Model

Losing every replica

Replication, quorums and erasure coding all divide by a failure probability that is assumed to be independent.

P (all n lost) = p^{n} (independent) vs \approx p_{common} (one common cause)

$p$: Failure probability; yearly probability that one disk fails
$n$: Replicas; copies kept
$p_{common}$: Common cause; yearly probability of a defect that takes all disks of the batch together

Recurring principle: Independence is assumed

How it behaves

One input on the horizontal axis, the others held fixed.

independent: pⁿone common cause at 5%

Data table

Yearly chance of losing every copy, by replicas (p = 1% per disk)
Replicas n	series	Chance all are lost in a year
1	independent: pⁿ	0.01
1.06	independent: pⁿ	0.008
1.13	independent: pⁿ	0.006
1.19	independent: pⁿ	0.004
1.25	independent: pⁿ	0.003
1.31	independent: pⁿ	0.002
1.38	independent: pⁿ	0.002
1.44	independent: pⁿ	0.001
1.5	independent: pⁿ	0.001
1.56	independent: pⁿ	0.001
1.63	independent: pⁿ	0.001
1.69	independent: pⁿ	0
1.75	independent: pⁿ	0
1.81	independent: pⁿ	0
1.88	independent: pⁿ	0
1.94	independent: pⁿ	0
2	independent: pⁿ	0
2.06	independent: pⁿ	0
2.13	independent: pⁿ	0
2.19	independent: pⁿ	0
2.25	independent: pⁿ	0
2.31	independent: pⁿ	0
2.38	independent: pⁿ	0
2.44	independent: pⁿ	0
2.5	independent: pⁿ	0
2.56	independent: pⁿ	0
2.63	independent: pⁿ	0
2.69	independent: pⁿ	0
2.75	independent: pⁿ	0
2.81	independent: pⁿ	0
2.88	independent: pⁿ	0
2.94	independent: pⁿ	0
3	independent: pⁿ	0
3.06	independent: pⁿ	0
3.13	independent: pⁿ	0
3.19	independent: pⁿ	0
3.25	independent: pⁿ	0
3.31	independent: pⁿ	0
3.38	independent: pⁿ	0
3.44	independent: pⁿ	0
3.5	independent: pⁿ	0
3.56	independent: pⁿ	0
3.63	independent: pⁿ	0
3.69	independent: pⁿ	0
3.75	independent: pⁿ	0
3.81	independent: pⁿ	0
3.88	independent: pⁿ	0
3.94	independent: pⁿ	0
4	independent: pⁿ	0
4.06	independent: pⁿ	0
4.13	independent: pⁿ	0
4.19	independent: pⁿ	0
4.25	independent: pⁿ	0
4.31	independent: pⁿ	0
4.38	independent: pⁿ	0
4.44	independent: pⁿ	0
4.5	independent: pⁿ	0
4.56	independent: pⁿ	0
4.63	independent: pⁿ	0
4.69	independent: pⁿ	0
4.75	independent: pⁿ	0
4.81	independent: pⁿ	0
4.88	independent: pⁿ	0
4.94	independent: pⁿ	0
5	independent: pⁿ	0
5.06	independent: pⁿ	0
5.13	independent: pⁿ	0
5.19	independent: pⁿ	0
5.25	independent: pⁿ	0
5.31	independent: pⁿ	0
5.38	independent: pⁿ	0
5.44	independent: pⁿ	0
5.5	independent: pⁿ	0
5.56	independent: pⁿ	0
5.63	independent: pⁿ	0
5.69	independent: pⁿ	0
5.75	independent: pⁿ	0
5.81	independent: pⁿ	0
5.88	independent: pⁿ	0
5.94	independent: pⁿ	0
6	independent: pⁿ	0
1	one common cause at 5%	0.05
1.06	one common cause at 5%	0.05
1.13	one common cause at 5%	0.05
1.19	one common cause at 5%	0.05
1.25	one common cause at 5%	0.05
1.31	one common cause at 5%	0.05
1.38	one common cause at 5%	0.05
1.44	one common cause at 5%	0.05
1.5	one common cause at 5%	0.05
1.56	one common cause at 5%	0.05
1.63	one common cause at 5%	0.05
1.69	one common cause at 5%	0.05
1.75	one common cause at 5%	0.05
1.81	one common cause at 5%	0.05
1.88	one common cause at 5%	0.05
1.94	one common cause at 5%	0.05
2	one common cause at 5%	0.05
2.06	one common cause at 5%	0.05
2.13	one common cause at 5%	0.05
2.19	one common cause at 5%	0.05
2.25	one common cause at 5%	0.05
2.31	one common cause at 5%	0.05
2.38	one common cause at 5%	0.05
2.44	one common cause at 5%	0.05
2.5	one common cause at 5%	0.05
2.56	one common cause at 5%	0.05
2.63	one common cause at 5%	0.05
2.69	one common cause at 5%	0.05
2.75	one common cause at 5%	0.05
2.81	one common cause at 5%	0.05
2.88	one common cause at 5%	0.05
2.94	one common cause at 5%	0.05
3	one common cause at 5%	0.05
3.06	one common cause at 5%	0.05
3.13	one common cause at 5%	0.05
3.19	one common cause at 5%	0.05
3.25	one common cause at 5%	0.05
3.31	one common cause at 5%	0.05
3.38	one common cause at 5%	0.05
3.44	one common cause at 5%	0.05
3.5	one common cause at 5%	0.05
3.56	one common cause at 5%	0.05
3.63	one common cause at 5%	0.05
3.69	one common cause at 5%	0.05
3.75	one common cause at 5%	0.05
3.81	one common cause at 5%	0.05
3.88	one common cause at 5%	0.05
3.94	one common cause at 5%	0.05
4	one common cause at 5%	0.05
4.06	one common cause at 5%	0.05
4.13	one common cause at 5%	0.05
4.19	one common cause at 5%	0.05
4.25	one common cause at 5%	0.05
4.31	one common cause at 5%	0.05
4.38	one common cause at 5%	0.05
4.44	one common cause at 5%	0.05
4.5	one common cause at 5%	0.05
4.56	one common cause at 5%	0.05
4.63	one common cause at 5%	0.05
4.69	one common cause at 5%	0.05
4.75	one common cause at 5%	0.05
4.81	one common cause at 5%	0.05
4.88	one common cause at 5%	0.05
4.94	one common cause at 5%	0.05
5	one common cause at 5%	0.05
5.06	one common cause at 5%	0.05
5.13	one common cause at 5%	0.05
5.19	one common cause at 5%	0.05
5.25	one common cause at 5%	0.05
5.31	one common cause at 5%	0.05
5.38	one common cause at 5%	0.05
5.44	one common cause at 5%	0.05
5.5	one common cause at 5%	0.05
5.56	one common cause at 5%	0.05
5.63	one common cause at 5%	0.05
5.69	one common cause at 5%	0.05
5.75	one common cause at 5%	0.05
5.81	one common cause at 5%	0.05
5.88	one common cause at 5%	0.05
5.94	one common cause at 5%	0.05
6	one common cause at 5%	0.05

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Where it appears

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Persistence & Durability
When a system says "yes, your data is safe", what exactly has it promised, and what did it have to do to keep that promise?
$p^{3} = 0.0 1^{3} = 1 0^{- 6}$
Read it in place →