reliability modeling and optimization of new product ... · 1 reliability modeling and optimization...
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Mohammad Sadegh MobinPhD Candidate in Engineering Management
Department of Industrial Engineering and Engineering ManagementWestern New England University
Springfield, MA
PhD advisor: Dr. Zhaojun (Steven) Li
2017
Reliability Modeling and Optimization of New Product Development Process
1
Reliability Modeling and Optimization of New Product Development Process
Part 1: Reliability Growth Planning (RGP) Modeling and Optimization Part 2: Verification and Validation (V&V) Activities Planning and Optimization
Overview
Continuous
Product
DevelopmentHigh % of
total
revenue
Consumer needs
changes
Marketing
environment
changes
To stay ahead of
Competition
Changing
technology
Not to lose
market share
2
New Product Development (NPD)
3
Prototype/pilot (Build components/
system)Prototype test
(Test components/ System)
Production phase Field
performance
Verification &Validation
(System and process V&V)
Business case(new idea)
Concept design(System requirement
identification)
Detail design(Component requirement
identification)
New Product Development (NPD)
Planning
Product/Process design & development
Product/Process V&V Production
NPD ChallengesNPD programs are often plagued with:
Cost overruns, Schedule delays, and Quality issues.
Product Company Issues Year Source
787
DreamlinerBoeing Co Delay due to a structural flaw 2009
The Wall Street
Journal
Chevy Volt General Motors Cost overrun during design 2009 CNN Money
The
Honda/GE
HF120
turbofan
engine
Honda
Design issues: An unanticipated test
program glitch. A part of the gearbox
failed during the test. Rebuild the
engine and begin the test again.
2013 Flying
F-35
United Technologies
Corp.’s Pratt and Whitney
unit
Delays in delivering engines. Quality
flaws and technical issues. Systemic
issues and manufacturing quality
escapes.
2014
Defence-
aerospace.com
Bloomberg Business
SikorskyUS Marine Corps'
(USMC's)
A failure in the main gear box and need
for redesign of the component.
Problems with wiring and hydraulics
systems. Budget constraints.
2015 HIS Jane’s 360
5
NASA’s main projects that faced
cost and time overrun:
The International Space Station.
Prime contract had grown: 25%
(from $783M to $986M, the 3rd increase in 2
years).
The NASA Ares-I launch system.
Cost overrun: 43%
(from $28 billion original estimate to $40 billion)
The Department of Defense (DoD)
The set of 96 major new weapon system
development programs (2000-2010) have:
an average development cost growth of
42%,
an average delay of 22 months.
“50% of the DOD’s NPD programs faced cost
overrun”.
“80% experienced an increase in unit costs from
initial estimates”.
NPD Challenges
Objective
Improve the NPD process by reducing:
Time to market delay (Scheduling)
Cost overrun (Budgeting)
Quality flaws (Reliable product)
Model and optimize the NPD reliability process in terms of
cost, time, and product reliability
Proposing a model to improve the reliability growth planning (RGP).
Providing a quantitative model to improve product V&V activities planning.
Part1: RGP
Multi-Objective and Multi-Stage Reliability Growth Planning
(MO-MS-RGP)
Test Time
MT
BF
(D
ays)
1.000
10.00
100.0
1000
Initial MTBF:
3 days
Achieved
MTBF:
70.0 days
Reliability goal = 73
390 Days
A single stage Reliability Growth Plan
One RG plan can be:
390 Days,
Required test units
Required test time
Total cost: $50k
Objective of RGP: To determine the number of test units, test time, and cost to maximize the reliability growth.
Another RGP can be:
490 Days,
Test units and test time
Total cost $70k490 Days
8
Reliability Growth Planning (RGP)
Duane Model (1964)
o An empirical model, based on the learning curve,
o Also known as power law model
o Duane model in terms of cumulative failure rate:
𝒍𝒏 𝑪 𝒕 = 𝜹 − 𝜶 𝒍𝒏 𝒕
𝐶 𝑡 : The average failure rate 𝐶 𝑡 = 𝑁(𝑡)/𝑡
𝑁 𝑡 : The cumulative number of failures up to time 𝑡 during the reliability growth
testing.
