Question

A Component has an exponential time-to-failure distribution with mean of 10,000 hours.

a) The component has already been in operation for its mean life. What is the probability that it will fail by 15,000 hours?

Answer 1

The probability that the component will fail by 15,000 hours is approximately 0.7769.

Step-by-step explanation:

Since the time-to-failure distribution follows an exponential distribution, we can use the formula:

P(X < x) = 1 - e^(-x/mean)

where X is the time-to-failure and mean is the average life of the component.

Given that the mean life is 10,000 hours:

P(X < 15,000) = 1 - e^(-15,000/10,000)

P(X < 15,000) = 1 - e^(-1.5)

P(X < 15,000) = 1 - 0.2231

P(X < 15,000) = 0.7769