Advances in reliability analysis and its applications

Springer Series in Reliability Engineering

Mangey Ram

Hoang Pham   Editors

Advances in

Reliability

Analysis and its

Applications

Springer Series in Reliability Engineering

Series Editor

Hoang Pham, Department of Industrial and Systems Engineering, Rutgers

University, Piscataway, NJ, USA

More information about this series at http://www.springer.com/series/6917

Mangey Ram • Hoang Pham

Editors

Advances in Reliability

Analysis and its Applications

123

Editors

Mangey Ram

Department of Mathematics

Graphic Era Deemed to be University

Dehradun, Uttarakhand, India

Hoang Pham

Department of Industrial

and Systems Engineering

Rutgers University

Piscataway, NJ, USA

ISSN 1614-7839 ISSN 2196-999X (electronic)

Springer Series in Reliability Engineering

ISBN 978-3-030-31374-6 ISBN 978-3-030-31375-3 (eBook)

https://doi.org/10.1007/978-3-030-31375-3

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Preface

Nowadays, in system reliability engineering, advances in reliability analysis is

perhaps one of the most multidimensional topics. This quick development has truly

changed the environment of system engineering and this global design. Now with

the help of simulations and virtual reality technologies, we can start more of the

modeling task.

The aspects dealt in chapter “Time Varying Communication Networks:

Modelling, Reliability Evaluation and Optimization” are (i) TVCN models for

representing features like mobility, links, and topology, (ii) description of the notion

of Time-Stamped-Minimal Path Sets (TS-MPS) and Time-stamped-minimal Cut

Sets (TS-MCS) for TVCNs as an extension of MPS and MCS, respectively, that are

widely used in static networks, (iii) techniques for enumerating TS-MPS and

TS-MCS, and evaluating reliability measure(s)—particularly two-terminal relia￾bility, expected hop, and slot counts along with some other related metrics, and

(iv) discussion on several recent optimization problems in TVCNs.

In chapter “Methods for Prognosis and Optimization of Energy Plants Efficiency

in Starting Step of Life Cycle”, appropriate methods are provided for prognosis and

optimizing the effectiveness based on the quality of design, production and testing,

assembly and trial release, exploitation, and development of procedures for prog￾nosis of the complex systems behavior based on the characteristics of certain

constituent elements of the system and the possible impact of human factors and

environment itself on the system.

In chapter “Planning Methods for Production Systems Development in the

Energy Sector and Energy Efficiency”, methods used in planning the development

of the electric power system differ with respect to optimization technique (linear

programming, nonlinear programming, etc.), type of approximation (linear, non￾linear), and economic valorization (with inflation, without inflation).

In chapter “The Integral Method of Hazard and Risk Assessment for the

Production Facilities Operations”, problems of creation of integrated index within

the development of control methods of HPF industrial safety condition are desig￾nated and the problem of such object’s management modeling because of prece￾dents, based on classes of states, is solved (there is an event/there is no event).

v

Chapter “Multi-level Hierarchical Reliability Model of Technical Systems:

Theory and Application” describes an assessment methodology for various sus￾tainability indicators of technical systems, such as reliability, availability, fault

tolerance, and reliability-associated cost of technical safety-critical systems, based

on Multi-Level Hierarchical Reliability Model (MLHRM).

Chapter “Graph Theory Based Reliability Assessment Software Program for

Complex Systems” presents the reliability of the theoretical background and graph

theory. After that, the developed MATLAB GUI application based on graph theory

for the reliability assessment of complex systems has been discussed.

In chapter “Reliability and Vacation: The Critical Issue”, a comparative study of

different vacation policies on the reliability characteristics of the machining system

is presented. For that purpose, the queueing-theoretic approach is employed and the

Markovian models are developed for various types of vacation policies, namely,

N-policy, single vacation, multiple vacations, Bernoulli vacation, working vacation,

vacation interruption, etc.

In chapter “Software Multi Up-Gradation Modeling Based on Different

Scenarios”, it has been checked out which release performs best for a particular

type of real-life scenario using the unified modeling approach. The intent of this

chapter is to consider the increasingly ambitious requirements of the customers and

the benefits of situating new features in the software.

