Integrating reliability in conceptual process design an optimization approach

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 5, Issue 7, July (2014), pp. 83-93 © IAEME
83
INTEGRATING RELIABILITY IN CONCEPTUAL PROCESS
DESIGN: AN OPTIMIZATION APPROACH
W. Nziéa
, D. Evenga Mang E.b
, J. B. Samonc
a
Senior Lecturer, Department of Mechanical Engineering, National Advanced School of
Agro-Industrial Sciences, University of Ngaoundere, Cameroon, correspondent author
b, c
PhD Student, National Advanced School of Agro-Industrial Sciences, University of Ngaoundere,
Cameroon
ABSTRACT
The key objective of this study is to develop a systematic theoretical framework for
integrating reliability of industrial plants into the design process from the conceptual stage to the
useful life. This framework will allow designers to specify quantitative targets for reliability and
arrive at optimal design parameters. In industry, at the conceptual stage, the benchmark data from
similar plants and the designer's own experience often replace the more systematic quantitative
reliability analysis for setting reliability targets. In the most favourable cases, the quantitative
reliability analysis is performed at the basic engineering stage of the process design; in the worst
cases, it is done at the detailed engineering stage. The industry often takes a more 'reactive' approach:
improving RAM performance by adjusting the maintenance management, using mostly qualitative
tools, such as RCM, FTA, FMECA, etc at the operational stage. Although this approach does
improve the system's RAM performance compared to the status quo, long-term benefits can only be
achieved by taking a knowledge-based approach: setting quantitative RAM targets in the design
phase that can be controlled throughout the life span of the plant.
Keywords: Reliability, Optimization, Integrated Reliability Model,
1. INTRODUCTION
A major objective of this work is, to ensure that reliability characteristics are included in
system/product design. Specific qualitative and quantitative requirements are identified through the
needs analysis, the accomplishment of feasibility studies, and the development of system operational
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requirements and the maintenance concept. These requirements are addressed through the
implementation of program planning activities and the organisational tasks identified respectively.
Of particular significance is the day-to-day design participation process and the program tasks
that are directed to facilitate the incorporation of “reliability in design”. As the responsible design
team progresses towards the definition of specific design configuration, must be considered several
different design factors, acquiring the proper balance between reliability and the many other factors
that must be addressed to meet the consumer needs. This consideration is best accomplished through
the representation of a reliability specialist as part of the design team.
The success in meeting this objective is highly dependent on having the appropriate tools
available for accomplishing the necessary design analysis and evaluation activities. The utilization of
models for the purpose of requirements allocation, the availability of various design analysis
methods to help in design definition process, and the use of tools for system/product evaluation are
key areas where the reliability specialist can contribute positively to ultimate design output. The next
section of this paper covers some of these key tools, technologies, and aids encountered in literature.
2. LITERATURE SURVEY
Various degrees of freedom to improve the reliability measures are listed in Fig. 1.1.
Considering the overwhelming number of factors that influence overall plant reliability, it is not
surprising that there is a myriad of methods, both qualitative and quantitative, and software tools that
are available today to support RAM studies during plant's life cycle.
Fig. 1.1: Typical plant life cycle (H. D. Goel, 2004)

85
At each stage the loop reliability process is depicted in the following fig. 1.2.
Fig. 1.2: Reliability design process (Ebeling C. E., 1997)
In literature a number of review papers have appeared in the last few decades that provide a
detailed survey of topics that include reliability-availability analysis methods (Dhillon B. S., 1999),
(Sathaye et al., 2000), reliability optimization (Kuo and Prassad, 2000) and, maintenance
optimization (Dekker, 1996). More detailed information on these topics can be found in standard
reliability engineering textbooks such as (Henley and Kumamoto, 1992), (Billinton and Allan, 1992),
and (Kuo et al., 2001).
The calculation of number of components, component’s reliability, stage reliability, and the
system reliability represents an Integrated Reliability Model (IRM) according to (Kuo and Rajendra
Prasad, 2000). The classic approach of this work was proposed in (Lakshminarayana K. S. and al.,
2013) to optimize a class of IRM for redundant systems with volume and weight as the other
constraints. Notwithstanding unreliability of systems still remains researchers’ preoccupation issue.
2.1 Reliability growth curve
New systems and products often display a lower reliability during the early development
phases. System reliability can be improved by analyzing and fixing some failures modes
experienced. Reliability growth is a very relevant concept as far as maintainability analysis is
concerned and can contribute to the overall effectiveness of the system infrastructure. And the curve
in the Duane model can be expressed as:
)log()log()log( TMTBFMTBF sc β+= (1)
Where MTBFc and MTBFc are the cumulative and starting mean time between failures, T is the total
test or operating time, and β is the slope of growth curve.
To fully realise the benefits of system reliability growth, it must be properly managed. Fig.
2.1 is illustrative of the adapted management and planning of that process (Blanchard et al., 1994)
improved in this work.

