295
Systems Integration Management
The quality loss function developed by Taguchi (1990) is used to describe
quality in terms of smaller-the-better (STB), larger-the-better (LTB), and
nominal-the-best (NTB) characteristics. An STB output response results
when it is desirable to minimize the performance, with the ideal target for
performance being zero. Examples of STB 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 LTB output response reflects cases
when it is desirable to maximize the result, the ideal target being infinity.
Examples of LTB output responses are strength of material or fuel efficiency.
The NTB 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 NTB
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.
A great many papers relate to the quality loss function largely from only
one side of the quality characteristics (Kapur and Wang 1996; Chung and
Chao 2005; Yahya and Chanwut 2007). Here, we derive a quality loss function
for broader applicability in managing quality characteristics, regardless of
domain and characterization, regardless of input and output, and irrespective of preference or specifics for any discipline or field. We are particularly
interested in loss functions as a means to determine the effectiveness and
efficiency of integration.
There is some common ground that reconciles traditional and Taguchi
views of quality. Quality is viewed as a step function such as a product or
service is good or bad. In reality of course, there may be a preponderance of
characteristics that in aggregation transition from acceptable to unacceptable
(or vice versa), but the general sentiment assumes that the product or service
quality is uniformly good between the lower specification and the upper
specification, and bad outside these limits. Even traditional decision makers
and those using Taguchi’s loss function will make the same judgments, as
they both will set upper and lower limits for acceptability. However, the limits may not be equally distributed from a target value that is deemed the best
trade-off between good and bad. If decision makers consider both the position of the average and the variance, and if the averages are equal and/or the
variances are equal, then the traditional decision maker and one using
Taguchi’s loss function will make the same decision. Typically, the traditional
decision maker calculates the percentage of defective units over time, when
both the average and the variance are different. Both the average performance
and variation from a target value are measures of quality (Taguchi et al. 1989).
Further, Taguchi formulates and it is widely held that the customer becomes
increasingly dissatisfied as performance departs farther from the target value
for performance of a function. His extensive work with manufacturers over
the last 30 years suggests that a quadratic curve best represents a customer’s