Weibull MTTF Numeric Integral

Problem

Mean time to failure of a Weibull life distribution is the integral of the reliability R(t) = exp(-(t / lam)^k) from 0 to infinity. Approximate it on [0, t_max] with the trapezoid rule using steps intervals. Return 0.0 for invalid arguments.

Hint

For k = 1 the exact MTTF is lam, and for k = 2 it is lam * Gamma(1.5).

Test cases

case 1

in: [1,1,20,1000]

expected: 1.0000333310498923

case 2

in: [2,1,50,2000]

expected: 2.000026041571072

case 3

in: [1,2,10,5000]

expected: 0.8862269254527574

case 4

in: [1,1,0,10]

expected: 0

Starter codePython

import math


def mttf_weibull_integral(lam, k, t_max, steps):
    # Your code here
    pass

4 test cases · run your code against them in the editor