RELIABILITY ENGINEERING I
MODULE 3.3
Moment Es*ma*on
Example 3.3.1: Ten iden6cal devices are tested un6l
failure at 6mes:
tn = 1.7, 3.5, 5.0, 6.5, 8.0, 9.6, 11.0, 13.0, 18.0, 22.0
Markov Process
()
Given a stochas-c process whose state at -me t is X t , and whose history of
states is X s , s t, the process is a con-nuous Markov process i
<
()
Pr
Module 3.6
Goodness of Fit X2 Test
Goodness of Fit X2 Test
Let us now consider the t ask of tes=ng whether our
data set ts a par=cular distribu=on.
This task is called tes=ng for goodnessoft, i.e.
Does
RELIABILITY ENGINEERING I
MODULE 4.3
Fault Tree/Event Tree Methodology
1
Fault Trees
Faulttrees are logic diagrams that link primary or
secondary faults (Basic Events) to an undesirable
RELIABILITY ENGINEERING I
MODULE 4.2
Failure Modes and Eects Analysis
The FMEA was rst developed by the aerospace industry in mid 60's. The FMEA analysis describes
inherent causes of events that l
RELIABILITY ENGINEERING I
MODULE 2.5
Discrete Probability Distribu0ons
Commonly Used in Reliability
Engineering
1
Some Deni:ons
Consider a discrete random variable r.
The mean or expected value
RELIABILITY ENGINEERING I
MODULE 2.6
Con0uous Probability Distribu%ons
Commonly Used in Reliability
Engineering
1
Some Deni:ons
expected value E( t ) mean m dt t p( t )
0
2
2
variance Var( t ) dt ( m t ) p( t )
0
2
Module 3.5
Condence Intervals
Instead of being interested in a point es:mate, we
may be interested in an interval on parameter of
our distribu:on, where we know we will nd with
probability .
We denote this i
Module 4.4
Common Cause Failures
Physical Elements of a Dependent Event
Component
A
Root Cause
Hardware
Human
Environmental
External to system
Coupling
Mechanism
Func;onal
Spa;al
Human
Component
B
Component
C
2
Dependent Fa
Markov Models and Availability Part II
Example
Derive the availability of a system of two iden7cal units in which either unit fails
during opera7on at a rate , but only one unit is required to make the system
fu
RELIABILITY ENGINEERING I
MODULE 4.1
Reliability Block Diagrams
A reliability block diagram is a graphical procedure, which
describes the system opera?on in terms of successful
"signal" transmission be
Module 3.1
Probability Plo2ng
Probability plo,ng is the least mathema3cally intensive
method of parameter es3ma3on.
The method involves a physical plot of the data on a specially
constructed paper
RELIABILITY ENGINEERING I
MODULE 2.3
Probability Distribu>on
Func>ons
Probability Distribu.on Func.ons
Let p(x)dx be the probability that the stochas.c
variable x is between x and x+dx. The p(x)
RELIABILITY ENGINEERING I
MODULE 2.4
Probability Concepts for Failure Analyses
1
Probability Concepts for Failure Analysis
Failure: Total loss of design func1on
DegradaHon: Par1al loss of de
RELIABILITY ENGINEERING I
MODULE 3.2
Maximum Likelihood Es1mator
The maximum likelihood es?mator es?mates
the M parameters of the distribu?on
f (t, 1, 2 , ., M ) (m = 1,., M )
From
ln L = 0, (m =