𝛿, 𝛼 > 0 , 𝛼 is known as growth rate
Duane Reliability Growth Model
Challenges for multi-stage RGP in early product development stage:
1. How to allocate test units and time to individual stage.
2. How to determine the proportion of new technology introduction in each stage
The schematic of multi-stage reliability growth planning
11
Multi-Stage Reliability Growth Planning
RGP Literature Review
Significant contribution: Multi-objective & Multi-stage RGP
Author
Early
design
stage
Field (test)
stage
Single
objective
Multi
objective
Single -
stage
Multi-
stage
Duane (1964) [1] No Yes Yes No Yes No Crow (1974) [2] No Yes Yes No Yes No Lloyd (1986) [3] No Yes Yes No Yes No Robinson and Dietrich (1987) [4] No Yes Yes No Yes No Coit (1998) [5] No Yes Yes No Yes No Walls & Quigley (1999) [6] Yes No Yes No Yes No Walls & Quigley (2001) [7] No Yes Yes No Yes No Quigley and Walls (2003) [8] No Yes Yes No Yes No Krasich et al. (2004) [9] Yes No Yes No Yes No Johnston et al. (2006) [10] Yes No Yes No Yes No Jin and Wang. (2009) [11] No Yes No Yes Yes No Jin et al. (2010) [12] No Yes Yes No Yes No Jin et al. (2013) [13] No Yes Yes No Yes No Jin and Li (2016) [14] Yes Yes Yes No Yes No Jackson (2016) [15] No Yes Yes No Yes No Li et al (2016) [16] Yes No No Yes No Yes
Author
Early
design
stage
Field (test)
stage
Single
objective
Multi
objective
Single -
stage
Multi-
stage
Duane (1964) [1] No Yes Yes No Yes No Crow (1974) [2] No Yes Yes No Yes No Lloyd (1986) [3] No Yes Yes No Yes No Robinson and Dietrich (1987) [4] No Yes Yes No Yes No Coit (1998) [5] No Yes Yes No Yes No Walls & Quigley (1999) [6] Yes No Yes No Yes No Walls & Quigley (2001) [7] No Yes Yes No Yes No Quigley and Walls (2003) [8] No Yes Yes No Yes No Krasich et al. (2004) [9] Yes No Yes No Yes No Johnston et al. (2006) [10] Yes No Yes No Yes No Jin and Wang. (2009) [11] No Yes No Yes Yes No Jin et al. (2010) [12] No Yes Yes No Yes No Jin et al. (2013) [13] No Yes Yes No Yes No Jin and Li (2016) [14] Yes Yes Yes No Yes No Jackson (2016) [15] No Yes Yes No Yes No Li et al (2016) [16] Yes No No Yes No Yes
Proposed MO-MS-RGP Model
Objectives :
1. Minimize failure rate at the final stage
2. Minimize total development time
3. Minimize total test cost
Decision
variables:
1- Number of test units for each
subsystem in each stage
2- Test time for each subsystem
in each stage
1- Total product test
time
2- Number of available
test units in each
development stage
Constraints:
Stage 1 Stage 2 Stage 3
Initial
MTBF
(stage 1)
Initial
MTBF
(stage 2)
Initial
MTBF
(stage 3)
MTBF at the
end of stage 1
MTBF at the
end of stage 2
MTBF at the
end of stage 3
Test
time for
stage 1
Test
time for
stage 2
Total time
Reliability Goal
MT
BF
Proposed MO-MS-RGP Model
Min: 𝜆𝑛 = 𝑓 𝜆 𝑖−1, 𝜆 𝑛(𝑖), 𝛼𝑖 , 𝑇𝑖
Min: 𝜏 = 𝑖=1𝑛 𝜏𝑖 , 𝑖 = 1, … , 𝑛
Min: 𝐶 = 𝑖=1𝑛 𝐶𝑖 , 𝑖 = 1, … , 𝑛
s.t. 0 ≤ 𝜏 ≤ 𝜏𝑢
𝑁𝑙(𝑖) ≤ 𝑁𝑖 ≤ 𝑁𝑢(𝑖) , 𝑖 = 1, … , 𝑛
Decision variables:
• 𝑛𝑖𝑗• 𝑡𝑖𝑗
𝒇𝟏𝒇𝟐
𝒇𝟑 An optimal solution (RGP)
* Time (Yrs.)* Cost ($)* Reliability (MTBF (YRS.))* Number of test units for each sub-system in each stage* Planned testing time for each sub-system in stage
Method 1: Creating a weighted composite objective function
Shortcomings: 1. Difficulties in determining appropriate utility functions (weights).
2. Objectives have different scale and cannot easily be added up.
Method 2: Consider one as main objective function and others as constraints
Shortcomings: 1. Difficulties in determining boundary values.
