12 1. INTRODUCTION TO RELIABILITY IN MECHANICAL DESIGN
Table 1.3: Estimation of the reliability and the probability of failure of the components
Service Years One Year Two Years ree Years Four Years Five Years
Number of Working
Components
9989 9974 9961 9944 9917
Reliability 0.9989 0.9974 0.9961 0.9944 0.9917
Cumulative
Number of Failures
11 26 39 56 83
Probability of
Failure
0.0011 0.0026 0.0039 0.0056 0.0083
Example 1.2
It is assumed that a company designs and manufacture a mechanical unit with a reliability 0.95
for a service life of 2 years. Estimate how many of the mechanical units will fail at the end of
two years if 50,000 of the mechanical unit are in service.
Solution:
e reliability of the mechanical unit is 0.95. So, the probability of failure of the mechanical
unit will be:
F D 1 R D 1 0:95 D 0:05:
According to the definition of the probability of failure, the estimation of the numbers of failures
of the mechanical units at the end of 2 years in service will be:
n D F 50;000 D 0:005 50;000 D 2;500:
1.5 IMPORTANCE OF RELIABILITY
A component, device, or system is designed per specifications to properly and safely perform
its intended functions. However, throughout the history of engineering design some of them
failed to perform the intended functions. For instance, some caused disasters such as the Space
Shuttle Challenger Disaster, which happened on January 28, 1986, causing a financial loss of
around $3.2 billion as well as the tragic human loss of seven astronauts. e factor of safety,
is defined as the ratio of component material strength index, such ultimate strength, to the
component actual stress index such as component maximum stress. However, the intention of
the factor of safety is never used to predict or estimate the likelihood of component failure.
e reliability-based mechanical component can address this issue. It is commonly agreed that
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