Reliability and Safety of Complex Technical Systems and Processes: Modeling – Identification – Prediction - Optimization

418 Pages·2011·4.888 MB·English

by  Krzysztof Kołowrocki, Joanna Soszyńska-Budny (auth.)

Springer Series in Reliability Engineering
For furthervolumes:
http://www.springer.com/series/6917
Krzysztof Kołowrocki
•
Joanna Soszyn´ska-Budny
Reliability and Safety of
Complex Technical Systems
and Processes
Modeling—Identification—Prediction—
Optimization
123
Krzysztof Kołowrocki Joanna Soszyn´ska-Budny
Maritime University Maritime University
ul. Morska81-87 ul. Morska81-87
81-225 Gdynia 81-225 Gdynia
Poland Poland
e-mail: [e-mail] e-mail: [e-mail]
ISSN 1614-7839
ISBN 978-0-85729-693-1 e-ISBN978-0-85729-694-8
DOI 10.1007/978-0-85729-694-8
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Preface
This book is concerned with the identification, evaluation, prediction and opti-
mization of operation, reliability, availability and safety of technical systems
related to their operation processes. The main emphasis is on multi-state systems
composed of ageing components and changing their structures and their compo-
nent’s reliability and safety characteristics during the operation processes. In this
book these systems are called the complex technical systems. The practical
importanceofsuchanapproachinreliabilityandsafetyidentification,assessment
and prediction, and analyzing the effectiveness of operation processes of real
technical systems is evident.
Mostrealtechnicalsystemsareverycomplexanditisdifficulttoanalyzetheir
reliability, availability and safety. Large numbers of components and subsystems
andtheiroperatingcomplexitycausetheidentification,evaluation,predictionand
optimization of their reliability, availability and safety to be complicated. The
complexityofthesystems’operationprocessesandtheirinfluenceonchangingin
time the systems’ structures and their components’ reliability characteristics are
very often metinreal practice. We meet complextechnical systems, forinstance,
in piping transportation of water, gas, oil and various chemical substances.
Complex technical systems are also used in electrical energy distribution, in
telecommunication, in rope transportation, in maritime transport and in shipyard
andporttransportsystemsusingbeltconveyersandelevators.Ropetransportation
systems such as port elevators and ship-rope elevators used in shipyards during
ship docking and undocking are model examples of such systems.
Taking into account the importance of the safety and operating process
effectivenessofsuchsystemsitseemsreasonabletoexpandthetwo-stateapproach
tomulti-stateapproachintheirreliabilityandsafetyanalysis.Theassumptionthat
the systems are composed of multi-state components with reliability states or
safety states degrading in time gives the possibility for more precise analysis of
their reliability, safety and operation processes’ effectiveness. This assumption
allowsustodistinguishasystemreliabilityorsafetycriticalstatetoexceedwhich
iseitherdangerousfortheenvironmentordoesnotassurethenecessarylevelofits
operation process effectiveness. Then, an important system reliability or safety
v
vi Preface
characteristic is the time to the moment of exceeding the system reliability or
safety critical state and its distribution, which is called the system risk function.
Thisdistributionisstrictlyrelatedtothesystemmulti-statereliabilityfunctionand
thesystemmulti-statesafetyfunctionandthesearethebasiccharacteristicsofthe
multi-state system. In the case of large systems, the determination of the exact
reliability functions of the systems and the system risk functions leads us to very
complicatedformulaethatareoftenuselessforreliabilitypractitioners.Oneofthe
important techniques in this situation is the asymptotic approach to system reli-
abilityevaluation.Inthisapproach,insteadofthepreliminarycomplexformulafor
the system reliability function, after assuming that the number of system com-
ponentstendstoinfinityandfindingthelimitreliabilityofthesystem,weobtainits
simplified form. This aspect of complex technical systems is also considered in
this book.
Theconvenienttoolsforanalyzingtheseproblemsaresemi-Markovmodeling
the systems’ operation processes and multi-state approach to the systems’ reli-
ability evaluation that is proposed in this book.