86
Fig. 2.1: Reliability growth management process
3. INTEGRATING RELIABILITY FRAMEWORK PROPOSED
Integrating reliability optimization formulation into an existing framework will lead to one
integrated design, reliability and maintenance optimization framework which in some cases could be
computationally expensive. In this work, a decomposition strategy is adopted to decompose the large
synthesis, reliability and maintenance optimization problem into manageable sub-problems:
reliability optimization and process synthesis, and maintenance and design optimization problems.
Thus, the following section will start with the illustration of common failures taxonomy, and forward
strategies to integrate reliability in design process will be tackled.
3.1 Identification of life cycle systems failures
The various failures causes in Fig. 3.1 are not necessarily disjoint. There is, for example, an
obvious overlap between “weakness” failures and “design” and “manufacturing” failures. Failure
mechanisms are, defined as the “physical, chemical or other processes that has led to a failure.” A
common interpretation of this term is the immediate causes to the lowest level of indenture, such as
wear, corrosion, hardening, pitting, and oxidation.
This level of failure cause description is, however, not sufficient to evaluate possible
remedies. Wear can, for instance, be a result of wrong material specification (design failure), usage
outside specification limits (misuse failure), poor maintenance - inadequate lubrication (mishandling
failure), and so forth.
Fig. 3.1: Life cycle common failure causes of a system

87
And the table 1 below highlights exhaustively the reasons of those failures.
Table 1: Reasons of system life cycle failures
3.2 Mathematical Model of failed System
Let’s us delineate the failed mode system by FS. It is a function of numerous causal technical
and operational variables in design, manufacturing, commissioning and useful life period (see table
1). According to the network components assembly configurations, reliability of the functioning
system is expressed in by [19]:
)(1)( tFtR −= (1)
F(t) is the probability of FS (unreliability). Thus in case of:
• Series configuration: 













−= ∫ ∑=
duutR
t n
i
i
0 1
)(exp)( λ (2)
The failure of one element of the n elements in series leads to the failure of the system. λi is
the element failure rate.
• Parallel configuration: ∏ ∫=
















−−−=
n
i
t
i duutR
1 0
)(exp11)( λ (3)

88
The failure of all de n elements is necessary to fail the system.
• Parallel-series configuration: ( )∏ ∏= =






−−=
n
i
p
j
ij
j
tRtR
1 1
)(11)( (4)
The system is an hybrid one, where pj elements are in parallel, and n subsystems are in series, Rij
being the element reliability.
• Series-parallel configuration: ∏ ∏= =






−−=
p
i
n
i
ij tRtR
i
1 1
)(11)( (5)
Each of p branches has ni series elements, whereas Rij (t) is the jth
element of the i-branch.
• r - out - of – n: G System with independently and Identically Distributed Components
The reliability is equal to the probability that the number of working components is greater
than or equal to r. Thus:
( ) knk
n
rk
k
n trtrCtR
−
=
−= ∑ )(1)()( (6)
r(t) is the component reliability.
• System which configuration can’t be a hybrid one (see the following classical example
illustrated by the reliability diagram of figure 3.2).
Figure 3.2: Classical non hybrid system
Assuming the independence of components, the reliability of the system is expressed with
obvious annotations (Pagès A. 1980):
( ))(1
52
41
)(
52
41
)( 33 tRRtRRtR
SPPS
−





+





= (7)
3
1 4
52

89
In (7) formula the reliabilities of components system 1, 2, 4 and 5 respectively in parallel-
series and series-parallel configurations are considered while component 3 is on functional mode or
on failed mode.
So whatever the system configuration defined already early in design stages, some reliability
indicators such as, the Mean Time To First Failure (MTTF), the failure rate of the system can be
predefined according to following well known formulations:
∫
+∞
=
0
)( dttRMTTF (8)
)(
)(
)(1
)(
)(
tR
dt
tdR
tF
dt
tdF
t −=
−
=λ (9)
Thus systems reliability improvement can start early in design and continue till useful life by
a well predefined maintenance strategy.
3.3 Reliability optimization at the design stage
3.3.1 Problem statement
The design of systems that should fulfil well defined requirements during use life period
needs maximal reliability. Also, some constraints of technical (volume, weight, spatial configuration,
etc.) or economical (cost, budget, etc.) natures must be considered at the early design stages.
Next to this work, the statement is highlighted with the parallel-series configuration system
composed with i = 1, 2. . . K stages and ni + 1 identical components of Pi reliability at each stages.
The optimal redundancy configuration system results to the following problem:
( )[ ]∏=
+
−−=
K
i
n
i
i
PnMaxR
1
1
11)(
s. t. ji
K
i
ij CnC ≤∑=1
mj .....1=∀
ni is a positive integer Ki .....1=∀
Cij represent the costs of each system component involved in technological and economical
constraints relation of (8).
3.3.2 Problem solution
The following algorithm gives in general very good solution, although not necessary optimal
(A. Pagès et al., 1980):
Step1. (Cj, j from 1 to K, are data).
For i from 1 to K, ni = 0.
∑∑ ==
==
K
i
i
K
i
i LogPLogRLogR
11
.
(10)

