082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

28 Probability
Contents 28.1 Introduction 903
28.2 Introducingprobability 904
28.3 Mutuallyexclusiveevents:theadditionlawofprobability 909
28.4 Complementaryevents 913
28.5 Conceptsfromcommunicationtheory 915
28.6 Conditionalprobability:themultiplicationlaw 919
28.7 Independentevents 925
Reviewexercises28 930
28.1 INTRODUCTION
Probability theory is applicable to several areas of engineering. One example is reliabilityengineeringwhichisconcernedwithanalysingthelikelihoodthatanengineering
system will fail. For most systems calculating the exact time of failure is not feasible
but it is often possible to obtain a good estimate of whether or not a system will fail in
a certain time interval. This is useful information to have for any engineering system,
butitisvitalifthefailureofthesystemresultsinthepossibilityofinjuryorlossoflife.
Examplesincludethefailureofhigh-voltageswitchgearsothatthecasingbecomeslive,
or electricalequipment producing a spark whilebeing usedunderground inamine.
Probability theory is also used extensively in production engineering, particularly in
the field of quality control. No manufacturing process produces components of exactly
the same quality each time. There is always some variation in quality and probability
theory allows this variation to be quantified. This enables some predictability to be introduced
into the activity of manufacturing and gives an engineer the confidence to say
components of a certainquality can be supplied toacustomer.
Afinalexampleisinthefieldofcommunicationengineering.Communicationchannelsaresubjecttonoisewhichisrandominnatureandsoismostsuccessfullymodelled
usingprobabilitytheory. We will examine some ofthese concepts inmore detailinthis
chapter.