2. Defining boundaries may reduce the solution space.
Method 3: Multi-Objective Evolutionary Algorithms (MOEAs)
e.g., MOPSO, NSGA, etc.1. Simultaneously optimizing two or three (or more) conflicting objectives.
2. Effective methods in exploring feasible solutions and providing a population of approximately
optimal solutions (Pareto-optimal frontier).
3. Apply evolutionary operators, e.g., crossover and mutation to generate variety of new solutions.
Solution Methodologies
Overview of the proposed solution methodology
Mathematical model:
• Objective functions
• Constraints
• Decision variables
A set of Pareto-
optimal solutions
Inputs
(Minimization objective functions)
Outputs
(Maximization objective functions)
Data
Envelopment
Analysis (DEA)
Multiple
Objectives
Evolutionary
Algorithm
Optimal
efficient
solutions
17
Proposed Solution Methodology
Case Study Application of MS MO RGP for next generation dual engine development process
istage
Group description λijθ1
(%)
θ2(%)
θ3(%)
cij($1000)
mi αi Nl(i) Nu i
1Engine Block 1.38 100 0 0 600
2 0.4 4 8Turbocharger 0.03 100 0 0 45
2
Engine control 0.24 0 80 0 50
4 0.3 8 16Cooling System 0.02 0 100 0 30
Fuel System 0.20 0 80 0 40
Lubricating system 0.05 0 80 0 20
3
Engine control 0.24 0 0 20 12.5
3 0.2 6 20Fuel system 0.20 0 0 20 10
Lubricating system 0.05 0 0 20 5
Min: 𝜆𝑖=3 = 𝑓 𝜆 𝐼(𝑖−1), 𝜆 𝑛(𝑖), 𝛼𝑖 , 𝑇𝑖
Min: 𝑖=1𝑛 𝐶𝑖 = 𝐶1 + 𝐶2 + 𝐶3
Min: 𝜏 = 𝑖=1𝑛 𝜏𝑖 = 𝜏1 + 𝜏2 + 𝜏3
s.t. 0 ≤ 𝜏 ≤ 𝜏𝑢⟹ 0 ≤ 𝜏1 + 𝜏2 + 𝜏3 ≤ 3.54 ≤ 𝑛11 + 𝑛12 ≤ 88 ≤ 𝑛21 + 𝑛22 + 𝑛23 + 𝑛24 ≤ 166 ≤ 𝑛31 + 𝑛32 + 𝑛33 ≤ 20
𝜏𝑢: 3.5 years
The effective work hours in each year: 2000 hours
The variable cost per hour: $2000
18 decision variables:
• 𝑛𝑖𝑗 (discrete)
• 𝑡𝑖𝑗 (continuous)
Obtaining Pareto optimal frontier for RGP using NSGA-II
0.50.6
0.70.8
0.91
1.11.2
1.31.4
1.5
00.5
11.5
22.5
33.5
0
3000
6000
9000
12000
15000
f1(x): Failure rate of stage 3f
2(x): Projected total test time
f 3(x
): P
roje
cted
to
tal
test
co
st 1 = 0.4
2 = 0.3
3 = 0.2
n(1)
= 1.41
n(2)
= 0.51
n(3)
= 0.49
19
Optimal Solutions
DEA applications
0.50.6
0.70.8
0.91
1.11.2
1.31.4
1.5
00.5
11.5
22.5
33.5
0
3000
6000
9000
12000
15000
f1(x): Failure rate of stage 3f
2(x): Projected total test time
f 3(x
): P
roje
cted
to
tal
test
co
st CCR solutions
NSGA-II solutions
Inputs Output DEA Models
DMUs Time Cost Reliability CCR CCR BCC BCC
(Yrs.) ($) MTBF (Yrs.) (I-O) (O-O) (I-O) (O-O)
DMU 01 3.45 15.38 2.13 0 0 1* 1* DMU 02 0.79 4.56 0.79 0 0 1* 1* DMU 04 3.28 14.72 2.13 0 0 1* 1* DMU 07 0.82 4.67 0.83 0 0 1* 1* DMU 10 2.30 10.87 1.88 0 0 1* 1
DMU 15 0.88 4.91 0.89 1* 1* 1* 1* DMU 19 0.80 4.60 0.81 0 0 1* 1* DMU 26 3.23 14.53 2.10 0 0 0 1* DMU 31 2.66 12.31 1.96 0 0 0 1
DMU 34 1.76 8.57 1.58 0 0 1* 1*
DMU 36 2.57 11.96 1.94 0 0 0 1
DMU 38 2.25 10.68 1.86 0 0 1* 1* DMU 48 0.79 4.56 0.79 0 0 1* 1* DMU 51 2.22 10.56 1.86 0 0 1* 1* DMU 56 1.83 8.84 1.62 0 0 0 1*
DMU 58 2.29 10.84 1.87 0 0 0 1
DMU 67 1.86 8.95 1.64 0 0 0 1
DMU 69 1.78 8.65 1.60 0 0 1* 1*
DMU 70 2.55 11.88 1.94 0 0 1 1
DMU 86 1.20 6.20 1.18 1* 1* 1* 1*
DMU 87 1.86 8.94 1.63 0 0 0 1
DMU 96 1.22 6.27 1.20 1* 1* 1* 1*
DMU 98 1.21 6.23 1.19 1* 1* 1* 1*
20
Optimal Efficient Solutions
21
Conclusions and Future Research
Uncertainties in the variables of the RGP model:e.g. uncertainty in the failure rate, reliability growth, etc.
