# Manual for Life Cost Based FMEA

probably the most overused and incorrectly used distribution (Wasserman, 2003). In the real world, processes are noisy and do not conform to a nice bell shape curve. It also has infinite tails at both ends. Since ILC failures are not process oriented failures, we will not use the normal distribution.

4.2.1. Exponential distribution The exponential distribution is widely used in electronics and probabilistic modeling. It is applicable for modeling constant failure-rate phenomena.

## R(t) = e^{-λt }

The unique property of the exponential distribution is:

∫ ∞ = 0 M T T F

R(t) =

1 λ

The exponential distribution is widely used for modeling time-to-failure of electronic components. It is also widely used to model failure at the system level. Component manufacturers usually specify the MTTF for their component and this value can be used to model the overall MTTF of the system.

When multiple components are in series and if one fails the whole system shuts down, the MTBF of the overall system uses the following equation:

n

^{MTBF = }∑

i =1

1 i λ

(13)

where n is the number of components in the system. Thus, for n components of identical failure rate λ, the expected MTBF = n/λ.

4.2.2

Weibull distribution Weibull is a distribution that can be modeled for a wide range of phenomena. The Weibull distribution is expressed in the form of:

λ(t) =

1 ) ( − β θ θ β t

Where λ is decreasing with time for β<1; it is increasing with time for β>1; and β

=1 corresponds to a constant failure-rate. β is the shape factor and θ is the mean

time to failure. phenomena that corrosion, creep,

The three parameter Weibull distribution is take a shortest time to evolve, such as failures and other degradation phenomena.

used

to model

due

to fatigue,

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

21/26

January 2009