they work, the way work is done needs to change, the way work is managed needs to change, knowledge and skills need to change, the way organizations are led needs to change. Obviously, all of these take time. Not accepting this reality will be more devastating in the future for any organization that wants to win customers' hearts by consistently delivering highest quality products.

Dr. Genichi Taguchi talked about quality as loss to society and how that loss is estimated using a "Quality Loss Function." He talked about robustness - the functional stability of products or processes in the face of ubiquitous variation in the usage conditions (noise factors). He talked about a product development process involving system, parameter and tolerance design steps. He suggested that engineers focus less on meeting requirements and more on discovering combinations of design variable values that (1) stabilize the function and (2) control the adjustment or "tuning" of that function. He talked about ideal functions.

Dr. Taguchi asked engineers and engineering leadership to look at technical work in an entirely different light.

What happened?

Well, since the word "quality" was part of the "Quality Loss Function," the quality experts in the organization took over that concept.

Robustness sounded like product performance in the field. So robustness was delegated to the reliability and validation engineers. Noise factors seemed similar to best case and worst case conditions, so that, too, was a good fit to reliability and validation engineering.

His recommended product development system sounded a lot like existing concurrent engineering and optimization methodologies. System engineers looked at Dr. Taguchi's comments and said, "We already do this - there's nothing new here!"

Parameter design was seen as setting design variable values at levels that met requirements in all conditions. Since parameter design borrowed orthogonal arrays from design of experiments, Taguchi's methods were often seen as a form of Design of Experiment. In most engineering organizations, Designed Experiments were organized by a quality expert when engineering had a problem. Parameter design was delegated to quality and product engineering. Often, an experiment was conducted only if a problem of sufficient magnitude presented itself. Taguchi's parameter design methods were roundly criticized by statisticians for, among many other things, a lack of statistical rigor. Even today, "Taguchi Designs" remain a subset of most statistical computer programs. A subset only "recommended" for preliminary, screening experiments.

1.1 What Is Quality as Loss?

One of our client engineers once had a car with a noisy transmission. He took it to the dealer because the noise bothered him. The dealer attached a machine to the transmission. It printed out a report.

"Your transmission is within specification," the dealer said.

There was nothing more to be done. He drove the car for a couple of years. He was glad when he could replace it with a new one. He never bought that brand of car again - even though their transmission was in specification. The dealer's machine and the printout said so.

Dr. Genichi Taguchi defines quality as "Quality may be assessed as the minimum loss imparted by the product to society from the time the product is shipped." The larger the loss, the poorer is the quality. This kind of thinking says that there is a difference among products even if they are within specification.

The "ideal" amount of noise from an automotive transmission is zero (yes, it's impossible to achieve). As the noise from the transmission increases it will bother some people more than others. But when the noise bothers someone enough, he or she will suffer a loss. They have to take the time to drive to the dealer and wait while the service technician conducts a diagnosis. There will be a dollar value for his time. The drive, diagnosis and report out will take about two hours. Two hours at that time in this person's life is probably worth about $250. Is that the total loss? What about the company's loss of a future sale? How much is that worth? What is the profit the company would make from the sale? The loss suffered by the company who made the noisy transmission is certainly more than $250.

If an automotive manufacturer makes a very, very noisy transmission, a customer might insist that it be replaced. It doesn't matter if the transmission is in or out of specification. The customer wants it replaced. The total loss to society is probably around $3500 (including customer inconvenience). It doesn't matter whether the transmission is under warranty or not. If under warranty, the manufacturer pays; if not, the customer pays. Either way "society" is out $3500 for each transmission that is so noisy it needs to be replaced.

Using this type of data, the quality in regards to audible noise of any transmission can be estimated. The actual amount of audible noise in decibels could be placed along the bottom axis. Dr. Genichi Taguchi is suggesting that every transmission that makes any noise at all contributes a slight amount of loss to society.

The redefinition of quality that you, as the technical leader of your organization, need to embrace is that producing parts within specification is absolutely necessary. However, only producing parts that meet requirements is no longer competitive.

For long-term success in the marketplace, we must focus on producing low-cost products that lower the loss to society. The average dollars lost by society due to audible transmission noise can be estimated for the transmissions made by your company versus the transmissions made by your competition. The long-term competitive position of your company correlates well with such estimates. Products with lower quality loss to society do better over time in the market. Where do your products rate?

While automobiles provide value to society such as transportation and pleasure of driving, automobiles are producing significant amounts of losses. Those losses include emissions, global warming, and automobile accidents. Dr. Taguchi always dreamt about accident-free automobiles and automobiles that clean air.

1.2 What Is Robustness?

What is robustness? You may have to dust off some of your old textbooks (or go online), but you can do it. The ideas aren't that complicated for a technically trained person like you. Let's define robustness as the ability of a product or process to function consistently as the surrounding uncontrollable or uncontrolled factors vary.

An example is the power window system in the driver's side door of your car. Does it perform today as well as it did the day you took delivery of it? On an extremely cold morning? On a hot summer day? When you are sitting in the car with the motor off? At 50 mph? Has the window ever stopped working entirely?

If two window systems are being compared, the more robust window system is the one that performs most consistently over a large number of cycles, at low and high temperatures, when running on battery power, or when the car is moving a high speed.

Higher robustness means that a product will last longer in the field, that is, in the hands of the customer. No matter how old the vehicle, no customer should have to awkwardly open the door of her car on a cold winter day to pay and pick up her order at the drive-through window. Only window systems with high levels of robustness can meet that requirement.

Robustness is easy to understand. We appreciate the chain of coffee stores that provides a cup of coffee with consistent taste, aroma, and temperature, regardless of whether we buy it in Seattle or Shanghai. We gravitate toward products that perform consistently over a long useful life. A carpenter needs a circular saw that will last for years of hard use after being thrown into the back of a pickup truck. The expensive two-fuel stove in our kitchen shouldn't have the control panel fail in the first month we own it.

One common misunderstanding about robustness is that more expensive products tend to be more robust. We think that we have to pay for robustness. But is a luxury brand car more robust than a small traditional sedan of one-quarter of the price? In many regards, probably not. More importantly, robust optimization provides methods by which high robustness can be achieved at low cost.

1.3 What Is Robust Assessment?

Robustness is a measurement, not a requirement to be reached. Robustness is only meaningful in comparison. Is my product more or less robust than my competitor's? By how much? Is...