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# Manual for Life Cost Based FMEA

system will shut down. First, we will consider systems that are not redundant and then consider systems that are in redundant.

a. No Redundancy in System

# We can estimate the availability of a system that has components in series

using the following equation:

A Sys

= (A single component

)n

(10)

Where A is availability and n is the total number of components in the system.

b. Redundancy in system

If the component has low reliability but the system requires a high availability, a redundant system is one solution to achieve the requirement. The engineer has to evaluate if it’s more cost effective to design and build a high reliability component or to build a redundant system.

Standby Reliability Model When identical components are in parallel and in a standby mode, only one component is activated at a time. If the active component fails the other component hooked up in parallel is switched on. The overall reliability is calculated as a two-part configuration: the reliability of the first component and the reliability of the second part, after the first part fails. Thus, the calculation becomes the unreliability of the first component multiplied by the reliability of the second part after the first part fails if we assume perfect switching. For components in parallel, we use the following equation to calculate MTBF:

MTBFSet = n = i i 1 1 λ

(11)

where n is the number of identical component in parallel and λ is the failure

rate

of

one

component.

Thus,

for

two

identical

components

in

parallel

redundancy the expected MTBF of the set becomes 2/ λ. For example, if the MTBF of a motor is 50,000 hours, a redundant system with two identical motors will yield a MTBF of 100,000 hours.

Standby Reliability with Repair For identical components that are in parallel and one is repaired without interrupting the system, the following reliability equation is used to calculate the set.

k 1 = λ 1 + λ 2 + r k 2 = λ 1 λ 2

FMEA MANUAL By S. Rhee and C.M. Spencer

19/26

January 2009

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