Theaimofthisbookistopresentthegeneralreliability,availabilityandsafety
analytical models of complex non-repairable and repairable multi-state technical
systemsrelatedtotheiroperationprocessesthataredevelopedbytheauthorandto
apply them practically to real industrial systems and processes. The integrated
generalmodelsofcomplexindustrialsystems,linkingtheirreliability,availability
andsafetymodelswiththeiroperationprocessmodelsandconsideringvariablein
different operation states their reliability and safety structures and their compo-
nents reliability and safety parameters are proposed. The common usage of the
multi-state systems’ reliability and availability models and the semi-Markov
model for the systems’ operation processes in order to construct the joint general
system reliability and availability models related to their operation process is the
mainideaofthebook.Thejointmodelslinkingthereliabilityandsafetymodelsof
the multi-state systems and their varying in time operation processes models are
constructed and applied in the reliability, availability and safety analysis of real
complextechnicalsystems.Thesejointreliabilityandsafetymodelstogetherwith
the linear programming are proposed for the reliability, availability and safety
optimization and operation cost analysis of the complex technical systems.
The models and methods proposed in this book proposed in the book models
and methods are applied to reliability, availability and safety analysis, identifi-
cation,predictionandoptimizationoftheportandmaritimetransportationsystems
related to varying in time their operation processes, structures and components
reliability and safety parameters.
This book delivers a complete elaboration of the state of art on the method of
reliability and safety identification, evaluation, prediction and optimization for as
wideaspossiblearangeofcomplextechnicalsystems.Pointingoutthepossibility
ofthismethod’sextensivepracticalapplicationintheoperatingprocessesofthese
systems is also an important reason for this book. This book contains complete
actual solutions of the formulated problems for the considered complex technical
systems in the case of the exponential multi-state reliability functions of their
Preface vii
components.Thisassumptionisnecessaryintheanalyticalapproachtothesubject
considered.
This book consists of a Preface, Chaps. 1–7 presenting the main theoretical
results and their practical applications, Summary and Appendices including sta-
tistical tables that are used in the book. References suitable to the subjects con-
sidered in the particular chapters are provided at the end of each chapter.
In the Preface, the book introduction and its contents are presented.
In Chap. 1, the basic notions of ageing multi-state systems reliability analysis
are introduced. The system components and the system multi-state reliability
functions are defined. The mean values and variances of the multi-state systems’
lifetimesinthereliabilitystatesubsetsandthemeanvaluesoftheirlifetimesinthe
particular reliability states are defined. The multi-state system risk function and
themomentofexceedingbythesystemthecriticalreliabilitystateareintroduced.
Themulti-stateseries,parallel,‘‘moutofn’’,consecutive‘‘moutofn:F’’,series-
parallel, parallel-series, series-‘‘m out of k’’, ‘‘m out of l’’-series, series-consec-
i i
utive‘‘moutofk:F’’andconsecutive‘‘m outofl:F’’-seriesreliabilitystructures
i i
of the multi-state systems with degrading (ageing) components are defined and
theirreliabilityfunctionsdetermined.Asaparticularcase,thereliabilityfunctions
oftheconsideredmulti-statesystemscomposedofcomponentshavingexponential
reliabilityfunctionsaredetermined.Moreover,themulti-stateapproachtoanalysis
and defining the basic notions of the systems’ safety is proposed. The system
safety function and the system risk function that allow to define basic safety
structures of the multi-state systems composed of components with degrading
safety states are introduced. Applications of the proposed multi-state system
reliability and safety models to the evaluation and prediction of the reliability
characteristicsofanexemplarysystemandaportoiltransportationsystemandthe
safety characteristics of a maritime ferry technical system are presented as well.
InChap.2,theoperationprocessofthecomplextechnicalsystemisconsidered
and its operation states are introduced. The semi-Markov process is used to con-
struct a general probabilistic model of the considered complex technical systems
operation processes. To build this model the vector of probabilities of the system
operationprocessstrayingattheinitialoperationstates,thematrixofprobabilities
ofthesystemoperationprocesstransitionsbetweentheoperationstates,thematrix
of conditional distribution functions and the matrix of conditional density func-
tions of the system operation process conditional sojourn times at the operation
states are defined. To describe the system operation process the conditional
sojourn times at the particular operation states, the uniform distribution, the tri-
angular distribution, the double trapezium distribution, the quasi-trapezium dis-
tribution, the exponential distribution, the Weibull distribution and the chimney
distribution are suggested and introduced. Based on these assumptions from the
constructed model, the main characteristics of the system operation process are
found.Themeanvaluesofthesystemoperationprocessconditionalsojourntimes
at the particular operation states having these distributions are given. Moreover,
the distribution functions of the system operation process unconditional sojourn
times at the particular operation states, the mean values of the system operation
viii Preface
process unconditional sojourn times at the particular operation states, the limit
values of the transient probabilities of the system operation process at the par-
ticular operation states and the approximate mean values of the system operation
process total sojourn times at the particular operation states for the fixed suffi-
ciently large system operation time are determined. Applications of the proposed
modelfortheevaluationandpredictionoftheoperationprocesses’characteristics
oftheexemplarysystem,theportoiltransportationsystemandthemaritimeferry
technical system are presented as well.
