Solution Found!
In the article “Parameter Estimation with Only One
Chapter 4, Problem 9E(choose chapter or problem)
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 \(\alpha\) = 2.25 and \(\beta=4.474 x 10^{-4}\).
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?
Equation transcription:
Text transcription:
\alpha
\beta=4.474 x 10^{-4}
Questions & Answers
QUESTION:
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 \(\alpha\) = 2.25 and \(\beta=4.474 x 10^{-4}\).
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?
Equation transcription:
Text transcription:
\alpha
\beta=4.474 x 10^{-4}
ANSWER:
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.