In Chapter “A Hidden Markov Model for a Day-Ahead Prediction of Half￾Hourly Energy Demand in Romanian Electricity Market”, Mathematica code,

which relies on the maximum likelihood principle in Hidden Markov Model

(HMM) environment, has been developed. Also, HMM approach is an efficient way

in modeling short-term/day-ahead energy demand prediction, especially during

peak period(s), and in accounting for the inherent stochastic nature of demand

conditions which has been discussed.

Chapter “A General (Universal) Form of Multivariate Survival Functions in

Theoretical and Modeling Aspect of Multicomponent System Reliability Analysis”

presents particular bivariate and k-variate new models and also a general method for

their construction competitive to the copula methodology. The method follows the

invented universal representation of any bivariate and k-variate survival function

different from the corresponding copula representation.

Chapter “An Exact Method for Solving a Least-Cost Attack on Networks”

focuses on treating a particular problem of intelligent threats. This chapter attempts

to identify the optimal attack strategy on a network that completely prevents the

flow from reaching its destination.

In chapter “Reliability Analysis of Complex Repairable System in Thermal

Power Plant”, the performance of the cooling tower of a coal-fired thermal power

was analyzed under fuzzy environment. TFM was used to consider the vagueness

of the failure and repair time data. The results are useful in framing the optimum

maintenance interval for the considered system for improving plant availability.

Chapter “Performance Analysis of Suspension Bridge: A Reliability Approach”

investigates the ability to use the Markov process for degradation modeling of

suspension bridges by taking some of its important sections, namely, tower

vi Preface

foundation, tower, anchor, cable, and deck along with human error. Here, we also

identify various factors responsible for the deterioration of the major components

of the bridge, which further affects the working of the mainframe structure.

The engineers and the academicians will definitely gain great knowledge with

the help of this book entitled “Advances in Reliability Analysis and its

Applications”. This book also helps them in the analysis of reliability and its

applications. The book is meant for those students who have taken reliability

engineering as a subject to study. The material is proposed for postgraduate or

senior undergraduate level students.

Dehradun, India Mangey Ram

Piscataway, USA Hoang Pham

Acknowledgements The editors acknowledge Springer for this opportunity and professional

support. Also, we would like to thank all the chapter authors and reviewers for their availability for

this work.

Preface vii

Contents

Time Varying Communication Networks: Modelling, Reliability

Evaluation and Optimization ................................. 1

Gaurav Khanna, S. K. Chaturvedi and Sieteng Soh

Methods for Prognosis and Optimization of Energy Plants Efficiency

in Starting Step of Life Cycle ................................. 31

Z. N. Milovanović, Lj. R. Papić, V. Z. Janičić Milovanović,

S. Z. Milovanović, S. R. Dumonjić-Milovanović and D. Lj. Branković

Planning Methods for Production Systems Development in the Energy

Sector and Energy Efficiency ................................. 95

Z. N. Milovanović, Lj. R. Papić, S. Z. Milovanović,

V. Z. Janičić Milovanović, S. R. Dumonjić-Milovanović

and D. Lj. Branković

The Integral Method of Hazard and Risk Assessment

for the Production Facilities Operations ......................... 149

Alexander Bochkov

Multi-level Hierarchical Reliability Model of Technical Systems:

Theory and Application ..................................... 201

Igor Bolvashenkov, Jörg Kammermann, Ilia Frenkel

and Hans-Georg Herzog

Graph Theory Based Reliability Assessment Software Program

for Complex Systems ....................................... 235

Abdrabbi Bourezg and Hamid Bentarzi

Reliability and Vacation: The Critical Issue ...................... 251

Chandra Shekhar, Shreekant Varshney and Amit Kumar

ix

Software Multi Up-Gradation Modeling Based on Different

Scenarios ................................................ 293

Adarsh Anand, Priyanka Gupta, Yoshinobu Tamura and Mangey Ram

A Hidden Markov Model for a Day-Ahead Prediction of Half-Hourly

Energy Demand in Romanian Electricity Market ................. 307

Anatoli Paul Ulmeanu

A General (Universal) Form of Multivariate Survival Functions

in Theoretical and Modeling Aspect of Multicomponent System

Reliability Analysis......................................... 319

Jerzy K. Filus and Lidia Z. Filus

An Exact Method for Solving a Least-Cost Attack on Networks ...... 343

Asma Ben Yaghlane, Mehdi Mrad, Anis Gharbi and M. Naceur Azaiez

Reliability Analysis of Complex Repairable System in Thermal

Power Plant .............................................. 361

Dilbagh Panchal, Mohit Tyagi, Anish Sachdeva and R. K. Garg

Performance Analysis of Suspension Bridge: A Reliability

Approach ................................................ 373

Amit Kumar, Mangey Ram, Monika Negi and Nikhil Varma

x Contents

Time Varying Communication Networks:

Modelling, Reliability Evaluation

and Optimization

Gaurav Khanna, S. K. Chaturvedi and Sieteng Soh

Abstract In recent times, there has been a tremendous research interests and growth

in the direction of time varying communication networks (TVCNs) due to their

widespread applications. The examples of such networks include, but not limited

to, the networks like mobile ad hoc networks (MANETs), delay tolerant networks

(DTNs), vehicular ad hoc networks (VANETs) and opportunistic mobile networks

(OMNs). Some formidable challenges posed by such networks are long propaga￾tion delay, frequent disruption of communication between any two nodes, high error

rates, asymmetric link rates, lack of end-to-end connectivity, routing, etc. Thus, it is

vital for TVCN design, modelling and performance evaluation and/or comparison

to assess their performance through some quantifiable metrics like packet deliv￾ery ratio (PDR), average number of link failures during the routing process, routing

requests ratio, average end-to-end (E2E) delay, route lifetime and network reliability.

Although a plethora of tools and techniques are available that deal with the design,

modelling, analysis and assessment of reliability and other performance metrics of

static networks yet the same is not true for the present days’ TVCNs. This Chapter

describes extension of the reliability assessment techniques and performance metrics

used for static networks to the TVCNs. More specifically, the aspects dealt in this

chapter are: (i) TVCN models for representing features like mobility, links and topol￾ogy, (ii) description of the notion of time-stamped-minimal path sets (TS-MPS) and

time-stamped-minimal cut sets (TS-MCS) for TVCNs as an extension of MPS and

MCS, respectively that are widely used in static networks, (iii) techniques for enu￾merating TS-MPS and TS-MCS, and evaluating reliability measure(s)-particularly

G. Khanna · S. K. Chaturvedi (B)

Subir Chowdhury School of Quality and Reliability, Indian Institute of Technology

Kharagpur, Kharagpur, West Bengal, India

e-mail: [email protected]

G. Khanna

e-mail: [email protected]

G. Khanna · S. Soh

School of Electrical Engineering, Computing and Mathematical Sciences,

Curtin University, Perth, Australia

e-mail: [email protected]

© Springer Nature Switzerland AG 2020

M. Ram and H. Pham (eds.), Advances in Reliability Analysis

and its Applications, Springer Series in Reliability Engineering,

https://doi.org/10.1007/978-3-030-31375-3_1

1

2 G. Khanna et al.

two-terminal reliability, expected hop and slot counts along with some other related

metrics, and (iv) discussion on several recent optimization problems in TVCNs.

Keywords Evolving graphs · Network reliability · Sum-of-disjoint products · Time varying communication networks

1 Introduction

Recent advances in communication, computation and sensing capability have

resulted in the advent of multi-hop mobile ad hoc networking paradigms viz., Mobile

Ad hoc Networks (MANETs) and MANET-born networks like Delay Tolerant Net￾works (DTNs), Vehicular Ad hoc Networks (VANETs), Opportunistic Mobile Net￾works (OMNs) and Wireless Mesh Networks (WMNs) [1]. At the basic level, such

networks can be formed in a rapid manner by employing the popular devices like

smart phones, tabs, iPads, and laptops whose power, versatility and affordability is

increasing day-by-day [2]. All these communication networks have a common fea￾ture of time-varying or evolving topology. The change in network topology primarily

occurs due to a variety of intrinsic (predictable and inherent) interruptions like node

mobility and/or extrinsic (unpredictable) interruptions like shadowing and hardware

failures [3]. Although, modelling of topology changes are formidable tasks for net￾work designers and managers, yet these changes are often considered as an integral

part or nature of these systems rather as anomalies [4]. Some other daunting chal￾lenges posed by such networks are long propagation delay, frequent disruption of

communication between any two nodes, high error rates, asymmetric link rates, lack

of end-to-end connectivity, routing, etc. Thus, modelling and performance evaluation

of the above stated networks is an extremely challenging task which requires com￾putation of quantifiable metrics like packet delivery ratio (PDR), average number of

link failures during the routing process, routing requests ratio, average end-to-end

(E2E) delay, route lifetime and network reliability.

