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Date:      Mon, 9 Jul 2012 12:58:14 -0700 (PDT)
From:      Jason Usher <jusher71@yahoo.com>
To:        Zaphod Beeblebrox <zbeeble@gmail.com>
Cc:        freebsd-fs@freebsd.org
Subject:   Re: vdev/pool math with combined raidzX vdevs...
Message-ID:  <1341863894.36655.YahooMailClassic@web122501.mail.ne1.yahoo.com>

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Hello again,=0A=0A=0A--- On Fri, 7/6/12, Zaphod Beeblebrox <zbeeble@gmail.c=
om> wrote:=0A=0A=0A> ... so, again with simplistic assumptions,=0A> =0A> p(=
36drz3 --- 12 drives, 3 groups) =3D p(12drz3) * 3=0A> =0A> A "vanilla" RAID=
-Z2 (if I make an assumption to what you're=0A> saying) is:=0A> =0A> p(36dr=
z2) =3D 36 * p(f) * 35 * p(f)=0A> =0A> ... but I can't directly answer you =
question without knowing=0A> a) the=0A> structure of the RAID-Z2 array and =
p(f).=A0 If we use a=0A> 1% figure for=0A> p(f), then P(36drz3,12,3) =3D 0.=
035% and p(36drz2) =3D 4.3%=0A=0A=0A(snip)=0A=0A=0A> Put simply, you add th=
e probabilities of things where any=0A> can cause=0A> the failure (either d=
rive of R0 failing, any one of the 3=0A> plexes of a=0A> complex array fail=
ing) and you multiply things where all=0A> must fail to=0A> produce failure=
.=0A=0A=0AOk.  So let's start with those numbers from that hardforum link I=
 posted:=0A=0A(probability of data loss during a rebuild)=0A=0ARAID-10: =0A=
F =3D 5%=0A=0ARAID-Z1:=0A1 - (1 - F)^(9 - 1) =3D 33.7%=0AF=3D 33.7%=0A=0ARA=
ID-Z2:=0A1 - (1 - F)^(10 - 1) - (10 - 1) F (1 - F)^(10 - 2) =3D 7.1%=0AF=3D=
7.1%=0A=0ARAID-Z3:=0A1 - (1 - F)^(11 - 1) - (11 - 1) F (1 - F)^(11 - 2) - (=
11 - 1)(11 - 2) F^2 (1 - F)^(11 - 3) / 2=0AF =3D 1.15%=0A=0AAgain, doesn't =
really matter what F is, since we are only interested in the comparison...=
=0A=0AFrom what you said, above, striping 3 different raidz3 arrays togethe=
r into one pool is ADDITIVE ... so the 1.15% rises to 3.45%.=0A=0AYes ?=0A=
=0ASo we triple our risk by running all three raidz3 arrays in one pool, bu=
t we still have less than half the risk of a single raidz2 vdev (with no st=
riping) which is 7.1%.=0A=0AAm I on the right track here ?  I think I'm mis=
sing something because with one raidz3, I have a 1.15% chance of "losing a =
drive during rebuild" but I am thinking about competely healthy arrays who =
have a larger chance of blowing up because ONE OF THE OTHER vdevs blows fou=
r drives simultaneously.  =0A=0ASo I am really comparing 0% probability (if=
 they aren't combined in a zpool, I can take one vdev out and run over it w=
ith a train and the other vdev is unharmed) with X% probability, because no=
w something happening in the other vdev can ruin the healthy one...=0A=0AAm=
 I really the only person worrying about the interactive failure properties=
 of combining vdevs into a pool ?



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