Part III · Chapter 5 · Evidence · lesson 5

How many of these should exist by now?

14 min

Builds on Designed, or running? Decide for each one

A control that runs once a quarter. A period that opens on the first of January and closes on the thirtieth of September. Two hundred and seventy-three days.

Before anything else: how many completed instances of that control does the calendar say should exist by the end of it?

Predict

Quarterly control, nine-month period. How many instances are owed?

Two, because the control only has to bracket the periodThree, because three quarters fit inside nine monthsFour, since a quarterly control runs four times a yearIt depends on when in the quarter each one happened

Two different questions, and a bundle can fail either one.

How many? Whole cadence periods inside the window. A quarterly control over nine months owes three; a monthly control over a year owes twelve, not twelve and a sixth. One missing instance is one promise the cadence made and the register did not keep.

How much of the window is spoken for? Each artefact speaks to one cadence period. Two quarterly artefacts speak to a hundred and eighty-two days of a two-hundred-and-seventy-three-day window, and say nothing at all about the rest.

The two can disagree. Four artefacts for three expected periods looks like a surplus and is usually the same quarter filed twice, which fills the arithmetic without filling the gap.

Below is the case: the nine-month window, a quarterly cadence, two artefacts that survive and are findable, and a hundred and eighty days between the two of them. Read the summary before touching anything.

Evidence coverage

Hypothetical model, not a forecast

How much of an observation window the recorded artefacts actually speak to, and how long the longest stretch is that nothing speaks to at all.

It assumes

One recorded instance speaks to exactly one cadence period of the window, no more.
Instances expected is the whole number of cadence periods that fit inside the window.
An instance recorded outside the window counts for nothing inside it.
Days covered are clamped to the window, so surplus artefacts cannot overfill it.
A quarter is treated as ninety-one days and a nine-month period as two hundred and seventy-three.

It ignores

Whether a recorded artefact shows the control worked or merely that somebody ticked a box
Where in the window the gap sits — a gap over a migration weekend is not the same as a gap in August, and this arithmetic cannot tell them apart
Overlap: two artefacts covering the same fortnight are counted as two fortnights here, which is why days covered is clamped to the window
Retention: an artefact that existed and was deleted is indistinguishable from one that never existed
Backdated and reconstructed evidence, which fills the arithmetic without filling the gap
Whether the cadence was ever the right cadence for the risk

Leave the cadence at ninety-one days. Raise the artefacts recorded until the model reports artefacts beyond what the cadence expects, and no days of the window left unspoken for.

Cadence91

Days between scheduled operations of the control: 7 weekly, 30 monthly, 91 quarterly — the same figures the consistency engine uses, so a lesson's arithmetic and the referee's agree.

Instances recorded2

Operations with an artefact that survives and is findable.

Days of the window an artefact speaks to: 182
Instances the cadence expects across the window: 3
Instances with a surviving artefact: 2
Expected instances with no artefact: 1
Longest stretch between consecutive artefacts, in days: 180
Scheduled operations that fall inside that stretch: 1.98
Days of the window no artefact speaks to: 91
Share of the window no artefact speaks to: 0.333
Artefacts beyond what the cadence expects: 0

Days an artefact speaks to
Days nothing speaks to

The uncovered line sits flat on zero while the window is short enough for two artefacts to cover it, then lifts away and climbs steadily once the window outgrows them.
Window length, in days	Days an artefact speaks to	Days nothing speaks to
7	7	0
14	14	0
30	30	0
60	60	0
90	90	0
120	120	0
180	180	0
270	182	88
273	182	91

Not there yet — keep moving the controls.

Three owed, two held, one missing. A hundred and eighty-two days of the window spoken for and ninety-one days — a third of it — spoken for by nothing at all.

Then the figure that is not about counting: the longest stretch between consecutive artefacts is a hundred and eighty days, and nearly two scheduled operations of the control fall inside it. That is the same shortfall described in a way that is much harder to live with, because one missing instance sounds like an administrative slip and six months with nothing in them does not.

The surplus that is not credit

Push the recorded count to four and the model reports one artefact beyond what the cadence expects, with nothing left unspoken for. Both figures look better and nothing about the quarter nobody did has changed.

This is why the model reports surplus separately instead of netting it against the missing instances. Four quarterly artefacts in a nine-month window almost never means the control ran four times. It means the same quarter is in the folder twice, or a monthly report got filed as a quarterly one, or somebody reconstructed March in October. The arithmetic cannot tell any of those apart from genuine diligence, so it refuses to average them away.

When the cadence changed in the middle of the periodOptional

The division only works while there is one cadence.

Move the control from quarterly to monthly in May and the expected count is two arithmetics stitched together: whole quarters up to the change, whole months after it, and a stub in between belonging to neither. The model takes one cadence, so it will give you the right answer to a question that is no longer the one you have.

Two honest ways through. Run it twice, once over each part of the period with its own cadence, and add the two expected counts — which is correct and makes the stub a decision you have to state rather than one the arithmetic hides. Or run it at the slower cadence across the whole window, which understates what you owe and is the conservative direction for a count you are going to present.

The one thing worth avoiding is running it at the faster cadence across the whole window, which manufactures missing instances for months when nobody had promised them.

Check

A monthly control, a twelve-month window, eleven artefacts held.

One missing instance, and roughly a month unspoken forNothing missing, because eleven out of twelve rounds to completeTwelve missing, since no artefact covers the whole windowCannot be answered without knowing the dates of the eleven

Worth remembering

Instances owed is whole cadence periods inside the window: a quarterly control over nine months owes three.
Each artefact speaks to one cadence period, so two quarterly artefacts speak to a hundred and eighty-two days of two hundred and seventy-three.
The count and the coverage are different questions, and a bundle can pass one while failing the other badly.
The longest stretch between consecutive artefacts is the figure that is hard to live with, because six empty months do not sound like one missed instance.
Artefacts beyond what the cadence expects are reported separately rather than netted off, because they are usually the same period filed twice.
A cadence that changed mid-period makes the expected count two arithmetics stitched together, and the stub between them is a decision somebody has to state.