Despite the above challenges, multi-hop mobile ad hoc networking paradigms

have found a multitude of space and terrestrial applications. A few application areas

of such networks include disruption tolerant satellite networks [5], wildlife monitor￾ing (refer ZebraNet [6]), provisioning of internet facility in inaccessible/rural areas

of developing countries (see Daknet [7]), updates to online chatting systems (e.g.,

MSN) or social networking sites (e.g., Facebook, twitter), emails, firmware and soft￾ware updates, etc. These applications often necessitate that a user can tolerate a slight

delay in data delivery or do not need real time service provisioning [8]. There are

enormous other potential application areas of networks which vary/evolve with time

like neural networks, citation networks, social networks, disease dissemination and

many more. Some more worth mentioning works in this direction covering a variety

of such networks can be seen in [9–12]. Note that such time evolving/varying net￾works belong to a variety of domains and are known with many different names in the

literature, viz., temporal graphs, temporal networks, evolving graphs, time-varying

Time Varying Communication Networks: Modelling … 3

graphs(TVGs), time-aggregated graphs(TAGs), time-stamped graphs, dynamic net￾works, dynamic graphs, dynamical graphs,spatio-temporal networks and so on [13].

Thus, for the sake of uniformity, here onwards we would refer the multi-hop commu￾nication networking paradigms as time varying communication networks (TVCNs).

Today we have a plethora of well-defined state-of-the-art techniques for the relia￾bility analysis of static networks. Among them, Minimal Path Set (MPS) and Minimal

Cut Set (MCS) based methods have played a major role in static networks’ reliabil￾ity modelling and analysis problems. Note that a MPS, in general, is a path between

specified set of nodes whereby no nodes are traversed more than once and every link

in this set is needed for ensuring a successful communication. In contrast, a MCS

is a minimal set of links whose removal would cause a network graph to fail. The

path sets (cut sets) may not necessarily be disjoint and independent in the sense that

common links might be occurring in many paths (cuts). To this end, various sum-of

disjoint-products (SDP) techniques have been employed to make them disjoint and to

compute the network’s reliability (unreliability) from these disjointed MPS (MCS).

In addition, the path sets and cut sets can also be used to assess an upper/lower bound

on reliability as well, if the number of paths or cuts is exceedingly large to avoid

computational burden.

However, the current state-of-the-art for evaluating reliability of TVCNs still

appears to be at its infancy stage because the available analytical techniques for net￾work reliability analysis have mainly been developed for static networks and cannot

be extended directly on TVCNs without resorting to their substantial modifications.

Due to the frequent changes in topology and unpredictability of failures, TVCNs

do not possess continuous end-to-end connectivity between a set of specified nodes,

e.g., Source-Destination (S-D) node pair, as is observed in static networks [14]. More

specifically, TVCNs adhere to store-carry-and-forward mechanism of data transfer

by utilizing multi-hop communication via time respecting opportunistic path sets.

Consequently, to use widely employed MPS and MCS based methods for reliability

analysis in static networks, one has to devise means to enumerate terms similar to

MPS (or MCS) for TVCNs. We believe that in many applications of TVCNs like

in Low Earth Orbiting (LEO) satellite networks or in reconnaissance applications,

network reliability assessment is of great concern. In general, network reliability in

TVCN can be defined as the probability of successful transmission of data packets

among a set of designated nodes. In other words, their reliability evaluation assesses

how reliably data packets sent by source node(s) can be received at the destination

node(s).

In this chapter, we will briefly review the models for representing features like

mobility, links and topology of TVCNs. Further, we will describe a recent notion

of time-stamped-minimal path sets (TS-MPS) and time-stamped-minimal cut sets

(TS-MCS) for TVCNs as an extension of MPS and MCS, respectively of static net￾works. We will also describe methods to generate TS-MPS and TS-MCS, discuss

the results of research studies utilizing TS-MPS or TS-MCS for evaluating the relia￾bility measure(s), particularly two-terminal reliability (2-TR), expected hop and slot

counts along with some other related but useful network performance metrics, and

optimization problems in TVCNs.

4 G. Khanna et al.

2 Modelling Techniques

This section presents some existing models for representing various features of

TVCNs.

