Conversationally, you can describe system availability in terms of nines. A two nines (available 99% of the time) system would be built differently from a five nines system (99.999%).

Outside the realm of *high* availability, what could we call a system
available only 80% of the time? It’s
less than 90% (“one nine”), so it would strictly be zero nines. To be more
specific, we’ll need to introduce fractional nines. Having done that,
we could refer to it as 0.7 nines.

Let’s go through the math.

Start with the natural numbers. We have f:ℕ↦ℝ.

Nines | Availability (%) |
---|---|

1 | 90 |

2 | 99 |

3 | 99.9 |

4 | 99.99 |

5 | 99.999 |

Simplify by considering availability as a fraction (in [0,1]) rather than a percentage:

Nines | Availability |
---|---|

1 | 0.9 |

2 | 0.99 |

3 | 0.999 |

4 | 0.9999 |

5 | 0.99999 |

Note that this is exactly

$\mathrm{availability}\left(n\right)=1-{0.1}^{n}$In addition to the natural numbers, this function is defined for all reals. To plot using R:

avail <- function(n) { return(data.frame(n, a = 1 - 0.1 ^ n))} d_nat <- avail(1:7) d_real <- avail(seq(0, 7, 0.1)) svg(file = 'output.svg', width = 7, height = 5) ggplot() + geom_line(data = d_real, aes(x = n, y = a), color = 'red') + geom_point(data = d_nat, aes(x = n, y = a)) + coord_cartesian(ylim = c(0.75, 1), xlim = c(0, 6)) + xlab('Nines') + ylab('Availability') + scale_x_continuous(breaks=scales::pretty_breaks()) dev.off()

Here are some examples not restricted to natural nines.

“Nines” | Availability |
---|---|

0 | 0.0 |

0.1 | 0.2056718 |

0.5 | 0.6837722 |

1 | 0.9 |

1.5 | 0.9683772 |

3.5 | 0.9996838 |

Since the function is invertible, consider:

$\mathrm{nines}\left(a\right)=-{\mathrm{log}}_{10}(1-a)$Availability | “Nines” |
---|---|

0.0 | 0.0 |

0.09 | 0.04095861 |

0.5 | 0.30103 |

0.8 | 0.69897 |

0.9 | 1 |

So 80% availability is 0.69897, or approximately 0.7, “nines”. Likely nothing to boast about, but quantification is the first step.

(The 0.09 is included to foil attempts to consider a 9% available system as “one nine”: it’s 0.04 nines. However, extreme chutzpah may be appropriate in situations where a system is available less than ten percent of the time.)

(Music: Alkaline Trio, “We’ve Had Enough”)

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