Failure models
1
Summary
=
()
2. Cumulative failure density
=
0
3. Reliability function
R(t)=1-F(t)
1.
4.
=
()
()
2
Hazard function
The hazard function or hazard rate h(t) is the conditional
probability of failure in the interval t to (t+dt), given

System reliability
Reliability, R(t), is the
probability that a
body/equipment/device
performs adequately
over the interval [0,t].
Equipment/device
under consideration can
be an entire system, a
sub-system or a
component.
As an example, consider a mini

Design of experiments
Analysis of Variance
A fictive example is given*. Drilling bits at random are
selected and analysed for wearing. The results of abrasive
weara are given as:
8.36
9.02
2.91
5.62
3.83
9.70
3.17
6.32
1.25 10.37 12.15
7.34
5.41
6.01
6.07

Probability theory for reliability
analysis
Random variables
Sample estimate of population
parameters
Numerical descriptive measures are called
parameters for a population and statistics for a
sample.
These measures summarize in a population or
sample a

Introduction
Facts
Canada's mining industry plans to invest $136 billion in
projects over the next decade.
In 2010 capital spending in the Canadian mining industry
was $12.6 billion, which was 30% more from the previous
year.
Capital spends were on new

Data collection and preliminary
analysis of failure data
M Kumral
Reliability data
Best reliability data are those from a carefully
designed experiments in which all of the major
factors that could influence the response are
controlled.
This is particul

Parameter estimation
Graphical estimation
Graphical analysis of reliability data is based on the
concept of rectifying the data in such a way that
approximately straight lines can be generated when
the data are plotted. Then, the graph can be quickly
chec

Physical acceleration models
We are often unable to obtain a reasonable amount of test
data when stresses approximate normal use conditions.
Instead, components are forced to fail by testing at much
higher than the intended application conditions.
Acce