DOI 10.1007/s40430-017-0731-y TECHNICAL PAPER
A reliability‑based design framework for early stages of design
process
Murat Mayda1 · Seung‑Kyum Choi2
Received: 9 February 2016 / Accepted: 4 February 2017 / Published online: 15 February 2017 © The Brazilian Society of Mechanical Sciences and Engineering 2017
that the proposed framework is effective to achieve reliable design solutions that have uncertain quantitative character-istics to be used further in probabilistic structural analy-sis during the next design stages such as embodiment and detail design stages.
Keywords Early design · Uncertainty · Reliability estimation · Monte Carlo simulation
List of symbols
C(·) Capacity function
D(·) Demand function DP Design parameter
FCC(θ) Uncertain function-level capacity constraint
FDC Deterministic function-level demand constraint
FDC(θ) Uncertain function-level demand constraint
g(·) Limit-state function
OWV Overall weighted value
P(·) Probability
Pf Probability of failure
R Reliability
RP Reliability of a parallel system
RS Reliability of a series system SF Sub-function
SRQ System-level requirements SS Sub-solution
SV Solution variant
TCC Deterministic top-level capacity constraints
TCC(θ) Uncertain top-level capacity constraint
TDC Deterministic top-level demand constraint
WDP Relative importance weight of a design parameter
WRss Weighted reliability of a sub-solution
WRsv Weighted reliability of a solution variant
Ximin Minimum requirement value for ith sub-function Abstract The traditional decision-making process during
early design stages deals with deterministically evaluating the design candidates in accordance with concrete objec-tives by assuming optimal or nominal design performance values for the candidates. However, this may increase sub-jectivity in the decision process since the design knowledge during early design is usually imprecise and incomplete, and mostly needs to be iteratively updated throughout product design development. To diminish the subjectiv-ity, the knowledge of the design requirements can be pre-cisely and accurately represented by means of probabilis-tic constraints that describe the uncertainties in the design requirements; therefore, in this work, a systematic design framework supported by reliability analysis is developed in such a way that it is able to provide an effective connec-tion among the early design steps especially both at system level and component level. Thus, the probability of failures of the design candidates and their sub-solutions are investi-gated, based on design constraints with Gaussian distribu-tions, or lower and upper bounds, by utilizing Monte Carlo method. To illustrate the potential applicability and efficacy of the proposed framework, a two-finger gripper design problem is considered. The results clearly demonstrate
Technical Editor: Fernando Antonio Forcellini. * Murat Mayda
mmayda@kmu.edu.tr Seung-Kyum Choi schoi@me.gatech.edu
1 Department of Mechanical Engineering, Karamanoglu
Mehmetbey University, Karaman, Yunus Emre Yerleskesi, 70100 Karaman, Turkey
2 The George W. Woodruff School of Mechanical Engineering,
Ximax Maximum requirement value for ith sub-function
Xsmin Minimum system requirement value
Xsmax Maximum system requirement value
µi Mean value of a system requirement for ith sub-function
σi Standard deviation value of a system
require-ment for ith sub-function
µs Mean value of a system requirement
σs Standard deviation value of a system requirement
1 Introduction
The traditional decision-making process during early design stages is mainly carried out based on the nominal or optimal performance values obtained in case of deter-ministic system-level requirements (SRQ). However, the traditional decision process may increase subjectivity in the decision process since the design knowledge during early design is usually imprecise and incomplete, and mostly needs to be iteratively updated throughout product design development [7]. Representing the knowledge of the early design precisely and accurately by means of probabilistic constraints could be a remedy for that challenge. In this direction, there has been increasing interest in the integra-tion of early design stages and reliability. Reliability is the probability that a system will perform its function during a specified period of time and under specified service condi-tions [3]. The reliability estimation during early design is known to be a critical and useful tool to guide the decision-making process before the product is produced [16]. In particular, United States government programs and many companies typically demand reliability measures before the product development cycle starts in order to evaluate return on investment for the product [10]. Consequently, all of these necessities led the research community and industry to focus on the improvement of the reliability-based early design frameworks or methods.
Reliability-based decision-making during early design is a process of choosing design solutions or candidates in accordance with their reliabilities subject to exist-ing uncertain and/or deterministic conditions. Although many attempts have been made to integrate reliability and early design, there are still critical issues that need to be addressed in the context of reliability-based early design. First, there is a need for the product requirements to be represented precisely and accurately using probabilistic representations within their natural content or units, rather than non-probabilistic representations including linguistic or vague definitions. Second, it is necessary to obtain and represent the early design outputs or entities under uncer-tainty to reuse them effectively in further design stages. Third, there is still a need for a significant framework in
which all of the required early design steps organized based on reliability analysis can be connected to each other in a systematic manner. In this paper, we propose a reliability-based early design framework to handle all of the issues aforementioned.
The reminder of this paper is organized as follows: in Sect. 2, the existing work on the development of early design stages under uncertainty, and the research gaps are discussed. In Sect. 3, the reliability analysis and the tradi-tional early design framework are briefly introduced, and then the details of the developed early design framework are presented. In Sect. 4, a two-finger gripper design prob-lem is discussed by applying both the traditional determin-istic framework and the proposed probabildetermin-istic framework. In Sect. 5, conclusions are drawn concerning the applica-bility and limitations of the framework.
2 Related work
2.1 Reliability analysis methods
Many reliability analysis methods have been developed with the aim of exploring and estimating the failures of a system for especially the latter stages of engineering design, such as the embodiment design stage. These meth-ods include sampling methmeth-ods [Monte Carlo simulation (MCS), importance sampling, latin hypercube sampling (LHS), etc.] and structural methods (first-order reliability methods, second-order reliability methods, etc.) [3]. The concept of reliability herein is often utilized in structural optimization problems, namely, reliability-based design optimization methods [8, 12, 14, 23, 30]. In the early design stages, to identify the failures of the design candi-dates in advance, several reliability analysis methods have been developed, which include Quality Function Deploy-ment (QFD), Theory of Inventive Problem Solving (TRIZ), Failure Mode and Effect Analysis (FMEA), Fault Tree Analysis (FTA), reliability block diagram development, functional-failure analysis, fuzzy theory, etc [22]. Majority of these methods concentrate on how to identify possible failures within a system at concept level. In this work, MCS is chosen since it is more simple and powerful compared to others. Also, this method could provide opportunities to practically assess the design candidates in more quantita-tive manner, and to obtain design solutions that have uncer-tain quantitative characteristics to be used further in the lat-ter design stages.
2.2 Early design
The engineering design process includes all tasks that are required for the development of a new product. Several
design methodologies have been developed to conduct the engineering design process in a prescriptive or descriptive manner [6, 11, 24, 31, 33]. These methodologies primar-ily have focused on four design stages: product planning, conceptual design, embodiment design and detail design. Early design activities, which aim to develop a concept that responds to the product requirements, are implemented mainly within the first two stages. The next two design stages include the layout and form development of the con-cept solution, and the project documentation for the certain solution prior to production. The early design stages are of great importance, since about 75–80% of product devel-opment cost is determined during these stages, especially during conceptual design [4, 15, 25, 29]. In this paper, our focus is on the early design process, especially from the end of product planning to the beginning of embodi-ment design. The typical steps of the early design process focused include the following: (1) identifying and organ-izing the product requirements; (2) establishing functional structures to perform the requirements; (3) searching sub-solutions to represent the function structures; (4) generating alternative solution variants from the sub-solutions found, and (5) evaluating the solution variants against technical and economic criteria. These steps can be varied depending on aim-specific early design applications.
