It is normally the designer’s job to express functions in engineering terms so that engineering principles can be appropriately applied to the design problem at hand. As designers, we have to cast functions into terms that enable us to measure how well a design
realizes a specific function. That means that we have to establish both a range over which a measure is relevant to our design and the extent to which ranges of improvements in performance really matter.
When we talk about measuring the performance of a function, we are describing something that is conceptually the same as the metrics we introduced to measure the achievement of objectives. The thinking is very similar, so some of what we detailed in Chapter 4 about constructing metrics might be useful in this context, as what we say below is also relevant to thinking more deeply about objectives. But there are some key differences:
We have reserved the term metrics to apply only to scaling objectives.
We need a metric for each of the objectives that we will use in evaluating our design choices.
We use specifications to scale functions.
We need a specification for every function our design must perform, and designs must meet each and every specification. In fact, in some sense being fully functional can be considered a constraint on the design.
Metrics are applied in the past tense, to assess whether objectives have been achieved. Specifications, such as constraints, are projected into the future, when we specify in advance the functional or behavioral performance that must be achieved in order for a design to be considered to be successful.
How do we determine the range over which a measure is relevant to a design and decide how much improvement is worthwhile? Our conceptual starting point is similar to what economists call a utility plot (see Figure 6.5(a)): It graphs the usefulness of an incremental or marginal gain in performance against the level of a particular design variable.
Saturation Plateau 0 1 Level of Variable Too Low to Be Useful (a) Zone of Interest Saturation Utility (usefulness) Saturation Plateau 0 1 Level of Variable Useless (too little) Zone of Interest Saturated Utility (usefulness) (b)
Figure 6.5 Saturation curves showing that no additional benefit is achieved below some minimal realized level and above saturation. The actual shape of the hypothetical curve (a) is likely to be uncertain in most cases, while the linear approximation (b) is a design team’s effort to make the meaning more useful by making the curve crisper.
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We usually plot the utility or value of a design gain as the ordinate (y-axis) and normalize it to the range from 0 to 1. We plot the level of the attribute being assessed on the abscissa (x-axis). For example, consider using processor speed as a measure of a laptop computer performance. At processor speeds below 1 GHz, the computer is so slow that a marginal gain from, say, 500 to 750 MHz provides no real gain. Thus, for processor speeds below 1 GHz, the utility is 0. At the other end of the utility curve, say, above 5 GHz, the tasks for which this computer is designed cannot exploit additional gains in processor speed. For example, browsing the World Wide Web may be more constrained by typing or communication line speeds, so that an incremental gain from 5 to 5.1 GHz doesn’t change the normalized utility of 1. Thus, the utility plot is saturated at high speeds.
What happens at performance levels between those that have no value and those at or above saturation, say in the range 1–5 GHz for the computer design? We expect that changes do matter in this range, and that we will see incremental or marginal gains with increases in processor speed. In Figure 6.5(a) we show an S- or saturation curve that displays qualitatively the gain achieved as a (qualitative) function of the processor speed: No numerical values are attached to either axis. Thus, while no specific value of gains can be determined from the curve, the S-curve demonstrates zero utility at low processor speeds, shows a measurable increase over a range of processor speeds, and then plateaus (or saturates) at 1 because increased processor speeds produce no gains in utility.
The sort of behavior seen in a utility plot is rather common. We don’t always know the precise details of the S-curve: It may not look nearly as smooth as what we have sketched in Figure 6.5(a), so we approximate it by a set of straight lines, as we show in Figure 6.5(b). We still see regions where gains have no utility or are unavailable, as indicated by the horizontal lines at levels 0 and 1. In the range of interest, however, we model our utility level as a linear function of the design variable (e.g., processor speed). We are simply saying, qualitatively, that the linear curve defines a range within which we can expect to achieve gains by increasing the relevant design variable and, conversely, reduce gains by decreasing that design variable.
To take another example, suppose we are asked to design a Braille printer that is quiet enough to be used in office settings. None of the competing designs are quiet enough to be so used. How quiet does this design really have to be? To answer this question, we must determine the relevant units of noise measurement and the range of values of these units that are of interest. We should also find out how much noise is generated by current printer designs and whether listeners can distinguish different designs by their noise levels. If one printer produces the same noise level made by a pin dropped on a carpet, while another generates the noise level of a ticking watch, we would likely view both as quiet enough to be fully acceptable. Similarly, if one printer is as loud as a gas lawn mower, and another as an unmuffled truck, we gain no utility by distinguishing between these two designs as neither would be used in an office. (Note that this example shows a reverse S-curve in which we start at saturation because there is no gain to be made at such low levels of quietness, and then we degrade to a level of no utility for printers that are uniformly too loud.)
Since we measure sound intensity levels in decibels (dB), we know that some dB range is likely to be of interest, but what range? We answer this question by seeing how much noise is produced by other devices, and within different environments. We show sound intensities for various devices and environments in Table 6.1. With such environ- mental and exposure information in hand, we can identify a range of interest for a
performance specification for the Braille printer. New printer designs must generate less than 60 dB of noise in an office, and lower generated noise levels are considered gains, down to a level of 20 dB. All designs that generate less than 20 dB are equally good. All designs that produce more than 60 dB are unacceptable. Note that the printer noise levels we’re talking about here are well below the limits that OSHA, the U.S. Occupational Health and Safety Administration, prescribes for occupational safety.