Question

In the article “Parameter Estimation with Only One Complete Failure Observation” (W. Pang, P. Leung et al., In the International Journal of Reliability, Quality, and Safety Engineering, 2001: 109-122), the duration is modeled, in hours , of a certain type of bearing with the Weibull distribution with parameters  = 2.25 and  = 4.474x10-4. (3p) a) Determine the probability that a bearing will last more than 1 000 hours. b) Determine the probability that a bearing will last less than 2,000 hours. c) Determine the median duration of a bearing.

Answer 1

Given,

= 2.25

= 4.474 x 10^-4

a)

For Weibull distribution, P(X > x) =

Probability that a bearing will last more than 1 000 hours = P(X > 1000)

=

= 0.8489912

b)

For Weibull distribution, P(X < x) =

Probability that a bearing will last less than 2,000 hours = P(X < 2000)

=

= 0.5410086

c)

Median duration of a bearing =

=

= 1899.152 hours