Hand calculation Suppose that a new component is designed of

[Hand calculation] Suppose that a new component is designed, of which time to failure can be modeled by exponential distribution with constant failure rate (denoted by lambda [1/hours]). For safety design, let us consider estimating the failure rate lambda [1/hours] of the component using Bayesian updating. Based on the expert opinion, the prior distribution of lambda is uniform distribution between 1.0 x 10^-5 and 1.0 X 10^-3 a. Write the equation of prior distribution pi (lambda). Specify the domain clearly.

Solution

If x is the time to failure of the new component

then X is exponential with parameter lemda

Lemda is following a uniform distribution between 10^-5 and 10^-3

Expected value of lemda = 10^-3-10^-5

= 0.00099

Hence equation of prior distribution of lemda = uniform

and x follows exponential with lemda =0.00099