Reliability Flashcards
What is the deterministic approach to reliability
the focus on the physical processes leading to failure or failure mechanism
The assumption that failure behaves as a chemical process gives us what
the Arrhenius model for reaction rate, Q= Qo*e^(-Ea/kT)
- Ea = activation energy, eV
- k = boltzmann constant, 8.6 *10^-5
- T = temp in K
from the Arrhenius model for reaction rate, the MTTF is given by
MTTF = to * e^(Ea/nkT)
- Ea/n = effective activation energy
What are the 3 failure mechanisms in IC’s
- Corrosion;
- Electro-migration;
- Purple Plague
Describe the corrosion failure mechanism (hint: 2types)
- Anodic which independent of temp
- cathodic which temp dependent (Ea/n = 0.5eV)
Describe Electromigration
-Temp dependent with Ea/n = 0.5-0.8 eV
Purple Plague
-temp dependent with Ea/n = 1eV
In statistical reliability, a judgement about the expected reliability of a future system is made on
the basis of:
- Information about the field behavior of previously produced.
- Results of artificially accelerated reliability measurements of current components.
what is the failure distribution and it’s equation
the probability a system will fail at T, before or after t
- aka measure of unreliability
- F(t) = P(T
What is the reliability function?
- probabilty of survival between 0-t
- aka measure of reliability
- R(t)= P(T>=t) = 1 - F(t) (failure distribution)
what is the equation for the probability failure density
f(t) = dF(t)[failure distribution]/dt = -dR(t)[Reliability function]/dt
what is the hazard rate and its equation
conditional probability of system failure between t - t +dt[small change in t]
- z(t) = f(t)/R(t)
what is the hazard rate in terms of reliability
int. z(t) between 0-t = -ln(R(t)/R(0))
how does one obtain the MTTF from the reliability function
MTTF = int. R(t) between 0-infinity
When is the negative exponential distribution used
- when components fail independently of each other
- when there is failure at random moments with a constant hazard rate ie. z(t) = lambda [constant]
how does a constant hazard rate give a negative exponential distribution
int lambda[hazard rate] between 0-infinity = -ln(R(t)/R(0)) ==> R(t) = R(0) * e^-(lambda*t)
give the failure distribution in terms of reliability when there is a constant hazard rate
F(t) = 1 - R(0) * e^-(lambda * t)
give the MTTF when there is a constant hazard rate
MTTF = R(0)/lambda
for a series system, what is the reliability function R(t)
R(t) = ∏R(t) [for each component, n calculate the product of their own reliability functions]
in a series system for n identical components with reliability function given by Ro(t), the system reliability function is given by
R(t) = (Ro(t))^n
what is series system
system where all components must function to work
what is a parallel system
system where only 1 component must function to work
for ACTIVE paralell systems, R(t) is
R(t) = 1 - ∏(1-Ri(t)) where i is each component
if n components are indetical in a parallel system, the R(t) is
R(t)= 1 - (1-Ro(t))^n
