Page 309 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 289

Individual-X and moving-range charts generally are used when you can’t
group measurements into rational subgroups or when it’s more convenient to
monitor actual observations rather than subgroup averages. Each subgroup,
consisting of a single observation, represents a “snapshot” of the process at a
given point in time. The charts’ x axes are time-based, so the charts show a his-
tory of the process. For this reason, you must have time-ordered data; that is,
entered in the sequence from which the data were generated. If this is not the
case, then trends or shifts in the process may not be detected but instead may
be attributed to random (common-cause) variation.
If rational subgroups can be formed, X charts generally are preferred because
the control limits are calculated easily using the normal distribution. When
rational subgroups cannot be formed, then we must make assumptions about
the distribution of the process to calculate the statistical control limits on an
individual-X chart. This can be troublesome, particularly when the process
distribution is very skewed or bounded.
Individual-X charts are efficient at detecting relatively large shifts in the
process average, typically shifts of 2.5σ to 3σ or larger. If X charts can be used,
then their larger subgroups will detect smaller shifts much more quickly; see
“Statistical Process Control (SPC) Charts” for more detail. EWMA charts also
can be used at any subgroup size to increase the sensitivity to smaller process
shifts.

Methodology

An important consideration for the individual-X chart is the choice of curve fit

used for determining the control limits. There is a fundamental dilemma, in
that a distribution should not be fit to the data unless the data are from a con-
trolled process, yet the process distribution must be assumed to determine the
control limits. Because of this limitation, you may consider using other control
charts, such as the X chart or EWMA chart, to first establish process control
for a set of data; then a distribution can be fit to the data.

Individual-X Chart Calculations
Plotted statistic: The observation.
Centerline: The average (normal distribution); the median of the fitted dis-
tribution (nonnormal distributions).