What is the probability of an item failing in less than 5 hours if it has a constant failure rate of 1/hour?
What is the probability of an item failing in less than 5 hours if it has a constant failure rate of 1/hour?
If an item has a constant failure rate (lambda) of 1/hour, we can model the time to failure using the exponential distribution. The probability that an item fails within a certain time (t) is given by the cumulative distribution function (CDF) of the exponential distribution, which is 1 - e^(-lambda*t). Here, lambda = 1 and t = 5. Thus the probability of an item failing in less than 5 hours is 1 - e^(-1*5) = 1 - e^(-5). The approximate value of e^(-5) is 0.00674, so 1 - e^(-5) is approximately 0.99326.
How is this calculated? CAn someone point me to the page in CQE handbook 4th edition?
0.993 is failure within 1 hrs.