2.3 The use of reliability analysis methods in early design
It has been recognized that using reliability analysis meth-ods during early design is difficult because of the incom-plete nature of the early design [28]. However, the deci-sions made in this stage have a major effect on product reliability (Vinogradov 1996, [15, 18]). Therefore, various efforts have been made to integrate the reliability methods and early design activities.
Many hybrid early design methodologies based on QFD, TRIZ, FMEA and other methods have been developed [19, 20, 26]. Cooper and Thompson [5] express that this kind of hybrid design methodologies can be effective in identifying and decreasing the failures of design candidates during the early design. However, it can be quite difficult to automate the reliability-integrated early design process since these kinds of methodologies generally enhance the reliability of products in a qualitative way. With the aim of imple-menting this process under uncertainty in a more quanti-tative manner, several works have been conducted, which can be categorized into two groups: the functional design under uncertainty and the early design based on the system requirements under uncertainty.
As examples for the first group works, Avontour and Werff [1] developed a reliability analysis approach for early design by utilizing FTA and finite element method (FEM).
This approach aims to optimize the costs and the reliabil-ity during functional design. Kurtoglu and Tumer [13] pro-posed a functional-failure identification and propagation (FFIP) framework. The framework allows for the failure analysis at a highly abstract system level. In another work, a failure analysis method based on function flows and oper-ations was introduced, with the aim of improving reliability and quality of the product [2]. Similar to that work, Huang and Jin [10] introduced a design analysis framework for conceptual design by extending the traditional reliability stress and strength interference theory. This framework pri-marily focused on energy, material and signal (EMS) flows of sub-functions. Lough et al. [18] introduced a function-based early design method to perform risk assessments. O’Halloran et al. [22] developed an early design reliability prediction method (EDRPM) to facilitate decision-making in early design. The EDRPM is conducted at the functional level and takes into consideration the failure rates of com-ponents. In summary, most of the developments on the integration of reliability and functional design have been made based on EMS flows, the failures of functions and the failures rates of components or functions. These attempts have significantly contributed to the automation of the reli-ability-integrated functional design process. However, the incompleteness and inadequacy of the function structure, and the insufficient consistency across functions within the function structure are some of the limitations in this area [10]. On the other hand, if it is intended to evaluate the design alternatives by considering system-level require-ments under uncertainty, the functional design aspect may not be sufficient because of the difficulty of representing all of the system-level requirements by using EMS flows or function structures. For this purpose, an effort toward developing early design frameworks based on system-level requirements organized under uncertainty could be a rem-edy, which is related to the research direction of the sec-ond group of works. These efforts are briefly summarized below.
Neufeld et al. [21] introduced a reliability-based design optimization approach for an aircraft conceptual design by utilizing performance measure approach (PMA). This work shows how a deterministically optimized design problem changes with various reliability levels. For this purpose, first, a requirement list based upon specific design con-straints extracted from similar designs was prepared, and a design optimization problem was defined. The optimization problem was solved deterministically as well as using per-formance measure approach at various reliability levels, and the deterministic and probabilistic results were compared. Liu et al. [16] introduced an approach of neural network-based fuzzy synthetic assessment for the early design stage. The approach began with identifying primary engineering factors, such as design, material and manufacturing, and
specifying linguistic fuzzy criteria to be used in the assess-ment and evaluation process. After this step, the required data and judgments were collected for several similar prod-ucts developed previously. Then, according to the specified fuzzy criteria, fuzzy numbers for each engineering factor and the reliabilities of similar products were determined. Finally, by treating the fuzzy numbers as inputs and the product reliabilities as outputs, they trained a neural net-work. In consideration of such a neural network, they aimed to estimate the reliability of new products to be developed. In this work, they utilized experts’ knowledge and similar designs as data sources. Huang et al. [9] applied the linear physical programming model and the RAOGA-based fuzzy neural network model to evaluate design alternatives at the conceptual design stage. According to their methodology, if the evaluation criteria are quantified, then the linear physi-cal programming model can be used; if not, the fuzzy neu-ral network model can be used to evaluate the design alter-natives. In their work, the fuzzy numbers were defined for each specific design factor using the linguistic judgments such as very good, good and medium. After defining the fuzzy numbers, several design alternatives were evaluated in accordance with the criteria based on the fuzzy numbers. As data sources, they utilized experts’ knowledge. Sriramdas et al. [27] proposed a fuzzy arithmetic-based reliability allo-cation approach during early design and development. This approach considered the concept of reliability as the prob-ability that a system must perform its overall function under main engineering factors or limits such as complexity, cost, maintenance, time of operation, criticality and state-of-the-art. They called the consideration “Reliability Allocation”. They then assigned fuzzy numbers to the main engineer-ing factors for each subsystem of systems to be developed. The fuzzy numbers are set according to the linguistic terms (very high, high, medium and low) provided by expert design teams. As a result, they computed the allocated reli-ability of each subsystem according to the fuzzy numbers assigned and the desired system reliability. The second group of works primarily utilized similar designs and/or experts’ knowledge as data sources for the requirement list, and as a criteria, they took into consideration main (safety, complexity, operation time, etc.) or specific engineering factors (sizes, kinematic input and outputs, etc.) in order to assess or evaluate the design solutions. They mostly utilized performance measure approach, fuzzy theory and neural networks to realize reliability analysis during early design. These works often concentrate on two steps of early design stage: the reorganization of the requirement list under uncertainty, and the requirements list-based assessment and evaluation of solutions or design alternatives.
In summary, many attempts have been made to inte-grate reliability and early design. However, there are still critical issues that need to be addressed in the context of
reliability-based early design. First, there is a need for the product requirements to be represented accurately and pre-cisely using probabilistic representations within their natu-ral content or units, rather than non-probabilistic representa-tions including linguistic or vague definirepresenta-tions. Second, it is necessary to obtain and represent the early design outputs or entities under uncertainty to reuse them effectively in further design stages. Third, there is still a need for a significant framework in which all of the required early design steps organized based on reliability analysis can be connected to each other in a systematic manner. In this paper, we propose an early design framework to overcome these issues.
3 Proposed early design framework under uncertainty
In this section, an overview of how to conduct reliability analysis in engineering design is presented. Then, the tradi-tional early design framework is briefly explained. Finally, the proposed reliability-based early design framework envi-sioned in Sect. 1 is explained in detail.