In Chap. 3, there are presented the general reliability, availability and safety
analytical models of complex non-repairable and repairable multi-state technical
systems related to their operation processes. They are the integrated general
models of complex technical systems, linking their multi-state reliability, avail-
ability and safety models with their operation process models and considering
variable at the different operation states their reliability and safety structures and
their componentsreliabilityandsafety parameters. Theconditional reliabilityand
safety functions at the system particular operation states and independent of the
system particular operation states the unconditional reliabilityand safetyfunction
and the risk function of the complex technical systems are defined. These joint
models of the reliability, availability and safety and the variable in time system
operation processes are constructed for multi-state series, parallel, ‘‘m out of n’’,
consecutive ‘‘m out of n: F’’, series-parallel, parallel-series, series-‘‘m out of k’’,
‘‘m outofl’’-series,series-consecutive‘‘moutofk:F’’andconsecutive‘‘m outof
i i i
l: F’’-series systems. The joint models are applied for determining the reliability,
i
availability, renewal and safety characteristics of these systems related to their
varying in time reliability and safety structures and their components’ reliability
and safety characteristics. Under the assumption that the considered systems are
exponential,theunconditionalreliabilityandsafetyfunctionsofthesesystemsare
determined. Moreover, in the case of large-scale systems, the possibility of
combining the results coming from these joint models and the results concerning
the limit reliability functions of the considered systems is briefly presented. The
proposed models and methods are applied for the reliability and availability
analysis,evaluationandpredictionoftheexemplarytechnicalsystemandtheport
oil piping transportation system and for the safety analysis, evaluation and pre-
diction of the maritime ferry technical system related to varying in time their
operation processes, structures and components’reliability and safetyparameters.
In Chap. 4, there are presented the methods of identification of the operation
processesofcomplextechnicalsystems.Thesearethemethodsandproceduresfor
estimating the unknown basic parameters of the system operation process semi-
Markov model and identifying the distributions of the conditional system opera-
tion process sojourn times at the operation states. The formulae estimating the
probabilitiesofthesystemoperationprocessstrayingattheoperationstatesatthe
initial moment, the probabilities of the system operation process transitions
between the operation states and the parameters of the distributions suitable and
typical for the description of the system operation process conditional sojourn
times at the operation states are given. Namely, the parameters of the uniform
Preface ix
distribution, the triangular distribution, the double trapezium distribution, the
quasi-trapezium distribution, the exponential distribution, the Weibull’s distribu-
tion and the chimney distribution are estimated using the statistical methods such
as the method of moments and the maximum likelihood method. The chi-square
goodness-of-fit test is described and proposed to be applied for verifying the
hypotheses about these distributions’ choice validity. The procedure of statistical
data sets’ uniformity analysis based on Kolmogorov–Smirnov test is proposed to
beappliedtotheempiricalconditionalsojourntimesattheoperationstatescoming
from different realizations of the same complex technical system operation pro-
cess. The applications of the proposed statistical methods of the unknown
parametersidentificationofthecomplextechnicalsystemoperationprocessmodel
for determining the operation parameters of the exemplary system, the port oil
transportation system and the maritime ferry technical system are presented. The
procedure of testing the uniformity of statistical data sets is applied for the real-
izations of the conditional sojourn times at the operation states of the ferry tech-
nical system collected at two different operating conditions.
In Chap. 5, there are presented procedures and formulae estimating the
unknown parameters of the complex technical system components reliability and
safety models on the basis of statistical data coming from the components reli-
ability and safety states changing processes. The maximum likelihood method is
appliedtoestimatingtheunknownintensitiesofdeparturesfromthereliabilityand
safety state subsets of the multi-state system components having different expo-
nential reliability functions at various system operation states. This method is
appliedtothestatisticaldatacollectedindifferentkindsofempiricalexperiments,
includingcasesofsmallnumberofrealizationsandnon-completedinvestigations.
