340 Appendix 2: Product Upgrades Based on Minimum Expected Quality Loss
performance measures and selecting the best target value is not an easy
task. And further while it has been productive to improve product quality
by reducing the performance variability, defining and implementing
appropriate testing to achieve only a handful of nonconforming products
are confounded by misclassifying items as rejected/accepted or rejecting
conforming items (Arts 1998). Testing is an early feedback that presupposes
and validates specifications that are indeed sometimes the designer’s best
guess at the customer’s interests. In actuality, 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. We constructed a general quality loss function that would satisfy Taguchi conditions when the quadratic
order was satisfied.
The quality loss function developed by Taguchi (1990) is used to describe
quality in terms of smaller-the-better, larger-the-better, and nominal-thebest characteristics. A smaller-the-better output response results when it is
desirable to minimize the performance, with the ideal target for performance
being zero. Examples of smaller-the-better output responses are the wear on
a component, the amount of engine audible noise, the amount of air pollution, and the amount of heat loss. The larger-the-better output response
reflects cases when it is desirable to maximize the result, the ideal target
being infinity. Examples of larger-the-better output responses are strength of
materiel or fuel efficiency. The nominal-the-best characteristic results when
there is a finite target point (or domain of cooperative agreement) to achieve,
often associated through a negotiated outcome. In this case there are typically upper and lower specification limits on both sides of the performance
target, representing the maximum or minimum acceptable bounds for the
parties of the negotiation. Examples of nominal-the-best characteristics are
the plating thickness of a component, the length of a part, and the output
current of a resistor at a given input voltage.
The loss function is a means to quantify the benefits achieved for the customer by reducing variability around the target. It can help justify a decision
to invest, determine how much process improvement is needed when the
product is already capable of satisfying specifications, or determine the
appropriate period for a product upgrade. Accomplishing the goal of improving quality by minimizing the effects of variations in performance did not
necessarily need to come at the expense of eliminating the causes of that
variation. The aim was to immunize the product design to variations that
imparted customer value without an associated loss (Yao et al. 1999).
Types of Quality Loss Functions
Taguchi considers three cases of quality loss functions, including nominalthe-best, smaller-the-better, and larger-the-better. The methodology used to
performance measures and selecting the best target value is not an easy
task. And further while it has been productive to improve product quality
by reducing the performance variability, defining and implementing
appropriate testing to achieve only a handful of nonconforming products
are confounded by misclassifying items as rejected/accepted or rejecting
conforming items (Arts 1998). Testing is an early feedback that presupposes
and validates specifications that are indeed sometimes the designer’s best
guess at the customer’s interests. In actuality, 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. We constructed a general quality loss function that would satisfy Taguchi conditions when the quadratic
order was satisfied.
The quality loss function developed by Taguchi (1990) is used to describe
quality in terms of smaller-the-better, larger-the-better, and nominal-thebest characteristics. A smaller-the-better output response results when it is
desirable to minimize the performance, with the ideal target for performance
being zero. Examples of smaller-the-better output responses are the wear on
a component, the amount of engine audible noise, the amount of air pollution, and the amount of heat loss. The larger-the-better output response
reflects cases when it is desirable to maximize the result, the ideal target
being infinity. Examples of larger-the-better output responses are strength of
materiel or fuel efficiency. The nominal-the-best characteristic results when
there is a finite target point (or domain of cooperative agreement) to achieve,
often associated through a negotiated outcome. In this case there are typically upper and lower specification limits on both sides of the performance
target, representing the maximum or minimum acceptable bounds for the
parties of the negotiation. Examples of nominal-the-best characteristics are
the plating thickness of a component, the length of a part, and the output
current of a resistor at a given input voltage.
The loss function is a means to quantify the benefits achieved for the customer by reducing variability around the target. It can help justify a decision
to invest, determine how much process improvement is needed when the
product is already capable of satisfying specifications, or determine the
appropriate period for a product upgrade. Accomplishing the goal of improving quality by minimizing the effects of variations in performance did not
necessarily need to come at the expense of eliminating the causes of that
variation. The aim was to immunize the product design to variations that
imparted customer value without an associated loss (Yao et al. 1999).
Types of Quality Loss Functions
Taguchi considers three cases of quality loss functions, including nominalthe-best, smaller-the-better, and larger-the-better. The methodology used to