Reliability

Question 1

What is the deterministic approach to reliability

Answer 1

the focus on the physical processes leading to failure or failure mechanism

Question 2

The assumption that failure behaves as a chemical process gives us what

Answer 2

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

Question 3

from the Arrhenius model for reaction rate, the MTTF is given by

Answer 3

MTTF = to * e^(Ea/nkT)

- Ea/n = effective activation energy

Question 4

What are the 3 failure mechanisms in IC’s

Answer 4

• Corrosion;
• Electro-migration;
• Purple Plague

Question 5

Describe the corrosion failure mechanism (hint: 2types)

Answer 5

• Anodic which independent of temp

- cathodic which temp dependent (Ea/n = 0.5eV)

Question 6

Describe Electromigration

Answer 6

-Temp dependent with Ea/n = 0.5-0.8 eV

Question 7

Purple Plague

Answer 7

-temp dependent with Ea/n = 1eV

Question 8

In statistical reliability, a judgement about the expected reliability of a future system is made on
the basis of:

Answer 8

• Information about the field behavior of previously produced.
• Results of artificially accelerated reliability measurements of current components.

Question 9

what is the failure distribution and it’s equation

Answer 9

the probability a system will fail at T, before or after t

• aka measure of unreliability
• F(t) = P(T

Question 10

What is the reliability function?

Answer 10

• probabilty of survival between 0-t
• aka measure of reliability
• R(t)= P(T>=t) = 1 - F(t) (failure distribution)

Question 11

what is the equation for the probability failure density

Answer 11

f(t) = dF(t)[failure distribution]/dt = -dR(t)[Reliability function]/dt

Question 12

what is the hazard rate and its equation

Answer 12

conditional probability of system failure between t - t +dt[small change in t]
- z(t) = f(t)/R(t)

Question 13

what is the hazard rate in terms of reliability

Answer 13

int. z(t) between 0-t = -ln(R(t)/R(0))

Question 14

how does one obtain the MTTF from the reliability function

Answer 14

MTTF = int. R(t) between 0-infinity

Question 15

When is the negative exponential distribution used

Answer 15

• when components fail independently of each other

- when there is failure at random moments with a constant hazard rate ie. z(t) = lambda [constant]

Question 16

how does a constant hazard rate give a negative exponential distribution

Answer 16

int lambda[hazard rate] between 0-infinity = -ln(R(t)/R(0)) ==> R(t) = R(0) * e^-(lambda*t)

Question 17

give the failure distribution in terms of reliability when there is a constant hazard rate

Answer 17

F(t) = 1 - R(0) * e^-(lambda * t)

Question 18

give the MTTF when there is a constant hazard rate

Answer 18

MTTF = R(0)/lambda

Question 19

for a series system, what is the reliability function R(t)

Answer 19

R(t) = ∏R(t) [for each component, n calculate the product of their own reliability functions]

Question 20

in a series system for n identical components with reliability function given by Ro(t), the system reliability function is given by

Answer 20

R(t) = (Ro(t))^n

Question 21

what is series system

Answer 21

system where all components must function to work

Question 22

what is a parallel system

Answer 22

system where only 1 component must function to work

Question 23

for ACTIVE paralell systems, R(t) is

Answer 23

R(t) = 1 - ∏(1-Ri(t)) where i is each component

Question 24

if n components are indetical in a parallel system, the R(t) is

Answer 24

R(t)= 1 - (1-Ro(t))^n

Question 25

what is an m-out-of-n system

Answer 25

• system which isn’t pure series or pure parallel

- m/n components must function to work

Question 26

for n identical components in an ACTIVE m/n system, probability that m components function, R(t)

Answer 26

R(t) = ∑(n | i) *(Ro(t))^i * (1-Ro(t))^n-i

- n | i = n!/i!(n-i)!)[binomial coefficients where i = m]

Question 27

In failure detection, what is a monitored system

Answer 27

• system used to check correct function of a system channel

- if monitors have a high reliability, n-1 failures are allowed in redundant channels

Question 28

what is a non-adaptive majority voting

Answer 28

m/n system where majority of functional components are required

Question 29

In non-AM voting, if n is even m is…

Answer 29

m= n/2 + 1

Question 30

in non-AM voting, if n is odd m is…

Answer 30

m= (n+1)/2

Question 31

what is Adaptive Majority voting (AM voting) and when is it used

Answer 31

• system where each time a voter finds a failed chanel, that channel is disconnected so it isnt included
• system continues so long as there are 2 functional channels ie. 2/n system
• used when n > 3

Question 32

what makes a system active

Answer 32

when system is sharing power generation

Question 33

What would a typical RST cycle consist of

Answer 33

• soak in an environmental chamber at 70 degrees for a given period
• rapidly cooled to -55 degrees in the space of 20 minutes; left to soak at this temperature for a given period
• meanwhile subjected to vibrations during the hot and cold soaking periods