The goodness-of-fit test applied to verify the hypotheses concerned with the
exponential forms of the multi-state reliability functions of the particular com-
ponents of the complex technical systems at the variable operations conditions is
presented.Inthecaseoflackofdatacomingfromthecomponents’reliabilityand
safetystateschangingprocesses,thesimplifiedmethodofestimatingtheunknown
intensities of departures from the reliability and safety state subsets based on the
expertopinionsisproposed.Applicationsoftheproposedstatisticalmethodsofthe
unknown parameters identification of the complex technical system components
reliability and safety models to determine the reliability parameters of the
exemplarysystemandtheportoiltransportationsystemcomponentsandthesafety
parameters of the maritime ferry technical system components are presented as
well.
InChap.6,themethodsbasedontheresults ofthejointmodellinkingasemi-
Markovmodelingofthesystemoperationprocesseswithamulti-stateapproachto
system reliability and safety and the linear programming are proposed to the
complex technical systems at the variable operation conditions operation, reli-
ability, availability and safety optimization and cost analysis. The method of
optimizationofthecomplextechnicalsystemsoperationprocessesdeterminingthe
optimal values of limit transient probabilities at the system operation states that
maximizethesystemlifetimesinthereliabilityorsafetystatesubsetsisproposed.
x Preface
Thewayofoperationcostanalysisofthecomplextechnicalsystematthevariable
operation conditions and its application for the evaluation of the cost before and
after this system operation process optimization is presented. The methods of
corrective and preventive maintenance policy maximizing the availability and
minimizing the renovation cost of the complex technical systems at the variable
operation conditions are presented as well. The proposed methods are applied to
the operation, reliability and availability optimization and operation cost analysis
of the exemplary technical system and the port oil piping transportation system
andtotheoperationandsafetyoptimizationofthemaritimeferrytechnicalsystem
related to varying in time their operation processes, structures and components
reliability and safety parameters. The procedures of the corrective and preventive
maintenance policy optimization are proposed and applied to the exemplary sys-
tem, the port oil piping transportation system and the ferry technical system.
InthecomplementaryChap.7,themethodsbasedontheresultsincludedinthe
book that are not used in previous chapters, are applied to the reliability, avail-
ability and safety identification, prediction and optimization of various kinds of
systems. Direct applications of the results stated in the propositions of Chap. 3 to
the reliability, renewal and availability characteristics prognosis of the series and
parallel systems operating at the variable operation conditions are presented. The
results of the asymptotic approach to the reliability analysis of large systems are
applied tothereliabilitypredictionofthe large parallel-series system operating at
the varying conditions. The safety analysis of the steel cover is performed using
the results concerned with the consecutive ‘‘m out of n: F’’ systems. Finally, the
comprehensiveapplicationofthemethodsoftheoperation,reliability,renewaland
availability modeling, identification, prediction and optimization to the container
gantrycraneisperformedtopracticallyillustratetheoverallapproachtoreliability
and safety analysis of any complex technical systems.
This book concludes with a Summary that contains the evaluation of the
presented results, the formulation of open problems concerned with complex
technicalsystemsreliabilityandsafetyandtheperspectiveoffurtherinvestigations
on the considered problems.
Contents
1 Modeling Reliability and Safety of Multistate Systems
with Ageing Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Reliability Analysis of Multistate Systems . . . . . . . . . . . . . . . . 1
1.3 Safety Analysis of Multistate Systems . . . . . . . . . . . . . . . . . . . 22
1.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.4.1 Reliability of Exemplary System. . . . . . . . . . . . . . . . . . 24
1.4.2 Reliability of Port Oil Piping Transportation System. . . . 33
1.4.3 Safety of Maritime Ferry Technical System. . . . . . . . . . 40
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2 Modeling Complex Technical Systems Operation Processes. . . . . . 53
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.2 Semi-Markov Model of System Operation Process . . . . . . . . . . 53
2.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3.1 Operation Process of Exemplary System . . . . . . . . . . . . 62
2.3.2 Operation Process of Port Oil Piping Transportation
System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.3.3 Operation Process of Maritime Ferry
Technical System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3 Complex Technical Systems, Reliability, Availability
and Safety Evaluation and Prediction. . . . . . . . . . . . . . . . . . . . . . 79
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2 Reliability of Multistate Systems at Variable
Operation Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.3 Asymptotic Approach to Reliability of Large Multistate
Systems at Variable Operation Conditions . . . . . . . . . . . . . . . . 89
xi