3.1 Reliability analysis
Reliability analysis evaluates the probability of failure of components or structures by identifying their failure mode in which a performance value exceeds a specific design limit. The failure mode is called a limit-state, which is referred to as the margin of safety between the resistance and the load of structures [3]. The limit-state function, g(·), and probability of failure, Pf, can be defined, respectively, as
where C(·) is the capacity or resistance and D(·) is the demand or loading of the system. Both C(·) and D(·) are functions of random variables X.
If Pf is known, the reliability of the structure can be sim-ply obtained as R = 1 − Pf. However, the reliability cal-culation is given for only single failure mode. For a com-ponent with multiple failure modes, or a system that has several components with single failure modes, the overall system or component reliability for the multiple failure case can be evaluated depending on whether the failure ele-ments of the system are connected in series or parallel. The reliability of a series system with n failure elements, Rs, can be obtained by (1) g(X) = C(X) − D(X) (2) Pf =P(g(X) < 0), (3) RS= n i=1 Ri,
where Ri is the reliability of an individual failure element. The reliability of a parallel system with n failure elements,
Rp, can be obtained by
3.2 Traditional early design framework
In the traditional framework (Fig. 1), the first step is to identify design parameters (DP) that define SRQ in the engineering design context based on the given requirements list, and to quantify the DP as top-level capacity constraints (TCC). TCC refer to the system design limits with lower and upper bounds, or approximate maximum, minimum or nominal values of the system. Although it is difficult to quantify the deterministic TCC in the early stage, it is necessary to assume approximate constraints to be used as criteria for the evaluation step. The second step is to estab-lish sub-functions (SF) of the overall function of the sys-tem, search for sub-solutions (SS) for the SF, and combine the SS into solution variants (SV), which refer to the design candidates. The third step is to determine overall weighted values (OWV) for each SV and to choose the SV which has the maximum OWV as the most promising SV. To obtain the OWV, first, the top-level demand constraints (TDC) are evaluated against TCC. Here, TDC refer to nominal per-formance values of the system for each corresponding DP. Then, based on this evaluation, a score of the SV (1–10) corresponding to each DP is predicted by decision-makers, (4) RP= 1 − n i=1 (1 −Ri)
and a weighted value for each DP is determined by multi-plying each score by a relative weight of the correspond-ing DP which is assigned by decision-makers. Finally, the
OWV for each SV is obtained by summing all the weighted values. The OWV can be simply defined by
where Wi is the percentile weight of the ith design param-eter (DPi), and Sij is the score for the ith DP of the jth SV.
TDCij is the approximately top-level demand constraint for the ith DP of the jth SV. The values of Wi, TDCij, and Sij are determined approximately by decision-makers or experts.
If the OWV of the chosen SV does not meet the target
OWV, which is assigned by the decision-maker, then shape, size or configuration of the solution are changed, and the design process from Step 2 to Step 3 is repeated. The tradi-tional framework typically deals with nominal constraints or values and involves more conservative and subjective design procedures [14]. However, the number and content of the traditional framework steps can vary depending on where it is applied to or the aim of the design school. For more detailed information on this framework, please see [25].
3.3 The proposed early design framework
In this study, we propose a reliability-based early design framework including six basic steps (Fig. 2). In the first step of the proposed framework, which is different than that of the traditional framework, TCC(θ) (θ represents the uncertainty) is quantified in line with the DP defined from the SRQ by considering uncertainties of each vari-able (Step 1). TCC(θ) can be assigned by the designer as constraints with lower and/or upper bounds, or Gauss-ian distributions with mean and standard deviation. We herein choose Gaussian distributions due to their sim-plicity and convenience to represent the uncertainty of DP during early design. Step 2 is the same as that of the traditional framework. In Step 3, function-level capacity constraints (FCC(θ)) are obtained by allocating all of the TCC(θ) to the related SF. FCC(θ) stands for the capac-ity constraints of SF for each related DP, while TCC(θ) represents the capacity constraints of the overall system function. In Step 4, function-level demand constraints [FDC(θ)] with Gaussian distributions, which refer to the performance value of SS for each related DP are deter-mined. In Step 5, the reliability for each related DP of the SS is calculated based on the FCC(θ) and FDC(θ) using Eqs. (1) and (2) using sampling methods (e.g., MCS). Then, weighted reliabilities of each SS (WRss) are cal-culated by summing the multiplication of each reliability by relative importance weights of the related DP. Finally, (5)
OWVj=
n
i=1 SijWi
100 ,
Step1. Define nominal top-level capacity constraints (TCC) from SRQ
Step 2. Establish sub-functions (SF), search for sub-solutions (SS) to SF and combine SS into
solution variants (SV)
Step 3. Determine overall weighted values (OWV) of SV against TCC and choose an SV which has the maximum OWV
Does the SV meet the target OWV?
Yes - change shape, size
or configuration of the solution
No
Accept the SV as the promising concept
the weighted reliability of each SV (WRsv) is calculated using the calculated WRSS values. Accordingly, in Step 6, the SV that has maximum reliability is judged as the most promising solution or concept for the design prob-lem. If the reliability of the chosen SV does not meet the target reliability, then, shape, size or configuration of the solution are changed, and the design process from Step 4 to Step 6 is repeated. Because Steps 1, 2 and 6 are clearly understandable, we only explain other Steps (3, 4 and 5) in detail, as follows. In addition, all of the steps will be explicitly demonstrated with a case study in Sect. 4.
Step 3 Allocate TCC(θ) to SF and obtain FCC(θ) The following two sub-steps are used to obtain the
FCC(θ) by allocating the TCC(θ) to SF.
(a) Recall the TCC(θ), and construct the type of relation-ships between TCC(θ) and SF.
First, it is necessary to determine which SF can be involved in which TCC(θ). For this purpose, two types of relationships are needed to be determined by decision-makers, namely, complete or partial relationships. The complete relationship is a situation in which an SF must completely satisfy the corresponding constraint. In the par-tial relationship, an SF must parpar-tially or proportionally sat-isfy the corresponding constraint. For example, the energy constraint of a system must be completely satisfied by each SF because of the law of conservation of energy; there-fore, a complete relationship would be suitable to represent the relationship between them. On the other hand, for the weight constraint of the system, it must be partially satis-fied by each SF because each SS of the system would have different weights; in this case, for the relationship between them, a partial relationship would be suitable. The process of assigning relationships between SF and TCC(θ) is illus-trated in Fig. 3 by assuming some relationships between SF and TCC(θ) are known. In the example, TCC1(θ) has two partial relationships with SF1 and SF2, which are
indi-cated by two dashed lines to make it easy to understand in complex relationships. According to the assigned relation-ships, the conditions to obtain the FCC(θ) are illustrated in Table 1. From Table 1, the condition to satisfy TCC1(θ) is that the sum of FCC11(θ) and FCC21(θ) must be equal to TCC1(θ) because of the partial relationships. Here,
FCC11(θ) refers to the extent that SF1 must satisfy TCC1(θ). Likewise, FCC21(θ) refers to what extent SF2 must satisfy
TCC2(θ). On the other hand, the condition for TCC2(θ) is that FCC12(θ) and FCC22(θ) must be equal to each other and to TCC2(θ).
