Reliability Modeling and Optimization of New Product Development - - PowerPoint PPT Presentation
Reliability Modeling and Optimization of New Product Development Process Mohammad Sadegh Mobin PhD Candidate in Engineering Management Department of Industrial Engineering and Engineering Management Western New England University Springfield,
Mohammad Sadegh Mobin PhD Candidate in Engineering Management Department of Industrial Engineering and Engineering Management Western New England University Springfield, MA PhD advisor: Dr. Zhaojun (Steven) Li 2017
mobin.sadegh@gmail.com
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Part 1: Reliability Growth Planning (RGP) Modeling and Optimization Part 2: Verification and Validation (V&V) Activities Planning and Optimization
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Continuous Product Development
High % of total revenue Consumer needs changes Marketing environment changes To stay ahead of Competition Changing technology Not to lose market share
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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)
Planning Product/Process design & development Product/Process V&V Production mobin.sadegh@gmail.com
NPD programs are often plagued with:
Product Company Issues Year Source
787 Dreamliner Boeing 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 Sikorsky US Marine Corps' (USMC's) A failure in the main gear box and need for redesign of the component. Problems with wiring and hydraulics
2015 HIS Jane’s 360
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NASA’s main projects that faced cost and time overrun:
Prime contract had grown: 25%
(from $783M to $986M, the 3rd increase in 2 years).
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
“80% experienced an increase in unit costs from initial estimates”.
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Improve the NPD process by reducing:
Model and optimize the NPD reliability process in terms of cost, time, and product reliability
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Test Time MTBF (Days)
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
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 $70k 490 Days
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𝐷 𝑢 : The average failure rate 𝐷 𝑢 = 𝑂(𝑢)/𝑢 𝑂 𝑢 : The cumulative number of failures up to time 𝑢 during the reliability growth testing. 𝜀, 𝛽 > 0 , 𝛽 is known as growth rate
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An example of multi-stage NPD plan
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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
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Significant contribution: Multi-objective & Multi-stage RGP
Author Duane (1964) [1] Crow (1974) [2] Lloyd (1986) [3] Robinson and Dietrich (1987) [4] Coit (1998) [5] Walls & Quigley (1999) [6] Walls & Quigley (2001) [7] Quigley and Walls (2003) [8] Krasich et al. (2004) [9] Johnston et al. (2006) [10] Jin and Wang. (2009) [11] Jin et al. (2010) [12] Jin et al. (2013) [13] Jin and Li (2016) [14] Jackson (2016) [15] Li et al (2016) [16] Single
Multi
Single - stage Multi- stage Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No No Yes Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No Yes No No Yes No Yes
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Objectives :
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
MTBF
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Min: 𝜇𝑜 = 𝑔 𝜇 𝑗−1, 𝜇 𝑜(𝑗), 𝛽𝑗 , 𝑈𝑗 Min: 𝜐 = 𝑗=1
𝑜
𝜐𝑗 , 𝑗 = 1, … , 𝑜 Min: 𝐷 = 𝑗=1
𝑜
𝐷𝑗 , 𝑗 = 1, … , 𝑜 s.t. 0 ≤ 𝜐 ≤ 𝜐𝑣 𝑂𝑚(𝑗) ≤ 𝑂𝑗 ≤ 𝑂𝑣(𝑗) , 𝑗 = 1, … , 𝑜 Decision variables:
𝒈𝟐 𝒈𝟑 𝒈𝟒
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
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Method 1: Creating a weighted composite objective function
Shortcomings:
Method 2: Consider one as main objective function and others as constraints
Shortcomings:
Method 3: Multi-Objective Evolutionary Algorithms (MOEAs)
e.g., MOPSO, NSGA, etc.
