Problem 9E

In the article “Parameter Estimation with Only One Complete Failure Observation” (W. Pang, P. Leung, et al., International Journal of Reliability, Quality, and Safety Engineering, 2001:109-122), the lifetime, in hours, of a certain type of bearing is modeled with the Weibull distribution with parameters α=2.25 and β = 4.474 x 10-4.

a. Find the probability that a bearing lasts more than 1000 hours.

b. Find the probability that a bearing lasts less than 2000 hours.

c. Find the median lifetime of a bearing.

d. The hazard function is defined in Exercise 8. What is the hazard at t = 2000 hours?

Solution:

Step 1 of 3:

In an article the lifetime in hours of a certain type of bearing in modeled with the weibull distribution with parameters and .

We have to find

- The probability that a bearing lasts more than 1000 hours.
- Probability that bearing lasts less than 2000 hours.
- Median lifetime of a bearing.
- If the hazard function of T is defined as h(t) = . Then what will be the hazard rate if t= 2000 hours.