(b) Allocate the TCC(θ) to SF according to the conditions established.
At the beginning of the framework, the uncertainties of
TCC(θ) are already specified by the decision-maker using Gaussian distribution. In this sub-step of Step 3, the TCC(θ)
Step1. Define uncertain top-level constraints (TCC(θ)) from SRQ
Step 2. Establish sub-functions (SF), search for sub solutions (SS) to SF and combine SS into
solution variants (SV)
Step 3. Allocate TCC(θ) to SF and obtain function-level capacity constraints (FCC(θ))
Step 4. Find function-level demand constraints (FDC(θ)) of SS against DP Step 5. Estimate weighted reliability of SS and
SV (WRss and WRsv, respectively) Step 6. Choose an SV which has maximum WRsv
Does the SV meet target reliability? Yes - change shape, size or configuration of the solution No
Accept the SV as promising concept
Fig. 2 Proposed reliability-based early design framework
SF1 SF2 TCC1(θ) TCC2(θ) C: Complete P: Paral C P C P
is allocated to SF based on the type of relationship that has been determined in the previous sub-step. In the complete relationship, it is easy to allocate TCC(θ) to SF and to obtain FCC(θ) because TCC(θ) equals to FCC(θ) of SF. In the partial relationship, the related TCC(θ) must be propor-tionally divided for each related SF to obtain FCC(θ). The logical and mathematical expressions of the interactions are given below.
For the complete relationships:
If the relationship involves a bounded constraint, SFi must satisfy Xsmin ≤ Xs ≤ Xsmax, subject to Ximin = Xsmin,
Ximax = Xsmax.
If the relationship involves a Gaussian distribution, SFi
must satisfy N(µs, σs), subject to µi = µs, σi = σs.
For the partial relationships:
If the relationship involves a bounded constraint, then SFi must satisfy Ximin ≤ Xi ≤ Ximax, subject to
Xsmin =
n
i=1Ximin, Xsmax = n
i=1
Ximax,
If the relationship involves a Gaussian distribution, then SFi must satisfy N(µi, σi) proportionally subject to
µs =1n n i=1 µi, σs = n i=1 σi2,.
where SFi denotes ith sub-function, n denotes the number of sub-functions, Ximin and Ximax denote minimum and
maximum requirement values that the ith sub-function sat-isfy for the corresponding FCC(θ). Xsmin and Xsmax denote minimum and maximum requirement values that the sys-tem must satisfy for the corresponding TCC(θ). µs and σs represent the mean and standard deviation of the corre-sponding TCC(θ), and µi and σi represent the allocated mean and standard deviation of the corresponding FCC(θ) satisfied by the ith sub-function.
In the assignment of the relative requirement values to FCC(θ), similar designs, innovative ideas or experts’ knowledge should be considered to make a robust decision at the end of the design process.
Step 4. Find FDC(θ) of each SS for each related DP
FDC(θ) is the function-level demand of the SS for the related DP. In this case, to represent all of the FDC(θ), Gaussian distribution is used. If the related DP is based on a function of some uncertain and constant variables, the statistics of the FDC(θ), which are mean and standard deviation, are obtained by utilizing MCS. If the DP does
not have a function, then the statistics of the FDC(θ) are estimated approximately by a decision-maker. As an exam-ple, suppose the related DP is weight. Obtaining the exact weight of a solution at the early stage is quite difficult since the physical dimensions are uncertain; therefore, the weight constraint can be approximately estimated based on experi-ence. In another example, suppose the DP is a function of force, and its variables are the friction coefficient and the mass; thus, the force distribution can be easily and accu-rately obtained by MCS given that the friction coefficient and the mass has a Gaussian distribution with a mean and standard deviation.
Step 5 Estimate weighted reliability of SS and SV (WRss and WRsv)
To calculate the WRss and WRsv, respectively, the Pf val-ues and the reliability of the SS (Rss) for each related DP are obtained by utilizing MCS. Then, the WRss and WRsv can be calculated, based on the Rss. We formulate this anal-ysis process with the following mathematical expressions.
The limit-state function and reliability of the SS for each related DP, denoted by G(θ) and Rss, respectively, from the capacity-demand theory for failure probability analysis [from Eq. (1) and (2)], are given by the following:
The vector for the RSS can be written as
To find each WRss, consideration must be given to the relative importance of each DP involved in the SS on the WRss. The relative importance weights of the design parameters (WDP) involved in an SS can be a one-dimen-sional vector:
Here, k is the number of design parameters related to each SS, and k can vary depending on how many the design parameters are related to the current SS. WDP can be (6) G(θ ) = FCC(θ ) − FDC(θ ) (7) Rss = 1 − Pf = 1 −P(G(θ ) < 0). (8) Rss = [Rss1,Rss2,Rss3,...,Rssk]. (9) WDP=[WDP1, WDP2, WDP3, . . . , WDPk]
Table 1 Relationship conditions for SF and TCC(θ)
P and C stand for partial and complete relationships, respectively
Relationship conditions TCC1(θ) TCC2(θ)
SF1 P FCC11(θ ) C FCC12(θ )
SF2 P FCC21(θ ) C FCC22(θ )
determined via QFD analysis of customer needs, question-naire surveys or experts’ choices for return on investment. In the case study of this work, we assume that all of WDP are known in advance; thus, the values of approximate per-centile are given for the design example.
We then obtain the weighted reliability of an SS as:
From Eq. (3) or (4), the weighted reliability of an SV (WRsv), can be simply defined depending on whether the system is connected in the series or parallel, respectively, as follows:
Here, n is the number of SS within the system.
4 A case study
As a design problem, we consider a two-finger gripper that can pick up a rectangular part on the conveyor and release it at another location (Fig. 4). First, the case study is imple-mented as a deterministic case and the evaluation results of the design work are briefly provided. Then, the proposed (10) WRss = Rss[WDP]T (11) WRsv = n i=1 WRssi (12) WRsv = 1 − n i=1 (1 −WRssi).
probabilistic framework is applied for the same problem by considering uncertainties. Thereafter, to illustrate the advantage of the proposed framework compared to the tra-ditional early design framework, the Pf (probability of fail-ure) values are estimated for both deterministic and proba-bilistic cases by applying the same uncertainties.
4.1 Deterministic design framework
In this section, we illustrate how to progress through the three basic steps of the traditional design framework, depicted in Fig. 1, toward the design of the mechanical gripper.
Step 1 Define TCC with nominal values from SRQ When preparing the SRQ (see Table 2), all of the assumptions are made based on our experiences, litera-ture researches, and preliminary design calculations. After defining SRQ, we group the SRQ into five main charac-teristics or DP: gripping force, gripping velocity, energy, number of parts and weight of system as listed in Table 2. Then, the TCC that corresponds to each DP is determined. As an example of obtaining the TCC, the requirements, Rq1, Rq2 and Rq3 in Table 2, are associated with the grip-ping force, F, because the gripgrip-ping force is a function of the weight (mpart) and friction coefficient (µF). In the exam-ple, nominal µF and m
part are given as approximately 0.45 and 0.65 kg, respectively, and the TCC for the DP is given as the constraint, 7.1 ≤ F ≤ 7.6.
