Page 313 - The Handbook for Quality Management a Complete Guide to Operational Excellence

300 C o n t i n u o u s I m p r o v e m e n t M e a s u r e S t a g e 301

Conversion between two interval scales is accomplished by the
transforma tion
y = ax + b, a > 0

For example,
 9 
° = 32 +   5 × °C  
F

where a = 9/5 and b = 32. As with ratio scales, when permissible transfor-
mations are made statistical, results are unaffected by the interval scale
used. Also, 0° (on either scale) is arbitrary. In this example, zero does not
indicate an absence of heat.
Ratio scale measurements are so-called because measurements of an
object in two different metrics are related to one another by an invariant
ratio. For example, if an object’s mass were measured in pounds (x) and
kilograms (y), then x/y = 2.2 for all values of x and y. This implies that a
change from one ratio measurement scale to another is performed by a trans-
formation of the form y = ax, a > 0; for example, pounds = 2.2 × kilograms.
When permissible transformations are used, statistical results based on the
data are identical regardless of the ratio scale used. Zero has an inherent
meaning: in this example it signifies an absence of mass.
Reliability and Validity
Fundamentally, any item measure should meet two tests:

The item measures what it is intended to measure (i.e., it is valid). A
remeasurement would order individual responses in the same way
(i.e., it is reliable).
The remainder of this section describes techniques and procedures
designed to ensure that measurement systems produce numbers with
these properties. A good measurement system possesses certain proper-
ties. First, it should pro duce a number that is “close” to the actual property
being measured; that is, it should be accurate. Second, if the measurement
system is applied repeatedly to the same object, the measurements pro-
duced should be close to one anoth er; that is, it should be repeatable. Third,
the measurement system should be able to produce accurate and consis-
tent results over the entire range of concern; that is, it should be linear.
Fourth, the measurement system should produce the same results when
used by any properly trained individual; that is, the results should be
reproducible. Finally, when applied to the same items the measure ment sys-
tem should produce the same results in the future as it did in the past; that
is, it should be stable. The remainder of this section is devoted to discussing
ways to ascertain these properties for particular measurement systems. In
gen eral, the methods and definitions presented here are consistent with
those described by the Automotive Industry Action Group (AIAG).

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