Component-level approach in RGP:e.g. provide number of test units and test time for each component in different sub-systems.
Application and comparison of other evolutionary algorithms:e.g. Multi-objective Particle Swarm Optimization (MOPSO).
Ongoing and Future Research:
Conclusion:
A new approach in reliability growth planning (RGP)
o Correlates multiple stages of developing a new product.o Considers multiple objectives of NPD process.o Determines test time and test units for each subsystem in each stageo Provides efficient and optimal RGP for implementation
[1] Duane J., Learning curve approach to reliability monitoring, IEEE Transactions on Aerospace, 2(2), 563-6, 1964.
[2] Crow L.H.. Reliability analysis for complex, repairable systems. In Reliability and Biometry, ed. By F. Proschan
and R. J. Serfing, Eds: SIAM, 379-410,1974.
[3] Lloyd D.K., Forecasting reliability growth. Quality and Reliability Engineering International, 2(1),19-23. 1986
[4] Robinson D.G. and Dietrich D., A new nonparametric growth model. IEEE Transactions on Reliability, 36(4),411-8,
1987.
[5] Coit D.W., Economic allocation of test times for subsystem-level reliability growth testing. IIE transactions, 30(12),
1143-51, 1998.
[6] Walls L, Quigley J. Learning to improve reliability during system development. European Journal of Operation
Research, 119(2), 495-509, 1999.
[7] Walls L, Quigley J. Building prior distributions to support bayesian reliability growth modelling using expert
judgement. Reliability Engineering and System Safety, 74(2), 117-28. 2001.
[8] Quigley J. and Walls L., Confidence intervals for reliability-growth models with small sample-sizes, IEEE
Transactions on Reliability, 52(2), 257-62, 2003.
[9] Krasich M., Quigley J., Walls L., Modeling reliability growth in the product design process, Proceedings of the
Annual Reliability and Maintainability Symposium (RAMS), 424-30, 2004.
[10] Johnston W., Quigley J., and Walls L., Optimal allocation of reliability tasks to mitigate faults during system
development, IMA Journal of Management Mathematics, 17(2), 159-69, 2006.
[11] Jin T, Wang H., A multi-objective decision making on reliability growth planning for in-service systems,
Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics (SMC), 4677-83, 2009.
[12] Jin T., Liao H., and Kilari M., Reliability growth modeling for in-service electronic systems considering latent
failure modes, Microelectronics Reliability, 50(3), 324-31, 2010.
[13] Jin T., Yu Y., Huang H. Z., A multiphase decision model for system reliability growth with latent failures, IEEE
Transactions on Systems, Man and Cybernetics, 43(4), 958-966, 2013.
[14] Jin T., Li Z., Reliability growth planning for product-service integration, Proceedings of the Annual Reliability and
Maintainability Symposium (RAMS), 2016.
[15] Jackson C., Reliability growth and demonstration: the multi-phase reliability growth model (MPRGM),
Proceedings of the Annual Reliability and Maintainability Symposium (RAMS), 2016.
References
22
Journal Publicationso Mobin M., Li Z., Komaki M., A Multi-Objective Approach for Multi-Stage Reliability
Growth Planning by Considering the Timing of New Technologies Introduction,IEEE Transaction on Reliability, 66 (1), 97-110, 2017
o Li Z., Mobin M., Keyser T., Multi-objective and Multi-Stage Reliability GrowthPlanning in Early Product Development Stage, IEEE Transaction on Reliability,65(2), 769-781, 2016.
