Question

4.9 An automotive powertrain system consists of engine, transmission, and axle subsystems connected in logic series. The reliability target of the powertrain system is 0.98 at 36 months. Allocate the reliability target equally to each subsystem. 4.10 Refer to Problem 4.9. The lives of the engine, transmission, and axle sub- systems are assumed to be exponentially distributed with 6.3 x 10-5,3.1 >x 10-5, and 2.3 x 10-5 failures per month, respectively. Determine the reli- ability target of each subsystem using the ARINC method.

Answer 1

Since the subsystem are connected in a series connection therefore the failure of one component lead to the failure of whole assembly.

In this case the product of reliability of all the three components is in turn equal to the total reliability of the assembly.

Q1

Given

Total reliability of the assembly = .98

we get

assembli

where R₁,R₂ and R₃ are the individual reliabilities of the subsystems.

Given equal reliability allocation for each subsystem or component,

i.e.

R1 = = = Y R2 R3

We have

Therefore

.....................................................................................

Q2

Here failures per month are given for each component.

Since the reliability follows exponential function. i.e.

$R= e^{-\lambda t}$

Where

λ = failure rate of th subsystem

λ1-6.3 * 10

Corresponding reliability

(given)

operating time 36 months

Therefore answer is-

R₁ =  $e^{-{\lambda_1}*t}$ =
0.9977346

R₂ =  $e^{-{\lambda_2}*t}$ =
0.9988

R₃ = $e^{-{\lambda_3}*t}$ =
0.9991723
.