90
Step2. Choose i0 such that:
[ ] [ ])()1(
1
max)()1(
1
1
0000
1
ijiim
i
iji
iiiim
i
iji
nLogRnLogR
Ca
nLogRnLogR
Ca
r −+=−+=
∑∑ ==
.
While the set of positive numbers ai is chosen such that 1
1
=∑=
m
i
ia
Step3. If jji CC 〈0
j∀ from 1 to m,
Do 100
+← ii nn
)(log)1( 0000 iiii nRnLogRLogRLogR −++←
jijj CCC 0
−←
Go to step 2.
If not, END.
So the system maximal reliability and the numbers of components are defined.
3.3.3 Process model proposed synthesis
Basically, the main task of the design process is to create a relationship between the product
function, product structure, and product behaviour. The product function explains the effects of the
system and creates a correlation between the input conditions and output effects. Product behaviour
represents the interaction of the function with the environment and how the product fulfils its
function. This is a result of the properties and characteristics of the assemblies and parts in relation to
the environment and system use.
In order to fulfil the functional requirements and to obtain the desired system behaviour, it is
necessary to create a satisfactory design structure combining components (mechanical, electrical,
information, etc.) in corresponding assemblies and system configurations illustrated before. One of
the models for product structure creation is the V-model established by VDI-2206 as the “Design
methodology of mechatronic systems“ which contains a synthesis of the system in order to obtain a
design structure based on functional requirements, and an analysis aimed at integrating the system
reliability (M. Ognjanovic et al. 2012). This means a synchronized process of design structure
processing and a functional requirements’ transformation into design structure behaviour. For this
approach, known as Property-based design in (Krehmer, H et al, 2011), a monitoring system is
established to provide the desired system behaviour starting from the defined functional
requirements. In the clarification of the tasks design stage, reliability is one of the main functional
requirements, and, in the operation process of a technical system, reliability is one of the main
indicators of quality and system behaviour. By decomposing the desired reliability of the system
(functional requirement) to the design component level, the elementary reliability becomes the
design property of the component (Fig. 1). Design properties of the design components are the result
of the parts properties (intensive and extensive) and parts characteristics. These characteristics are
the physical and chemical description of the material, geometrical (shape, dimensions, etc.) and
structural (joints and parts) interactions.
In respect to the adapted growth reliability management process (see fig. 2.1) the reliability
integration from early design stages is sustained in the proposed platform that is highlighted next to
this section. However firstly the following fig. 3.3 delineates the loop of outstanding activities to
fulfil the objectives of this work [18].

91
Fig. 3.3: Cycle of Activities to Improve Reliability and Quality
At the early stages of design and after in the useful life (see Fig. 3.1), Fig. 3.3 illustrates how
the reliability optimization evolution should be managed by engineering designers according to
components/sub-systems assembly configurations, choice and treatment of materials, etc. (Goel et
al., 2002). And mathematical models developed in sections 3.2 and 3.3 are designers tools guidelines
as far as reliability assessment and the (10) problem finds optimal solution on the relevant algorithm
developed.
Fig. 3.3: Reliability optimization in graphical illustration

92
Fig. 3.4 shows a graphical example of how the critical top-level requirements (key
characteristics) of a product can be traced down to the manufacturing process parameters relatively
to fig. 3.1.
Fig. 3.4: Example of key characteristics in process manufacturing stage
In the useful life (Hossam A. Gabbar et al., 2003) develop the detailed system design and
mechanism of improved RCM process as integrated with CMMS. The proposed solution is
integrated with design and operational systems, consolidates some successful maintainability
approaches to formulate an effective solution for optimized plant maintenance and develops tasks
reliability-based preventive maintenance (RBPM) to sustain the product (system) reliability
optimization approach proposed in this paper.
4. CONCLUSION AND PERSPECTIVES
The contributions of this work are highlighted in section 3. In particular, the applications of
different optimization frameworks are put into the broader context of achieving system effectiveness
in different process design situations, on inherent or achievable reliability. Integrating
maintainability, availability and safety at the conceptual design stage has not been the aim of the
task, but as all those parameters are not disjoint, some guidelines are for the purpose are found
implicitly in this paper. Further recommendations for future work shall outline in details the
integration in process design of these last parameters including an outline for the future development
of a prototype of a process-engineering tool to manage maintenance strategies from the early process
design stages.
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93
[5] Dhillon, B. S., “Design reliability: fundamentals and applications “, CRC press Boca Raton
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