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Engineering Systems Integration
dissatisfaction with a product’s or service’s performance. The customer’s
view of the product is restricted to the operational and disposal stage of the
product or service lifecycle. A straightforward and accurate means of representing a quality characteristic is through a function that uniquely defines
the relation between a loss in EMMI and the deviation of the quality characteristic from its target value (Taguchi et al. 2005). For products or services
that are in operation, the quadratic form of loss functions matches well to
customer satisfaction (Taguchi et al. 2005).
A Taylor series expansion is often used to approximate a function as a
polynomial of terms whose first terms turn out to be reasonably close
approximations to that which would otherwise seems mathematically complicated (Mason et al. 2003). The first derivative of a Taylor series expansion
taken about the target value is a quadratic curve when the target value is set
to zero. The curve’s minimum (or nominal position) is centered on the target
value, which (Taguchi et al. 1989) has shown to provide the best performance
in the eyes of the customer. However, identifying the appropriate performance measures as well as selecting the best target value can be challenging.
Designers sometimes offer their best guess. The quadratic form was chosen
by Taguchi because it was both simple, and as it turned out, useful. Further,
after the Taylor expansion, higher powers in the series change the loss at the
target value by a very small margin, and for practical purposes can be
ignored within experimental error. Symmetric formulations of loss functions are assumed to be approximate and accurate to a first order. This
assumption is shown to be accurate since the result of development is indeed
what is placed into service by users, that is, that which is equivalent to a
Taguchi validated quadratic form of loss function. The general loss function
discussed in this book, provides the quantitative means to evaluate integration from conceptualization through disposal by adapting the order of the
loss function to the desired phase in the product’s lifecycle. Asymmetric loss
functions are most useful when integrating systems into a system of systems.
The reason for this situation (as distinct and different from that of integrating
a system) is the requirement for reversibility of actions to allow a system to
remain a system when it is no longer a part of a system of systems.
The loss function offers a way to quantify the benefits achieved by reducing
variability around a target performance value. It can help justify a decision to
invest further to improve a function that is already capable of meeting specifications, but there exists a requirement to achieve the same (or better) performance at a lower loss (e.g., in energy, matter, material wealth, or information).
According to Taguchi, the objective of minimizing the loss to a customer was to
improve product quality by minimizing the effects of variations in its performance while striving to achieve the performance target value. The narrower
the performance limits, the higher the quality (and within the same design
space, the higher the cost). However, achieving higher quality does not need to
come at the expense of eliminating the causes of that variation. Eliminating the
causes within an existing design must be invoked through solutions that are