Step 2 Establish SF, search SS for each SF and combine SS into SV.
The overall function of the gripper system is to pick up and release a rectangular part moving on the conveyor. Two function structures composed of mostly different SF are established as shown in Fig. 5. Both of the function struc-tures consist of three SF. The remaining design steps are conducted based on the two function structures.
In this step, at least one SS is found for each SF of each function structure, and the SS found for the SS are com-bined into SV. The SS, SF and the two SVs that are deter-mined for the given example are given in Fig. 6. In addition, some functional dimensions of the SV are also given in
0.08
0.035 0.03
Fig. 4 A gripper for the work part to be picked up and released Table 2 Requirements list
given under deterministic case for the mechanical gripper
System-level requirements DP TCC
Rq1. Dimensions of the part: 0.08 × 0.035 × 0.03 m Rq2. The weight of the part, mpart: ~0.65 kg Rq3. Friction coefficient, µF: ~0.45
Gripping force (F), N 7.1 ≤ F ≤ 7.5
Rq4. The angular displacement: α: ~20° Rq5. The opening or closing time: 1 s Rq6. The moment distance: r: ~0.1 m
Gripping velocity (v), m/s 0.032 ≤ ν ≤ 0.036
Rq7. The maximum system energy: 0.52 J Energy (E), J E ≤ 0.52 Rq8. The number of parts of the system: ~20 Number of the parts (NP) NP: ~20 Rq9. The weight of the gripper: ~1.2 kg Weight of the system (m), kg m: ~1.2
Fig. 6. These functional dimensions will be used in the pro-posed framework in this study. For example, the moment distance (r) is approximately given as 0.1 m by taking into account the width of the part (0.03 m), the distance from the top of the part to the end of the case (0.05 m), and the dimension from the end of the case to the center of the spur gear (0.035 m). The dimensions are assumed to be the same for the two SVs so that it is possible to conduct the objec-tive evaluation process for them.
Step 3 Determine OWV of SV against TCC and choose the most promising SV.
In this section, we present the deterministic evaluation results of each SV calculated at the end of the traditional early design process. In Table 3, an evaluation chart is given that indicates the comparison of SV1 and SV2 based on their OWVs.
From the data in Table 3, the OWV of each SV is simply calculated by Eq. (5), and compared. The SV which has the highest OWV is accepted as the most promising solution. In this example, SV2 is chosen to be the most promising solution since it has a higher OWV (8.3) than that of SV1 as seen in Table 3. As can be seen in Table 3, the traditional early design typically focuses on the evaluation of the sys-tem alternatives by assigning some importance scores to the SV. The TDC for each SV, which are also the design outputs of the early design stage, can be used in further design stages. However, these design outputs do not reflect the uncertain nature of early design because the design variables are assumed to be deterministic. In addition, from this evaluation table, it is not possible to see the impact of failed system components or solutions against each DP and under uncertainty.
4.2 Developed probabilistic design framework
Step 1 Define TCC(θ) from SRQ with uncertain values Similar to that of the deterministic case, the SRQ for the gripper problem is given in Table 4. Unlike the deter-ministic case, the TCC(θ) values of number of parts (NP) and weight of the system (m) are assumed to be Gaussian distributions as seen in Table 4. In addition to the uncer-tain variables, the friction coefficient (µF) and the angular displacement (α), which are the input variables of F and
ν, respectively, are assumed to be Gaussian distributions.
These assumptions are reasonable since all of the TCC(θ) naturally include uncertainties due to lack of information during the early design. For example, it is difficult to spec-ify the number of parts of the system at the beginning of the design so that we define the TCC(θ) for the NPs parameter using a Gaussian distribution with 20 mean and 1 stand-ard deviation (N (20, 1)). This definition could be updated based on experts’ experience.
Step 2 Establish SF, search for SS to SF and combine SS into SV
This step is exactly the same as the procedure in the deterministic case. Therefore, we carry out this probabilis-tic framework using the same SV1 and SV2.
Step 3 and 4 Allocate TCC(θ) to SF and obtain FCC(θ), and find FDC(θ) for SS
Following the process described in Sect. 3.3, the FCC(θ) and FDC(θ) are obtained for the two SVs, which are pre-sented in Tables 5 and 6, respectively. The FCC(θ) is denoted by the DP name with the subscript C (for capac-ity), and the FDC(θ) is denoted by the DP name with the subscript D (for demand). In the tables, the design variables
Fig. 5 Two functional
struc-tures (1 and 2) for the gripper
(a, b) Generate angular
motion
(SF1)
Decrease the velocity of the angular motion
(SF2)
Transmit the angular motion to fingers
(SF3)
Generate linear motion
(SF1)
Transmit the linear motion to the linkage
(SF2)
Transmit the linear motion to fingers (SF3)
(a)
(b)
EMEC. SMEC. MPART E’MEC. S’MEC. M’PART E’MEC. S’MEC. M’PART EMEC. SMEC. MPARTEMEC. – Mechanical energy
SMEC. – Mechanical signal
MPART – Material
E`MEC. – Mechanical energy (output)
S`MEC. – Mechanical signal (output)
Fig. 6 The SS, SF and the two
SVs for two functional struc-tures (a, b)
(a)
(b)
r = 0.1 m0.05
0.01
5
0.03
5
Generate angular motion Decrease the velocity of the angular motion Transmit the angular motion to fingers Generate linear motion Transmit the linear motion to the linkage Transmit the linear motion to fingersTable 3 The deterministic
evaluation results of the SV1 and SV2 Evaluation criteria (DPi) Wi (%) TCCi SV1 SV2 TDCij Sij TDCij Sij Gripping force 23 7.1 ≤ F ≤ 7.5 ~7.4 9 ~7.4 9 Gripping velocity 22 0.032 ≤ ν ≤ 0.036 ~0.035 9 ~0.035 9 Energy 15 E ≤ 0.52 ~0.72 4 ~0.52 7 Number of parts 22 NP ≤ 20 ~21 7 ~18 8 Weight 18 m ≤ 1.2 ~1.25 7 ~1.1 8 n i=1 Wi= 100 OWV1 = 7.45 OWV2 = 8.3
