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When
to Use an X-bar / R Chart
X-bar / Range charts are
used when you can rationally collect measurements in groups (subgroups)
of between two and ten observations. Each subgroup represents a "snapshot"
of the process at a given point in time. The charts' x-axes are time based,
so that the charts show a history of the process. For this reason, you must
have data that is time-ordered; that is, entered in the sequence from which
it was generated. If this is not the case, then trends or shifts in the
process may not be detected, but instead attributed to random (common cause)
variation.
For subgroup sizes greater
than ten, use X-bar / Sigma charts, since the range statistic is a poor
estimator of process sigma for large subgroups. In fact, the subgroup sigma
is ALWAYS a better estimate of subgroup variation than subgroup range. The
popularity of the Range chart is only due to its ease of calculation, dating
to its use before the advent of computers. For subgroup sizes equal to one,
an Individual-X / Moving Range chart can be used, as well as EWMA or Cu
Sum charts.
X-bar Charts are efficient
at detecting relatively large shifts in the process average, typically shifts
of +-1.5 sigma or larger. The larger the subgroup, the more sensitive the
chart will be to shifts, providing a Rational Subgroup can be formed. For
more sensitivity to smaller process shifts, use an EWMA or Cu Sum chart.
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