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Overview of the proposed solution methodology
Mathematical model:
A set of Pareto-
Inputs (Minimization objective functions) Outputs (Maximization objective functions)
Data Envelopment Analysis (DEA) Multiple Objectives Evolutionary Algorithm
Optimal efficient solutions
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i stage Group description λij θ1 (%) θ2 (%) θ3 (%) cij ($1000) mi αi Nl(i) Nu i 1 Engine Block 1.38 100 600 2 0.4 4 8 Turbocharger 0.03 100 45 2 Engine control 0.24 80 50 4 0.3 8 16 Cooling System 0.02 100 30 Fuel System 0.20 80 40 Lubricating system 0.05 80 20 3 Engine control 0.24 20 12.5 3 0.2 6 20 Fuel system 0.20 20 10 Lubricating system 0.05 20 5
Min: 𝜇𝑗=3 = 𝑔 𝜇 𝐽(𝑗−1), 𝜇 𝑜(𝑗), 𝛽𝑗 , 𝑈𝑗 Min: 𝑗=1
𝑜
𝐷𝑗 = 𝐷1 + 𝐷2 + 𝐷3 Min: 𝜐 = 𝑗=1
𝑜
𝜐𝑗 = 𝜐1 + 𝜐2 + 𝜐3 s.t. 0 ≤ 𝜐 ≤ 𝜐𝑣 ⟹ 0 ≤ 𝜐1 + 𝜐2 + 𝜐3 ≤ 3.5 4 ≤ 𝑜11 + 𝑜12 ≤ 8 8 ≤ 𝑜21 + 𝑜22 + 𝑜23 + 𝑜24 ≤ 16 6 ≤ 𝑜31 + 𝑜32 + 𝑜33 ≤ 20
𝜐𝑣: 3.5 years The effective work hours in each year: 2000 hours The variable cost per hour: $2000
18 decision variables:
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0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.5 1 1.5 2 2.5 3 3.5 3000 6000 9000 12000 15000
f1(x): Failure rate of stage 3 f2(x): Projected total test time f3(x): Projected total test cost
1 = 0.4 2 = 0.3 3 = 0.2 n(1) = 1.41 n(2) = 0.51 n(3) = 0.49
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0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0.5 1 1.5 2 2.5 3 3.5 3000 6000 9000 12000 15000
f1(x): Failure rate of stage 3 f2(x): Projected total test time f3(x): Projected total test cost
CCR solutions NSGA-II solutions
Inputs Output DMUs Time Cost Reliability (Yrs.) ($) MTBF (Yrs.) DMU 01 3.45 15.38 2.13 DMU 02 0.79 4.56 0.79 DMU 04 3.28 14.72 2.13 DMU 07 0.82 4.67 0.83 DMU 10 2.30 10.87 1.88 DMU 15 0.88 4.91 0.89 DMU 19 0.80 4.60 0.81 DMU 26 3.23 14.53 2.10 DMU 31 2.66 12.31 1.96 DMU 34 1.76 8.57 1.58 DMU 36 2.57 11.96 1.94 DMU 38 2.25 10.68 1.86 DMU 48 0.79 4.56 0.79 DMU 51 2.22 10.56 1.86 DMU 56 1.83 8.84 1.62 DMU 58 2.29 10.84 1.87 DMU 67 1.86 8.95 1.64 DMU 69 1.78 8.65 1.60 DMU 70 2.55 11.88 1.94 DMU 86 1.20 6.20 1.18 DMU 87 1.86 8.94 1.63 DMU 96 1.22 6.27 1.20 DMU 98 1.21 6.23 1.19
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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)
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[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
[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.
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Journal Publications
Growth Planning by Considering the Timing of New Technologies Introduction, IEEE Transaction on Reliability, 66 (1), 97-110, 2017
Planning in Early Product Development Stage, IEEE Transaction on Reliability, 65(2), 769-781, 2016.
Conference Presentations
Engineering Product Development, Accelerated Stress Testing and Reliability Conference (ASTR 2016), Florida, USA.
Programming, The Institute for Operations Research and the Management Sciences Annual Conference (INFORMS 2014), California, USA.
Growth Planning in Early Product Development Stage, Industrial and Systems Engineering Research Conference (ISERC 2014), Montreal, Canada.
