Bidirectional positioning repeatability

Bidirectional positioning repeatability concerns repeated arrivals at a commanded position using both approach directions. Retain the direction labels: the combined behavior can include both return-to-return scatter and a positioning reversal error. The manufacturer's method forms direction-specific means and spreads before reporting an axis-level summary over several targets.^[ref]

For an original example, independently read the following errors at one target, in micrometres:The means are 0.2 and 1.2, and each direction has sample standard deviation $s=0.2\mu \mathrm{m}$. If a declared analysis pools all six observations, its sample variance decomposes exactly asHere the within-direction sum of squares is $0.16\mu {\mathrm{m}}^2$ and the between-direction term is $1.50\mu {\mathrm{m}}^2$. Consequently,The larger pooled spread is mostly explained by approach direction. This is an original variance identity with a stated sample-standard-deviation convention, not a replacement definition for every manufacturer's repeatability tolerance.

A physical study repeatedly traverses the target from both sides and records final settled displacement with independent metrology. Report target positions, approach distances, order, load and environmental conditions. A directional mean difference may be almost invisible if only within-direction scatter is reported; pooling without direction labels hides its cause. Neither statistic alone establishes measurement accuracy, and one target does not characterize the full travel range.