Page 114 - Six Sigma Demystified

Chapter 5 m e a s u r e s tag e 95

in the best of worlds, when frequency distributions are applied to derive proba-
bilistic estimates of requirements, there is uncertainty in the final result. In
service industries, specifications are often similar to desirability levels: We may
say that we want to be seen by the doctor within 45 minutes of arrival, but
we’re not likely to walk out at that moment if we think service is pending in
just a few more minutes. Rather, we’ll start complaining after 30 minutes,
which will build to irritability and then disgust (at least for some of us).
Taguchi (1986) expressed this notion in terms of a loss function, where the
loss to society (the inverse of customer satisfaction) is maximized at some value
within the customer requirements and then minimized outside the range of
acceptable values. For example, with a bilateral specification, the maximum
value of the product or service may be at the midpoint between the specifica-
tions. As you move in the direction of either specification limit, the value is
reduced in some fashion, typically exponentially, as shown in Table 5.1. For
example, a five- day delivery is undesirable, but a two- day delivery is preferred
over the four- day delivery.
Although the specifications provide reasonable guidelines on acceptability
to the customer, they are not absolute. Tainting the data by removing the objec-
tivity of a measured value (or choosing a somewhat subjective attribute data
over a more objective measured value) represents a loss in informational con-
tent that is not warranted or desired.
Rather, the statistical value of the data improves as the resolution increases, at
least until a resolution is reached that can reliably estimate the variation in the
data. For a proper statistical analysis, the standard deviation must be estimated,
which requires enough information (i.e., resolution) to the right of the decimal
point to measure the variation. For example, using the data in the “Measure A”

column of Table 5.1, the standard deviation is calculated as 0.548. The data in this
column have been rounded up or down owing to poor resolution of the measure-
ment system. How accurate is this estimate of variation? The data in the “Measure
B” and “Measure C” columns of the table represent two possible sets of data that,
when rounded, would result in the “Measure A” data. In one case, the variation is
overestimated by “Measure A”; in the other, variation is underestimated. Note that
there are many other possible data sets that would result in the same rounded data
shown by “Measure A,” but in all cases the rounding produces an inaccurate result.
These inaccuracies would increase the probabilities of rejecting when the hypoth-
esis is true, a false- alarm error, or accepting when the hypothesis is false, a
failure- to- detect error. Practically, the value of the improved estimates must be
balanced against the cost of obtaining the increased data resolution.