Table 4 Requirements list
given under uncertainty for the mechanical gripper
System-level requirements DP TCC(θ)
Rq1 Dimensions of the part: 0.08 × 0.035 × 0.03 m Rq2 The weight of the part, mpart: ~N (0.65, 0.002) kg Rq3 Friction coefficient, µF: ~N (0.45, 0.005)
Gripping force(F), N 7.1 ≤ F ≤ 7.5
Rq4 The angular displacement, α: ~N (20, 0.3)° Rq5 The opening or closing time: 1 s
Rq6 The moment distance: r: ~0.01 m
Gripping velocity(ν), m/s 0.32 ν ≤ 0.036
Rq7 The maximum system energy: 0.52 J Energy (E), J E ≤ 0.52 Rq8 The number of parts of the system: ~N (20, 1) Number of the parts (NP) NP: ~N (20, 1) Rq9 The weight of the gripper: ~N (1.2, 0.077) kg Weight of the system (m), kg m: ~N (1.2, 0.077)
Table 5 SF, their SS and constraints for SV1 in the probabilistic case
SF (for SV1) SS FCC(θ) FDC(θ) Variables for FDC(θ)
1. Generate angular motion Electric motor EC: ~N (0.52, 0.05) ED: ~N (0.46, 0.08) –
NPC: ~N(2, 0.5) NPD: ~N (1, 0.3) –
mC: ~N(0.420, 0.05) mD: ~N (0.400, 0.06) –
2. Decrease the velocity of the angular motion
Worm-gear EC ≤ 0.52 E D = Fwormrα.π 180 Fworm: ~N (6.6834, 0.0743) N, α: ~N (600, 0.3)°, r = 0.0125 m NPC: ~N(6, 0.5) NPD: ~N (5, 0.8) – mC: ~N(0.360, 0.03) mD: ~N (0.350, 0.07) – 3. Transmit the angular
motion to gripping fingers
Two-finger 7.1 ≤ FC ≤ 7.5 FD = mpart .10 2µF N µ F: ~N (0.45, 0.005), m part: ~N (0.65, 0.002) kg 0.032 ≤ vC ≤ 0.036 v D = 2π rα 360 m/s α ~N (20, 0.3)°, r = 0.1 m EC ≤ 0.52 E D = 2.FDrπ .α 180 j FD: ~N (7.2231, 0.0803) N, α: ~N (20, 0.3)°, r = 0.1 m NPC: ~N (12, 1.5) NPD: ~N (11, 1.7) – mC: ~N (0.420, 0.05) mD: ~N (0.410, 0.06) kg –
Table 6 SF, their SS and constraints for SV2 in the probabilistic case
SF (for SV2) SS FCC(θ) FDC(θ) Variables for FDC(θ)
1. Generate linear motion Pneumatic cylinder EC: ~N (0.52, 0.05) ED: ~N (0.40, 0.04) j – NPC: ~N (2, 0.5) NPD: ~N (1, 0.3) – mC: ~N (0.420, 0.05) mD: ~N (0.370, 0.04) kg – 2. Transmit the linear motion to
the next linkage
Rack gear EC ≤ 0.52 ED = Fgearx j Fgear: ~N (72.2299, 0.8035) N, x: ~N (0.007, 0.0005) m NPC: ~N (6, 0.5) NPD: ~N (3, 0.2) –
mC: ~N (0.360, 0.03) kg mD: ~N (0.200, 0.02) kg –
3. Transmit the linear motion to fingers Two-finger 7.1 ≤ FC ≤ 7.5 FD = mpart.10 2µF N µ F: ~N (0.45, 0.005), m part: ~N (0.65, 0.002) kg 0.032 ≤ vC ≤ 0.036 v D = 2π rα 360 m/s α ~N (20, 0.3)°, r = 0.1 m EC ≤ 0.52 E D = 2FDrπ α 180 j FD: ~N (7.2231, 0.0803) N, α: ~N (20, 0.3) °, r = 0.1 m NPC: ~N (12, 1.5) NPD: ~N (11, 1.7) – mC: ~N (0.420, 0.05) mD: ~N (0.410, 0.06) kg –
required to find some FDC(θ), including specific formulas, are also presented. The known formulas are used to find the statistics of the FDC(θ) by MCS. On the other hand, in the case of the FDC(θ) not including formulas and inputs, they are assumed to be a Gaussian distributions with the esti-mated means and standard deviations as given in Table 5. As an example for the FDC(θ) including formula and inputs, let us consider the gripping velocity parameter, v, of the two-finger SS. Here, the formula of the parameter is given by
The variables of v are the rotating angle of the fin-ger: α ~N (20, 0.3)° and the moment distance: r = 0.1 m. When making the optimal estimation of the rotating angle, we consider some design rules. For example, as the angle approaches zero, the holding capability of the fingers decreases, the probability of the surface damage increases, and the flexible working distance decreases. Likewise, as the angle approaches 360°, the energy need increases, the productivity decreases and so forth. Therefore, it is (13)
vD=
2π rα 360
required to find the optimal estimation of the rotating angle. We assume the threshold limit value of this angle to be 20° (mean) and the deviation to be 0.3° based on the informa-tion from similar designs and the preliminary design calcu-lations. Similarly, other inputs and corresponding FDC(θ) for sub-function solutions are determined in the same way.
Step 5 Estimate reliability of SS and SV.
We calculate the Pf values of SS and SV, based on the obtained FCC(θ) and FDC(θ), using MCS with 100,000 samples. We observe that the MCS method converges to accurate results for more than 10,000 realizations. Other simulations are similarly implemented.
To choose the most promising SV, the final task is to calculate the weighted reliability of each SV as explained in Sect. 3.3. To that end, from the Pf values of SS, all of the Rss are obtained as Rss = 1 − Pf, and each WRss is found using Eq. (10). Thereafter, the overall weighted sys-tem reliability, WRsv, is easily calculated using Eq. (11), assuming all of the components are connected in series. Tables 7 and 8 show the results of the reliability estima-tions for SV1 and SV2, respectively. As an example, let us consider the reliability of the electric motor solution. This sub-solution is responsible for three DPs or criteria: energy,
Table 7 Reliability estimations
for SV1 SF SS DP Pf WDP (%) WRSS WRSV
F1 Electric motor Energy (E) 0.2624 25 0.79529 0.359661
Number of parts (NP) 0.0432 45
Weight (m) 0.3989 30
F2 Worm-gear Energy (E) 0.9999 25 0.55061
Number of parts (NP) 0.1446 45
Weight (m) 0.4478 30
F3 Two-finger Gripping force (F) 0.0611 23 0.82133
Gripping velocity (v) 0.0184 22
Energy (E) 0.0481 15
Number of parts (NP) 0.3296 22
Weight (m) 0.4491 18
Table 8 Reliability estimations
for SV2 SF SS DP Pf WDP (%) WRSS WRSV
F1 Pneumatic cylinder Energy (E) 0.0305 25 0.90772 0.66855
Number of parts (NP) 0.0432 45
Weight (m) 0.2174 30
F2 Rack gear Energy (E) 0.3463 25 0.91342
Number of parts (NP) 1.0e−8 45
Weight (m) 5.0e−6 30
F3 Two-finger Gripping force (F) 0.0611 23 0.82133
Gripping velocity (v) 0.0184 22
Energy (E) 0.0481 15
Number of parts (NP) 0.3296 22
number of parts and weight. Based on the three criteria, it is required to find the reliability estimation for the elec-tric motor. Accordingly, from the information in Table 7, the weighted reliability estimation for the electric motor is
WREl.Mo.= 0.795.
