Question

The lifetime of a drill bit in a mechanical operation, in hours, has a Weibull distribution with α = 0.5 and β = 2.2. Calculate the probability that the bit will fail after 2.8 hours

Answer using 4 decimals.

Answer 1

1 Solution : in hours let Jandom variable x represent the life trimetich a drill bit un mechanical operation x fallours weifell distribution, coith the parameters a 2=0.5 and ß=2.2 The probability density function of a us: 0:5 (2.2) 21 2.2 2.2-1 -0.52 е 270 f(x;0.5, 22); { 0; fet calculate the probability that the but will ofoil before essage 2.8 hours of P(x528) F(2.8) = 1-2-0.5x462 si-e-0.5 x(2-8)2:2 e Einė4.816 -1-0.0081 10.9919 ñ 1