Length Variation What comes off the machines

Mean Leg Length mm

Length CV %

Pairing Tolerance mm

Length difference a pair may carry and still be sold

Shift For the yield figures

Socks per Shift nos

Cost per Sock cost

Pairing Yield with Sorting

— %

When socks are binned by length before pairing

Variation, Pairing & Loss

Length Standard Deviation: — mm
Spread of the Difference: — mm
Tolerance in Difference Sigmas: — z
Yield without Sorting: — %
Sorting Bin Width: — mm
Bins Required: — nos
Expected Singles per Shift: — nos
Pairs per Shift: — nos
Cost of the Singles: — cost
CV at which One Bin Suffices: — %

Random pairing is the pessimistic bound and sorted pairing the optimistic one, and a real operation sits between them: it does not pair blind, but it also does not sort perfectly, and socks are pulled for pairing in the order they arrive rather than from a settled distribution. Read the two figures as the range the process lives inside, and the gap between them as what a sorting investment is worth. The bin model assumes production is spread across bins evenly enough that each ends with an odd sock about half the time, which holds when the run is long relative to the bin count and fails on a short run or a narrow size where one bin holds almost everything - there the singles count is close to one, not half the bin count. Length variation is treated as normal, which is a fair description of machine-to-machine and cycle-to-cycle scatter and a poor one where a single faulty machine is producing a second population; a bimodal distribution has far worse pairing behaviour than its overall CV suggests, and the tell is a pairing yield well below what this predicts. Nothing here covers the other pairing criteria - shade, welt, toe closure and foot size - each of which multiplies the bin count and therefore the singles.

Sock Pairing Yield from Length Variation — free, with the formula and a worked example, at Textile School.