Question

A device has a constant failure rate with a MTTF of 2 months. One hundred of the devices are tested to failure. (a) How many of the devices do you expect to fail during the second month

Answer 1

Answer: the number of devices expected to fail during the second month is 24

Step-by-step explanation:

Given that

The device has a constant failure rate with MTTF of 2 months.

As the device has constant failure rate so it has exponential failure distribution

f(t) = λe^-λt

Here MTTF = 1/ λ

so  λ = 1/2 Months⁻¹ = 0.5 Months⁻¹ and from the question,  Number of devices = 100

E( 1 < x < 2) = E ( x < 2) - E (x < 1)

so E(x < X) can be calculated with λ  = 0.5 Months⁻¹ will be calculated as the failure function

f(x) = λ exp ( - λ×t) for t > 0

F (x>0) = 1 - exp( - λx)

so E ( 1 < x < 2) = E ( x < 2) - E (x < 1)

E ( x < 2) = 1 - exp(-0.5 × 2) = 0.6321 ; E (x<1) = 1 - exp(-0.5 × 2) = 1 - exp( -0.5) = 0.3934

so E ( 1 < x < 2) = 0.6321 - 0.3934 = 0.2387

so the number of devices expected to fail during the second month is;

100 × 0.2387 = 23.87 ≈ 24