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User interface design with matrix algebra
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6. EXAMPLE 3: THE FLUKE 185 DIGITAL MULTIMETER
Our final example is a digital multimeter, an electrical measuring instrument. The
Fluke 185 has ten buttons, four of which are soft buttons with context-sensitive
meanings, and a rotary knob with seven positions. It has a 6.5×5cm LCD screen
with about 50 icons, as well as two numeric displays and a bar graph. It has the
most complex user interface of the examples considered in this paper. Furthermore,
it is a safety critical device: user errors with it can directly result in death. For
example, if the Fluke 185 meter is connected to the AC mains electricity supply
but set to read DC volts, it will not warn that the voltage is potentially fatal.
As a general purpose meter, it can be connected to sensors, such as the Fluke
carbon monoxide sensor, and a misreading could lead to gas poisoning — if the
meter is set to AC volts it would read 0 whatever the DC voltage from the sensor.
When measuring amps the meter, cables and the device being tested could overheat
and cause a fire (or even an explosion). And so on; user/design error can lead to
immediate and possibly catastrophic physical consequences.
A multimeter should only be used by competent users, and therefore the trade-offs
between usability and interface complexity are different than general use products
(such as mobile phones). However, unlike a professional interface (such as an aircraft cockpit), multimeters may be used by users competent in the domain but who
do not fully understand or have forgotten details of the user interface. Thus the user
interface should not have many modes, feature interactions, timeouts or other features that are not essential in the domain; where possible it should utilise warnings,
utilise interlocks, and be self-explanatory, etc. Such issues are very important and
require careful consideration, based on a deep understanding of the domain (both
technical and regulatory) and of human error and so on. These issues go beyond
matrix algebra and this paper is silent on them, beyond noting the general point
that there is a danger that technical concerns take precedence over user interface
concerns, and that user interface quality will suffer. As a case in point, the Fluke
185 conforms to seven types of safety standard and a quality standard (ISO9001),
but to no user interface standard.
6.1 Partitioned matrices
Matrices are normally considered as arrays of numbers or scalars; in fact any values
can be used, provided they can be ‘added’ and ‘multiplied.’ Matrices themselves
have these properties, and therefore matrices can be built up, or partitioned, out
of submatrices. Consider a matrix M partitioned into four submatrices:
M=
...
M11 .... M12
...........................
...
M21 .... M22
The submatrices (M11 etc) need not all be the same size, though they must
conform (be the right size) for the operations required of them. Thus if this partitioning of M is used to multiply a state vector s, partitioned as (s1 ... s2 ), then the
number of columns of s1 must equal the number of rows of M11 etc. If s and M
conform in this way, the partitions can be multiplied out: