Page 253 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 233

Johnson Distributions
Johnson distributions are used for measurement (continuous) data that do not
fit the properties of known distributions such as the normal and exponential
distribution. Quality improvement efforts often lead to nonnormal processes,
such as through narrowing or constraining the distribution or moving its loca-
tion to an optimal condition. Similarly, nature itself can impose bounds on a
process, such as a service process whose waiting time is physically bounded at
the lower end by zero. The proper design of a service process sets the process
wait time as close as economically possible to zero, causing the process mode,
median, and average to move toward zero. In manufacturing, concentricity or
roundness is also achieved in this manner. These processes will tend toward
nonnormality regardless of whether they are stable (in control) or unstable.

Johnson Distributions

Minitab

Use Stat\Quality Tools\Individual Distribution Identification to fit a Johnson dis-
tribution to the data. Use goodness-of-fit tests (described below) to determine
if an assumed distribution provides a reasonable approximation.

Excel

Using Green Belt XL Add-On

Use New Chart\Histogram (Note: The histogram also may be displayed as an
option with the X and individual-X control charts discussed later in Part 3.)
Use goodness-of-fit tests (described below) to determine if an assumed distri-
bution provides a reasonable approximation.

Methodology

Statistical distributions are characterized by up to four parameters:

• Central tendency. For symmetrical distributions (see “Skewness”), the
average (or mean) provides a good description of the central tendency
or location of the process. For very skewed distributions, such as incomes