Conference Presentationso Mobin M. and Li. Z., An Integrated Reliability Growth Planning in the New Complex
Engineering Product Development, Accelerated Stress Testing and ReliabilityConference (ASTR 2016), Florida, USA.
o Mobin M. and Li Z., Multi-stage Reliability Growth Planning Using DynamicProgramming, The Institute for Operations Research and the ManagementSciences Annual Conference (INFORMS 2014), California, USA.
o Li Z., Mobin M., Pervaiz M., Keyser T., Multi-Objective and Multi-Stage ReliabilityGrowth Planning in Early Product Development Stage, Industrial and SystemsEngineering Research Conference (ISERC 2014), Montreal, Canada.
Related Publications and Presentations
Section 2: V&V Planning
An Approach for Design Verification and Validation Planning and Optimization for New
Product Reliability Improvement
Scheduling
Challenges
Cost optimization
Reliability improvement
Failures prioritization
V&V effectiveness
Process iteration
A schematic summary of V&V process during NPD for reliability improvement
Failure modes (𝑓𝑖, 𝑖 = 1,… , 𝑛) Criticality (𝐷𝑖, 𝑆𝑖, 𝑂𝑖), V&V activities (𝑣𝑗, 𝑗 = 1,… ,𝑚)
Duration (𝑡𝑗)
Effectiveness (𝜃𝑖𝑗 , 𝛾𝑖𝑗)
Design Failure Modes and
Effects Analysis (DFMEA)
V&V Execution
V&V planning
NO
23
V&V Process in NPD
Final product design
Product Reliability Estimation
Meets reliability
goal?
YES
Literature Review
24
Models that
only focus on
product
requirements
and
configurations
o Quality Function Deployment (QFD) [19]
o Key Characteristics (KCs) [20]
o Design for X (DFX) [21]
Models that
only focus
on
scheduling
and
budgeting
o Project evaluation and review technique (PERT) [16]
o The general evaluation and review technique (GERT) [17]
o The dependency structure matrix (DSM) [18]
Scheduling
Cost optimization Reliability improvement
Failures prioritization
Process effectivenessProcess iteration
Objective function and constraints:Objective: Maximize the product reliability improvement.
Constraints: 1: Limited budget; 2: Limited time; 3: Cover all failure modes; 4: Precedence constraints
25
Objective of V&V activities planning: To determine an optimal set of V&V activities to be implemented in the limited time and cost,
and optimizing reliability.
V&V Activities PlanA schematic view of the V&V planning
Proposed Model for the V&V Planning
Objective: Maximize the product reliability improvement
Constraint 1: Total cost of performing V&V activities
Constraint 2: The critical failure coverage constraint
Constraint 3: Total V&V process time (makespan of V&V process )
Constraint 4: Precedence constraints for V&V activities
Subject to:
𝑴𝑨𝑿 𝑹𝑰𝑻𝒐𝒕𝒂𝒍 = 𝒊=𝟏
𝒏
𝑹𝑰𝒊 =
𝒊=𝟏
𝒏𝑹𝑷𝑵𝒊(𝒊𝒏𝒊𝒕𝒊𝒂𝒍)
𝑹𝑷𝑵𝒊(𝒏𝒆𝒘)
(𝒔𝒋 + 𝒕𝒋)𝒗𝒋 ≤ 𝒔𝒋′,∀ 𝒋 immediately preceding 𝒋′
𝑴𝒂𝒙𝒋=𝟏,..,𝒎; 𝒊=𝟏,…,𝒏
{(𝒔𝒋 + 𝒕𝒋) 𝒗𝒋 , ∀ 𝒊 = 𝟏,… , 𝒏} ≤ 𝑻
𝒋=𝟏
𝒎
𝒂𝒊𝒋 𝒗𝒋≥ 𝟏 , ∀ 𝒊 = 𝟏,… , 𝒏
𝒋=𝟏
𝒎
𝒄𝒋 𝒗𝒋 ≤ 𝑪
26
𝑅𝑃𝑁𝑖 (𝑖𝑛𝑖𝑡𝑖𝑎𝑙) = 𝐷𝑖 (𝑖𝑛𝑖𝑡𝑖𝑎𝑙) ∗ 𝑂𝑖 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 ∗ 𝑆𝑖 (𝑖𝑛𝑖𝑡𝑖𝑎𝑙)
𝐷𝑖 (𝑛𝑒𝑤) = 𝐷𝑖 (𝑖𝑛𝑖𝑡𝑖𝑎𝑙) ∗
𝑗=1
𝑚
(1 − (𝜃𝑖𝑗 ∗ 𝑣𝑗))
o 𝑚 V&V activities 𝑣𝑗 (𝑗 = 1,… ,𝑚) and (𝑣𝑗 ∈ {0,1})
o 𝑛 failures (𝑖 = 1,… , 𝑛).