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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 (𝑔
𝑗, 𝑗 = 1, … , 𝑜)
Criticality (𝐸𝑗, 𝑇𝑗, 𝑃𝑗), V&V activities (𝑤𝑘, 𝑘 = 1, … , 𝑛) Duration (𝑢𝑘) Effectiveness (𝜄𝑗𝑘 , 𝛿𝑗𝑘) Design Failure Modes and Effects Analysis (DFMEA) V&V Execution V&V planning NO
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Final product design Product Reliability Estimation Meets reliability goal? YES
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Models that
product requirements and configurations
Models that
scheduling and budgeting
Scheduling Cost optimization Reliability improvement Failures prioritization Process effectiveness Process iteration mobin.sadegh@gmail.com
Objective: Maximize the product reliability improvement. Constraints: 1: Limited budget; 2: Limited time; 3: Cover all failure modes; 4: Precedence constraints
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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.
A schematic view of the V&V planning
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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: 𝑵𝑩𝒀 𝑺𝑱𝑼𝒑𝒖𝒃𝒎 =
𝒋=𝟐 𝒐
𝑺𝑱𝒋 =
𝒋=𝟐 𝒐 𝑺𝑸𝑶𝒋(𝒋𝒐𝒋𝒖𝒋𝒃𝒎)
𝑺𝑸𝑶𝒋(𝒐𝒇𝒙)
(𝒕𝒌 + 𝒖𝒌)𝒘𝒌 ≤ 𝒕𝒌′,∀ 𝒌 immediately preceding 𝒌′ 𝑵𝒃𝒚
𝒌=𝟐,..,𝒏; 𝒋=𝟐,…,𝒐{(𝒕𝒌 + 𝒖𝒌) 𝒘𝒌 , ∀ 𝒋 = 𝟐, … , 𝒐} ≤ 𝑼 𝒌=𝟐 𝒏
𝒃𝒋𝒌 𝒘𝒌 ≥ 𝟐 , ∀ 𝒋 = 𝟐, … , 𝒐
𝒌=𝟐 𝒏
𝒅𝒌 𝒘𝒌 ≤ 𝑫
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𝑆𝑄𝑂𝑗 (𝑗𝑜𝑗𝑢𝑗𝑏𝑚) = 𝐸𝑗 (𝑗𝑜𝑗𝑢𝑗𝑏𝑚) ∗ 𝑃𝑗 𝑗𝑜𝑗𝑢𝑗𝑏𝑚 ∗ 𝑇𝑗 (𝑗𝑜𝑗𝑢𝑗𝑏𝑚) 𝐸𝑗 (𝑜𝑓𝑥) = 𝐸𝑗 (𝑗𝑜𝑗𝑢𝑗𝑏𝑚) ∗
𝑘=1 𝑛
(1 − (𝜄𝑗𝑘 ∗ 𝑤𝑘))
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A modified case study of power assembly design when developing a new next generation engine.
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The incidence matrix Cost and duration of each V&V activity Initial detectability, occurrence, and severity for each failure mode (𝜄𝑗𝑘 , 𝛿𝑗𝑘): Risk reduction percentage in 𝐸𝑗 𝑗𝑜𝑗𝑢𝑗𝑏𝑚 and 𝑃𝑗(𝑗𝑜𝑗𝑢𝑗𝑏𝑚) after conducting the V&V activity 𝑤𝑘 on the failure mode 𝑔
𝑗
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Decision variables (𝑤𝑘) and the starting time of each V&V activity
25 𝐽𝐽𝑗 = 850.132.
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Summary of results
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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
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[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.
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Journal Publications
Product Development Stages, Reliability Engineering and System Safety, (Under Review).
Conference Presentations
Validation (V&V) Activities for the New Product Reliability Improvement, 2017 IEEE Symposium on Product Compliance Engineering, California, USA.
Verification and Validation Activities Planning for the New Product Reliability
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Mohammad Sadegh Mobin (PhD Candidate),
Western New England University, Springfield, MA
mobin.sadegh@gmail.com