Furthermore, to explicitly observe the extent to which the failure probabilities have an impact on the reliabil-ity of the SV, a bar graph for the risk analysis of SV1 and SV2 is shown separately in Figs. 7 and 8. According to both Figs. 7 and 8, the worm-gear solution has the high-est probability of failure, especially for the energy criteria, because the worm-gear mechanisms have low-efficiency coefficients in low speeds. In other words, the system, SV1, could probably fail because the worm-gear solution needs more energy to perform its function. From this standpoint, it is possible to critically analyze the probability of failures and make reliability estimations of an SV, and accordingly improve the deficiencies of the solutions.
Step 6 Decide an SV which has maximum WRsv At the end of this design process, two SVs are com-pared according to their WRsv; thus, at the end of the first design iteration, SV2 can be judged as the most promising system solution since it has higher reliability than that of SV1. Consequently, the design outputs or
design constraints found under uncertainty for SV2 and with traditional content/units are presented in Table 9, which are intended to be used in further stages. We herein do not repeat the implementation of the frame-work to improve SV2; instead, we concentrate mostly on showing how to practically and effectively apply the proposed framework to a real design problem in detail.
Fig. 7 Graphical representation
of the Pf values of SV1 against DP
Fig. 8 Graphical representation
of the Pf values for SV2 against DP
Table 9 The last design outputs with their nature content/units for
SV2
SF SS DP FDC(θ)
F1 Pneumatic cylinder Energy N (0.40, 0.04) Number of parts N (1, 0.3) Weight N (0.370, 0.04)
F2 Rack gear Energy N (0.5056, 0.0366)
Number of parts N (3, 0.2) Weight N (0.200, 0.02) F3 Two-finger Gripping force N (7.2231, 0.0803)
Gripping velocity N (0.0349, 0.00052) Energy N (0.5043, 0.0094) Number of parts N (11, 1.7) Weight N (0.410, 0.06)
4.3 Comparison of the deterministic and probabilistic case
To quantitatively compare the deterministic and probabil-istic case results, we also calculate Pf of the determinis-tic case by using the determinisdeterminis-tic design data subject to the uncertain constraints of the probabilistic case. When applying Steps 4 and 5 of the probabilistic case for the
deterministic case, we obtain the deterministic FDC data and Pf results for SV1 and SV2 under the same FCC(θ) as given in Tables 10 and 11, respectively. Deterministic variables here, which are shown in bold text, are taken higher than mean values in the probabilistic case due to safety and conservative considerations. For example, whereas the mean value of energy parameter for the elec-tric motor in SV1 is taken as 0.46 in the probabilistic
Table 10 Deterministic FDC
data and Pf results for SV1 Solution FDC Variables for FDC Pf
Electric motor ED = 0.49 j – 0.2743 NPD = 1.2 – 0.0548 mD = 0.41 kg – 0.4207 Worm-gear E D = Fwormrθ π 180 Fworm: ~N (6.6834, 0.0743) N, α: ~N (600, 0.3)°, r = 0.013 m 1.0000 NPD = 5.5 – 0.1587 mD = 0.359 kg – 0.4867 Two-finger FD = m.102µF N µ F: ~N (0.45, 0.005), m = 0.665 kg 0.0903 vD = 2π rα 360 m/s α: ~N (20, 0.3)°, r = 0.101 m 0.0797 ED = 2.FDrπ .α 180 j FD: ~N (7.2231, 0.0803) N, α: ~N (20, 0.3)°, r = 0.101 m 0.1321 NPD = 11.6 – 0.3949 mD = 0.415 kg – 0.4602 Table 11 Deterministic FDC
data and Pf results for SV2 Solution FDC Variables for FDC Pf
Pneumatic cylinder ED = 0.43 j – 0.0359
NPD = 1.2 – 0.0548
mD = 0.39 kg – 0.2743
Rack gear ED = Fgearxj Fgear: ~N (72.2299, 0.8035) N, x = 0.0072 m 0.5035
NPD = 3.2 – 1.1e−8 mD = 0.245 kg – 6.0e−5 Two-finger FD = m10 2µF N µ F: ~N (0.45, 0.005), m = 0.665 kg 0.0903 vD = 2π rα360 m/s α: ~N (20, 0.3) °, r = 0.101 m 0.0797 ED = 2.FDrπ .α 180 j FD: ~N (7.2231, 0.0803) N, α: ~N (20, 0.3)°, r = 0.101 m 0.1321 NPD = 11.6 – 0.3949 mD = 0.415 kg – 0.4602
Table 12 Comparison of deterministic and probabilistic Pf for SV1
Sub-solutions and system Pf (determin-istic) Pf (probabil-istic) Difference (%) Electric motor 0.2194 0.2047 −6.72 Worm-gear 0.4674 0.4494 −3.86 Two-finger 0.2278 0.1787 −21.58 The system (SV1) 0.6790 0.6403 −5.7
Table 13 Comparison of deterministic and probabilistic Pf for SV2
Sub-solutions and system Pf (determin-istic) Pf (probabil-istic) Difference (%) Pneumatic cylinder 0.1159 0.0923 −20.40 Rack gear 0.1259 0.0866 −31.23 Two-finger 0.2278 0.1787 −21.58 The system (SV2) 0.4033 0.3315 −17.81
case, the certain value of energy parameter for the elec-tric motor in SV1 is taken as 0.49 in the deterministic case. We should consider the maximum value to ensure that the system will work. For other deterministic param-eters, the same conservative approach is used.
When the remaining tasks of the probabilistic case are applied, the deterministic and probabilistic Pf results obtained for both SV1 and SV2 are provided in Tables 12 and 13. From the Pf results, we observe that the con-servative deterministic data increases the Pf of the design solution by a minimum of 3.86% at the component level, and by a minimum of 5.7% at the system level, as com-pared with the probabilistic case. Therefore, the proposed probabilistic design framework provides more reliable solutions during early design compared to the traditional design framework. In addition, the proposed framework gives the Pf values of not only the system, but also the components of the system in detail, thus providing design outputs representing the uncertain nature of early design.
At first glance, the reliability of a product may seem to be less important in terms of customer needs; however, low reliability means more failures and ultimately results in customer dissatisfaction. Therefore, high reliability should be a basic criteria in the decision-making process. Moreo-ver, to design more competitive products, the reliability cri-teria should be formulated in such a way that the cricri-teria can be integrated with other aspects of product life such as cost, market, and productivity (Vinogradov 1996). From this standpoint, the proposed design framework provides flexibility to add new criteria or aspects to the list of sys-tem-level requirements.
5 Conclusion
During early design, representing SRQ under uncertainty accurately, obtaining the design solutions that have uncer-tain quantitative parameters, and establishing an effec-tive connection among the main steps of the design pro-cess are critical and challenging tasks. While the existing research, to some extent, has made progress toward this purpose, there is not yet significant progress that is able to overcome the challenging issues we have described. To that end, we developed a framework to enhance reliability-based decision-making during early design, which consists of six main steps. In the developed framework, we utilized Gaussian distributions to represent uncertainty in the early design variables. Thereafter, we implemented Monte Carlo simulations to estimate the reliability of the system solu-tion and its components. Through this framework, we can analyze and synthesize the promising design solutions that have uncertain constraints. The opportunity to obtain design solutions having uncertain quantitative parameters
can encourage the research community to make significant progress toward the automation of the reliability-based early design process as well as to build a bridge between early design and further design stages. To illustrate the effi-cacy and the applicability of the proposed framework in real applications, a case study including a two-finger grip-per design is implemented by following the steps of this framework. In addition, we applied the design problem in a deterministic case, and compared the Pf results of the deter-ministic and probabilistic cases. From this comparison, we observe that the probabilistic design based on the frame-work provides more robust solutions and the failure prob-abilities of sub-solutions of a solution variant during early design, compared to the traditional design framework.