Numerical Example A modified case study of power assembly design when developing a new next generation engine.
27
o Total budget (𝐶) for performing the V&V activities is $470K. o Total time of implementing V&V process is 480 days.
The incidence matrix Cost and duration of each
V&V activity Initial detectability, occurrence, and
severity for each failure mode
(𝜃𝑖𝑗 , 𝛾𝑖𝑗): Risk reduction percentage in 𝐷𝑖 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 and 𝑂𝑖(𝑖𝑛𝑖𝑡𝑖𝑎𝑙)after conducting the V&V activity 𝑣𝑗 on the failure mode 𝑓𝑖
Numerical Results
Decision variables (𝑣𝑗) and the starting time of each V&V activity
o The objective function value is obtained as: 𝑅𝐼𝑇𝑜𝑡𝑎𝑙 = 𝑖=125 𝐼𝐼𝑖 = 850.132.
o The reduction in total RPN is calculated as: 𝑆𝑢𝑚 𝑅𝑃𝑁 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 – 𝑆𝑢𝑚 𝑅𝑃𝑁 𝑛𝑒𝑤 = 3635.907. o Total cost of implementing the selected six V&V activities is $454,000. o Total implementation time is obtained as 405 days.
28
Summary of results
29
Conclusions and Future Research
Uncertainties in the variables of the V&V planning model:e.g. uncertainty in the DFMEA results, such as failure detectability and occurrence, time and cost of V&V activities, effectiveness, etc.
Possible iteration of V&V activities:e.g. V&V activities can be iterated with different effectiveness levels.
Multi-objective optimization applications:e.g. considering time and cost minimization as objective functions.
Ongoing and Future Research:
Conclusion:
A new mathematical approach to plan V&V activities
o Reliability improvement optimizationo Time and cost constraintso Failure coverageo Effectiveness of V&V activitieso Sequencing of V&V activities
[16] A.K. Bhattacharjee, S.D. Dhodapkar, and R.K. Shyamasundar, “PERTS: an environment for specification
and verification of reactive systems,” Reliability Engineering & System Safety, vol. 71, no.3, pp.299-310,
2001.
[17] W. Bernard, III. Taylor, and J. L. Moore, “R&D project planning with Q-GERT network modeling and
simulation,” Management Science, vol. 26, no. 1, pp. 44-59, 1980.
[18] S. D. Eppinger, D. E. Whitney, R. P. Smith, and D. A. Gebala, “A model-based method for organizing
tasks in product development,” Research in Engineering Design, vol. 6, no. 1, pp.1-13, 1994.
[19] D. Y. Kim, and P. Xirouchakis, “CO 2 DE: a decision support system for collaborative design,” Journal of
Engineering Design, vol. 21, no. 1, pp. 31-48, 2010.
[20] Y. M. Deng, G. A. Britton, and S. B. Tor, “Constraint-based functional design verification for conceptual
design,” Computer-Aided Design, vol. 32, no. 14, pp. 889-899, 2000.
[21] T.C. Kuo, S. H. Huang, and H.-C. Zhang, “Design for manufacture and design for ‘X’: concepts,
applications, and perspectives,” Computers & Industrial Engineering, vol. 41, no. 3, pp. 241-260, 2001.
References
30
Journal Publicationso Mobin M., Li Z., V&V Activity Planning Modeling and Optimization During New
Product Development Stages, Reliability Engineering and System Safety, (UnderReview).
Conference Presentationso Mobin M., Li. Z. An Integrated Approach to Plan the Design Verification and
Validation (V&V) Activities for the New Product Reliability Improvement, 2017IEEE Symposium on Product Compliance Engineering, California, USA.
o Mobin M., Li Z., A Simulation-Optimization Approach to Optimize the DesignVerification and Validation Activities Planning for the New Product ReliabilityImprovement. INFORMS 2016.
Related Publications and Presentations
Mohammad Sadegh Mobin (PhD Candidate),
Western New England University, Springfield, MA
Question & Comments