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From: saxena@hpsal2.HP.COM (Nirmal Saxena)
Newsgroups: comp.arch
Subject: Re: Synchronizer failure; MTBF
Message-ID: <2280011@hpsal2.HP.COM>
Date: 7 Sep 89 21:08:44 GMT
References: <26811@obiwan.mips.COM>
Organization: HP System Architecture Lab, Cupertino
Lines: 35



I am not sure if your analysis is entirely correct:

>>First, let's compute the probability that one or more of the 50,000
>>systems will fail sometime within 5 years due to a synchronizer failure:
>>
>>	P = 50000 * [1 - exp(-5/100)]
>>      P = 1

P should be:

	P = 1 - [1 - exp(-5/100]^50000 which is approximately unity.

>>Let's see what happens if we let the probability of 100 or more
>>failures be 33 percent.  (Thus we have a 1-in-3 chance of being fired by
>>the Big Boss because of >99 synchronization failures in the field).
>>
>>
>>           P(100 or more failures
>> 0.33  =     out of 50,000 units     =  (50,000 / 100) * [1 - exp(-5/m)]
>>             over a 5 year period)

>>solving,
>>    m  =  required MTBF of synchronizer = 7,573 years

The correct equation should be:

    0.33 = (sum from i=100 to 50000) { C(50000,i)*[1-exp(-5/m)]^(50000-i)
						  *[exp(-5/m)]^i }

    Then we have to solve for m.

    Here C(50000,i) is 50000 choose i (binomial coefficient)
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