Though this work has made significant steps to address the issues discussed before, there are some limitations in practice. First, we assumed the basic dimensions, includ-ing some inputs and outputs of solution variants accord-ing to our experience and preliminary design calculations. To assume or determine the quantitative parameters more accurately, future research is needed in a more objective context. Second, if the developed framework were to be applied to more complex systems in R&D departments, it could be possible to reap maximum benefit from the approach.
On the other hand, to enhance this framework, we sug-gest some new directions on this area: (1) using this frame-work along with optimization techniques to achieve more robust solutions; (2) developing a method or interface, based on the design outputs of this early design framework, in order to connect the early stage to the other design stages such as for probabilistic finite element analysis in embodi-ment design.
Acknowledgements This research was supported by the Scientific
and Technological Research Council of Turkey (TUBITAK), under the BIDEP 2219-International Postdoctoral Research Fellowship Programme.
References
1. Avontuur GC, Van Der Werff K (2001) An implementation of reliability analysis in the conceptual design phase of drive trains. Reliab Eng Syst Safety 73(2):155–165
2. Bai Z, Li X, Tan R, Lian B (2008) A function failure analysis method for improving reliability of the product based on GO-FLOW methodology. Industrial engineering and engineering management, 2008. IEEE international conference, pp 550, 555, 8–11 Dec
3. Choi S-K, Grandhi R, Canfield RA (2007) Reliability-based structural design. Springer, Berlin
4. Chong Y, Chen CH, Leong K (2009) A heuristic-based approach to conceptual design. Res Eng Design 20(2):97–116
5. Cooper G, Thompson G (2002) Concept design and reliability. Acta Polytechnica 42(2):3–12
6. Cross N (1984) Developments in design methodology. Wiley, Chichester
7. Fernandes J, Henriques E, Silva A, Moss MA (2014) Require-ments change in complex technical systems: an empirical study of root causes. Res Eng Design 26(1):35–37
8. Guo X-H, Jiao Z-X, Wang S-P (2009) Reliability-integrated conceptual design for hydraulic system. Advanced intelligent mechatronics, AIM 2009. IEEE/ASME international conference on, 1065–1069
9. Huang H-Z, Liu Y, Li Y, Xue L, Wang Z (2013) New evaluation methods for conceptual design selection using computational intelligence techniques. J Mech Sci Technol 27(3):733–746 10. Huang Z, Jin Y (2009) Extension of stress and strength
interfer-ence theory for conceptual design-for-reliability. J Mech Des 131(071001):1–11
11. Hubka V (1974) Theorie der Maschinensysteme. Springer, Ber-lin/Heidelberg, pp 6–117
12. Hyeong-Uk P, Joon C, Jaewoo L, Kamran B, Daniel N (2011) Reliability and possibility based multidisciplinary design optimi-zation for aircraft conceptual design. 11th AIAA aviation tech-nology, integration, and operations (ATIO) conference. Ameri-can Institute of Aeronautics and Astronautics
13. Kurtoglu T, Tumer IY (2008) A graph based fault identification and propagation framework for functional design of complex system. ASME J Mech Des 130(5):051401
14. Li F, Wu T, Hu M, Dong J (2010) An accurate penalty-based approach for reliability-based design optimization. Res Eng Design 21(2):87–98
15. Li W, Li Y, Wang J, Liu X (2010) The process model to aid innovation of products conceptual design. Expert Syst Appl 37(5):3574–3587
16. Liu Y, Huang H-Z, Ling D (2013) Reliability prediction for evolutionary product in the conceptual design phase using neu-ral network-based fuzzy synthetic assessment. Int J Syst Sci 44(3):545–555
17. Lough KG, Stone RB, Tumer IY (2006) Prescribing and Implementing the Risk in Early Design (RED) Method. Pro-ceedings of the IDETCC/CIE, Philadelphia, PA, Paper No. DETCC2006-99374
18. Lough KG, Stone R, Tumer IY (2009) The risk in early design method. J Eng Des 20(2):155–173
19. Mayda M, Börklü HR (2014) An integration of TRIZ and the systematic approach of Pahl and Beitz for innovative conceptual design process. J Brazil Soc Mech Sci Eng 36(4):859–870
20. Mayda M, Börklü HR (2014) Development of an innovative conceptual design process by using Pahl and Beitz’s system-atic design, TRIZ and QFD. J Adv Mech Design Syst Manufact 8(3):1–12
21. Neufeld D, Chung J, Behdinan K (2009) Aircraft conceptual design optimization with uncertain contributing analyses. AIAA modeling and simulation technologies conference. American Institute of Aeronautics and Astronautics, Chicago
22. O’halloran BM, Hoyle C, Stone RB, Tumer IY (2012) The early design reliability prediction method. ASME 2012 International mechanical engineering congress and exposition. Houston, Texas, USA: ASME
23. Ormon SW, Cassady CR, Greenwood AG (2002) Reliability pre-diction models to support conceptual design. Reliability, IEEE Trans 51(2):151–157
24. Pahl G, Beitz W (1977) Konstruktionslehre, 1st edn. Springer-Verlag, Berlin/Heidelberg, pp 15–250
25. Pahl G, Beitz W, Feldhusen J, Grote KH (2007) Engineering design-a systematic approach. Springer, Berlin
26. Sarno E, Kumar V, Li W (2005) A hybrid methodology for enhancing reliability of large systems in conceptual design and its application to the design of a multiphase flow station. Res Eng Design 16(1–2):27–41
27. Sriramdas V, Chaturvedi SK, Gargama H (2014) Fuzzy arithme-tic based reliability allocation approach during early design and development. Expert Syst Appl 41(7):3444–3449
28. Sun X (2014) Incorporating multicriteria decision analysis techniques in aircraft conceptual design process. J Aircraft 51(3):861–869
29. Tan R, Ma J, Liu F, Wei Z (2009) UXDs-driven conceptual design process model for contradiction solving using CAIs. Comput Ind 60(8):584–591
30. Tsai Y-T, Lin K-H, Hsu Y-Y (2013) Reliability design optimisa-tion for practical applicaoptimisa-tions based on modelling processes. J Eng Des 24(12):849–863
31. Ullman DG (2002) The mechanical design process. McGrawHill, New York
32. Vinogradov O (1991) Mechanical reliability. Hemisphere, New York
33. Weber C, Birkhofer H (2007) Today’s requirements on engineer-ing design science. Proceedengineer-ings of the international conference on engineering design (ICED 07), Paris
