634 Chapter 19 Probability and Statistics in Engineering
Statistical models are being used increasingly more often by practicing engineers to
address quality control and reliability issues, and to perform failure analyses. Civil
engineers use statistical models to study the reliability of construction materials
and structures, and to design for flood control and water supply management. Elec-
trical engineers use statistical models for signal processing or for developing voice-
recognition software. Mechanical engineers use statistics to study the failure of
materials and machine parts, and to design experiments. Manufacturing engineers
use statistics for quality control assurance of the products they produce. These are
but a few examples of why an understanding of statistical concepts and models is
important in engineering. We will begin by explaining some of the basic ideas in
probability and statistics. We will then discuss frequency distributions, measure of
central tendency (mean and median), measure of variation within a data set (stan-
dard deviation), and normal distributions.
19.1 Probability–Basic Ideas
If you were to ask your instructor how many students are enrolled in your engineering class this
semester, she could give you an exact number: say 60. On the other hand, if you were to ask her
how many students will be in the class next year, or the year after, she would not be able to give
you an exact number. She might have an estimate based on trends or other pieces of informa-
tion, but she cannot know exactly how many students will be enrolled in the class next year.
The number of students in the class next year, or the year after, israndom. There are many sit-
uations in engineering that deal with random phenomena. For example, as a civil engineer, you
may design a bridge or a highway. It is impossible for you to predict exactly how many cars will
use the highway or go over the bridge on a certain day. As a mechanical engineer, you may design
a heating, cooling, and ventilating system to maintain the indoor temperature of a building at a
comfortable level. Again, it is impossible to predict exactly how much heating will be required
on a future day in January. As a computer engineer, you may design a network for which you can-
not predict its future usage exactly. For these types of situations, the best we can do is to predict
outcomes using probabilitymodels.
Probability has its own terminology; therefore, it is a good idea to spend a little time
to familiarize yourself with it. In probability, each time you repeat an experiment is called
atrial. The result of an experiment is called anoutcome. Arandom experimentis one that
has random outcomes — random outcomes cannot be predicted exactly. To gain a better
understanding of these terms, imagine a manufacturing setting wherein cell phones are
being assembled. You are positioned at the end of the assembly line, and in order to per-
form a final quality check, you are asked to remove cell phones at random from the assem-
bly line and turn them on and off. Each time you remove a cell phone and turn it on and
off, you are conducting arandom experiment. Each time you pick up a phone is atrial,
with a result that can be marked as a good phone or a bad phone. The result of each exper-
iment is called anoutcome. Now, suppose in one day you check 200 phones, and out of
these phones, you find five bad phones. Then, the relative frequencyof finding bad phones
is given by 5/200 0.025. In general, if you were to repeat an experimentntimes underCopyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