2.1 Overview

Formally, a TVCN could be modelled as a network graph, G = (VG, EG), where

each node and/or link has a presence schedule defined for it. Corresponding to each

link l ∈ EG (node v ∈ VG) the link (node) existence schedule indicates the time

instances at which a link (node) is present, and possibly other parameters like traversal

distance, traversal cost and latency, etc., [15]. With the help of the link and node

existence schedules, changes in topology of a TVCN can be studied [16]. A number

of models have been proposed in the literature to study/predict the performance

characteristic(s) of TVCNs. A comprehensive discussion on them can be found in

[17] and the references therein. However, for the sake of completeness, here we

briefly summarize some noteworthy observations.

(1) In TVCNs, one of the prime network attribute is node mobility. A mobility model

attempts to capture the motion of mobile nodes with the change in their speeds

and directions over time. It is well-known that the real-life mobility patterns

of human beings and vehicles can be very complex to model depending on the

objectives of the mission [18]. A complex mobility pattern requires more param￾eters to be included into the mobility model, thereby, making the model very

complex. Performance assessment of TVCNs in the presence of node mobility,

characterized by some mobility model, generally requires an investigation of the

impact of change in node velocity and mobility patterns on network reliability,

protocols and application services. Such an analysis is of prime importance for

the better design and implementation of TVCNs. In a very simple classification,

mobility models can be categorized as: (i) Synthetic mobility models [19], and

(ii) Trace based mobility models [20, 21]. A synthetic mobility model depicts

randomly generated movements and creates synthetic traces while a trace-based

mobility model is developed by monitoring and extracting the features from the

real movement patterns of users carrying mobile nodes, thus epitomizes real￾ity [17]. Generally, a synthetic mobility model requires complex mathematical

modelling, but it can be easily applied to an arbitrary number of nodes and over

a large scale. Although several synthetic mobility models have been proposed

in the literature and many traces have been collected from the real-world experi￾ments to precisely model node movement, yet there is no universal model, which

caters all the requirements. Moreover, in the past, mostly the data traces have

been collected by deploying the mobile devices in a small region, usually a uni￾versity campus or a conference room, and require large time overhead (say six

months to one year) to collect a good amount of traces to avoid any biased data

Time Varying Communication Networks: Modelling … 5

from appearing in the data set. Interested readers may refer the recent reviews

on mobility models and data-trace repositories in [11, 22] for deeper insights.

Besides, it can be concluded from the cited literature that the trace collection is

a difficult job at present as deploying mobile phones on a large scale for data

collection is impractical and costly. It is evident that both techniques have their

own advantages and challenges. For the readers’ benefit, a list of the pros and

cons, and associated research challenges for both categories have been tabulated

in Tables 1 and 2, respectively.

(2) Random Graph model, originally introduced by Solomonoff and Rapoport in

1951 [23], can coherently describe many networks of arbitrary sizes. A random

graph/network is formed by adding links having some associated probability

between randomly selected node pairs. However, in TVCNs such a modelling

is not viable as link existence between nodes is not only distance dependent but

also depends on the time of the existence of the link. For instance, in a TVCN any

node pair having lesser Euclidean distance between them in comparison to their

transmission range will have high probability of link availability in comparison

to a node pair having a larger distance between them [24].

(3) TheRandom Geometric Graph (RGG) is used to draw a random graph by placing

a set of n vertices independently and uniformly on the unit square [0, 1]

2 in a

random fashion, and by connecting two vertices if and only if their Euclidean

distance is at most the given radius r [25, 26]. In other words, in RGG, the

mobile nodes in the network can communicate with each other if the Euclidean

Table 1 Pros and Cons of trace based and synthetic mobility models

Type Pros and Cons

Represents

reality

Deployment

cost

Computational

overhead

Scalable Complexity Availability

of models

Trace

based

models

Yes High Low No Low Few

Synthetic

models

No Low High Yes High Large

Table 2 Research challenges in trace based and synthetic mobility models

Index Synthetic models Trace based models

1 Difficult to design a widely acceptable

realistic and simple mobility model

Huge variation in collected trace data

with respect to day and time

2 Hard to decide a suitable model for a

given scenario

Missing data

3 Difficulty in validation via traces Requires filtering and pre-processing

4 Speed decay problem Sufficient samples need to be acquired

5 Extremely variable values for the

parameters of simulations