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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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A fault-tolerant system that processes transactions for a

Chapter 3, Problem 131E

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QUESTION:

Problem 131E

A fault-tolerant system that processes transactions for a financial services firm uses three separate computers. If the operating computer fails, one of the two spares can be immediately switched online. After the second computer fails, the last computer can be immediately switched online. Assume that the probability of a failure during any transaction is 10◊◊◊ and that the transactions can be considered to be independent events.

(a) What is the mean number of transactions before all computers have failed?

(b) What is the variance of the number of transactions before all computers have failed?

Questions & Answers

QUESTION:

Problem 131E

A fault-tolerant system that processes transactions for a financial services firm uses three separate computers. If the operating computer fails, one of the two spares can be immediately switched online. After the second computer fails, the last computer can be immediately switched online. Assume that the probability of a failure during any transaction is 10◊◊◊ and that the transactions can be considered to be independent events.

(a) What is the mean number of transactions before all computers have failed?

(b) What is the variance of the number of transactions before all computers have failed?

ANSWER:

Solution 131E

Step1 of 3:

Let us consider a random variable X it presents the number of transactions before all computers have failed. Also we have r = 3 and

Here our goal is:

a). We need to find the mean number of transactions before all computers have failed.

b). We need to find the variance of the number of transactions before all computers have failed.

Step2 of 3:

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