Availability — nines and the downtime allowed per year, month and day

On the left, Availability is the input, set to 99.9% at first. Allowed downtime in the middle is 100 minus the availability, 0.1%.

The four cards on the right multiply that share by a period: a year in minutes and in hours, a month in minutes and a day in seconds. Number of nines, at the lower left, comes into use below. Changing the availability updates the other cards.

Allowed downtime is (1 − availability) × period

An availability of 99.9% means that 99.9% of the period is spent up. The remaining 0.1% is the downtime allowed. As a formula:

Allowed downtime = (1 − availability) × period

This page counts a year as 365 days, a month as 30 days and a day as 24 hours. Leap years and months of 28 or 31 days are left out, so the figures here are not approximations of a real calendar; they are exact for this assumption.

A year is 365 × 24 × 60 = 525,600 minutes, and 0.1% of that is 525.6 minutes. That is Downtime per year on Board 1; Downtime per year (hours) shows 8.76 hours. A month is 30 × 24 × 60 = 43,200 minutes, and 0.1% of that is 43.2 minutes. A day is 24 × 60 × 60 = 86,400 seconds, and 0.1% of that is 86.4 seconds.

Number of nines — how many 9s in a row

Availabilities such as 99%, 99.9% and 99.99% are sometimes named by how many 9s they contain. 99.9% has three 9s and is called three nines; 99.99% is four nines.

Number of nines on Board 1 is −log(1 − availability ÷ 100). At 99.9% the allowed share is 0.1%, which is 0.001, or one tenth multiplied together three times. So the number of nines is 3.

Changing the availability on Board 1 gives the following.

In every column, each extra nine divides the value by ten, because the allowed share is divided by ten.

Values without a run of 9s work in the same formula. With the availability at 99.5, the number of nines is 2.30103 and the downtime per year is 2,628 minutes, between two nines and three.

One more nine is one step on a log number line

Board 2 puts the downtime allowed per year for four availabilities on a log number line. Period on the left is in days, 365 at first. The four cards in the middle calculate period × 1440 (minutes in a day) × (1 − availability), and the number line on the right places the four values.

5,256, 525.6, 52.56 and 5.256 minutes sit at equal intervals. A log number line makes each step a factor of 10, so values that shrink to a tenth each time are evenly spaced.

With the period set to 30, the four values become 432, 43.2, 4.32 and 0.432 minutes. The spacing between the points stays the same, and the scale runs from 0.1 to 1,000.

99.9% and 99.99% differ by only 0.09 points — how different is the downtime they allow?

With the availability on Board 1 set to 99.9, the downtime allowed is 525.6 minutes (8.76 hours) a year, 43.2 minutes a month and 86.4 seconds a day.

Setting it to 99.99 raises the availability by 0.09 percentage points, the difference between two percentages. The allowed downtime becomes 52.56 minutes (0.876 hours) a year, 4.32 minutes a month and 8.64 seconds a day, each a tenth (a factor of 10) of the value at 99.9%. A tenth is also a 90% decrease; Percentage change covers how to work that out.

The gap looks small because both numbers are close to 100. The allowed downtime is set by what remains below 100%, which is 0.1% and 0.01%. Going from 0.1% to 0.01% divides what remains by ten.

The same holds for the other nines. From 99% to 99.9% is a difference of 0.9 points, and from 99.99% to 99.999% is 0.009 points, yet the allowed downtime falls by a factor of 10 both times. The gap in availability shrinks by a tenth at each step, while the ratio of allowed downtime stays at a tenth.

Joining parts — in series and in parallel

So far the availability has been that of a single unit. When something is built from several parts, the way they are joined changes the availability of the whole. Board 3 gives two ways of combining parts, with the availability of the whole and its downtime per year.

Series is on the left and parallel on the right. The two cards at the top are the inputs: the availability of a part and how many are joined. Below them are the availability of the whole and the downtime allowed per year.

In series, parts form one chain, and the whole is down when any one part is down. The availability of the whole is the product of the parts' availabilities. With parts at 99.9% and a count of 3, 99.9% × 99.9% × 99.9% = 99.7003%, about 99.7%. The downtime allowed per year is 1,575.22 minutes (about 26.25 hours), about 3 times the 525.6 minutes of a single part, because the allowed 0.1% is counted three times.

In parallel, any of the parts can do the same work, and the whole is down only when all of them are down at once. With parts at 99% and a count of 2, the share of time both are down is 1% × 1% = 0.01%. The availability of the whole is 1 − (1 − 0.99)² = 99.99%, and the downtime allowed per year is 52.56 minutes.

Series: whole = part^count　　Parallel: whole = 1 − (1 − part)^count

Here are the results as the count changes. The series part stays at 99.9% and the parallel part at 99%.

In series, each added part adds about the same amount of allowed downtime. In parallel, each added copy divides the allowed downtime by 100. With parts at 99%, two copies give 99.99% and three give 99.9999%.

The parallel calculation assumes three things. A part going down is independent of the others going down. Any one copy can carry all of the work. Switching between copies takes no time and does not itself fail. Where copies share a power supply or a configuration, they are not independent, and the availability of the whole falls below 99.99%.

What this calculation does and does not say

How availability is measured — over what period, and what counts as down — is defined per contract or per service. The calculation here is a starting point for that conversation, not a guarantee.

The boards give the total downtime allowed within a period. They do not fix the length of any one outage or the number of outages. 525.6 minutes in a year is the same total whether it comes in one outage or in many short ones.

The 365-day year and the 30-day month are assumptions chosen to make the figures exact. In a real calendar a month has 28 to 31 days and a leap year has 366.

Read next — Resistors in parallel — the combined resistance from the branch currents Another case of joining parts in parallel: adding the branch currents to find the combined resistance of two resistors.

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