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Staffing math

How many qualified people do you need on every shift?

The rule names the number that must be present: one first aider, two keyholders, three German speakers. The question nobody writes down is how many have to hold the qualification for that number to be there on an ordinary Tuesday, once leave, sickness and lapsed certificates are priced in.

15 cases · 25 days leave and 8 days sickness assumed · each holder absent 12.6% of shifts

Holding exactly what you need is a coin flip

One required and one held is short on about 33 working days a year. A second holder takes that to 4.2; a third to 0.5. The first spare does most of the work and the second does most of the rest, and the pattern repeats one rung up for every requirement of two or three. The pages below run that ladder for specific qualifications at specific team sizes, and argue what is different about each.

How this is worked out

Each holder is treated as absent on some share of their rostered shifts: 25 days of paid annual leave plus 8 days of average sickness across 261 working days, which is 12.6 percent. A binomial across the holders gives the chance that fewer than the required number are present on a given shift, and multiplying by the shifts in a year turns that into a count a planner can argue with. Where an operation runs fixed crews, the arithmetic is done per crew and added up, because a holder on another crew is not on this shift.

The model treats absences as independent and every certificate as valid, and both are generous. Holders who trained together take leave together, and a lapsed certificate removes a holder for the weeks a renewal takes. Every figure here is therefore a floor on the real exposure. The leave and sickness inputs vary by country; the relief factor library carries sourced figures for 17 of them.

These pages do not state any regulator's minimum. A regulation typically names the number that must be appointed or present; the arithmetic here answers the question that follows, which is how many must hold the qualification for that number to be there on the day. Read the one next to it on how many of the team can be off at once for the same distribution applied to the whole roster.

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