Accelerated Stress Testing and Reliability Conference An Integrated Reliability Growth Planning in the New Complex Engineering Product Development Mohammadsadegh Mobin Zhaojun (Steven) Li Western New England University [email protected], [email protected]ASTR 2016, Sep 28- 30, Pensacola Beach, FL www.ieee-astr.org 1
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Accelerated Stress Testing and Reliability Conference
An Integrated Reliability Growth Planning in the New Complex Engineering Product
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
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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 (discrete)
2- Test time for each subsystem in each stage (continuous)
3- Percentage of introduced new contents of subsystem in each stage (continuous)
1- Total product development time
2- Number of available test units in each development stage
3- The lower and upper bounds on the test time of each subsystem in each stage
4- The lower and upper bounds on the number of test units for each subsystem in each stage
5- The lower and upper bounds on the percentage of subsystem added/introduced to the system
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Step 1
𝒇𝟏 𝒇𝟐
𝒇𝟑
𝒇𝟏 𝒇𝟐
𝒇𝟑
To obtain final Pareto optimal solutions
through iteratively generating and assessing
the intermediate solutions in the Pareto
frontiers.
Fast Non-dominated sorting
genetic algorithm (NSGA-II)
Step 2 Multiple Criteria Decision
Making (MCDM)
To compare the optimal solutions in terms
of their objective values and as a result,
reduce the number of optimal solutions into
a workable size.
Considering:
all feasible solutions,
quality and diversity of solutions,
all objective functions simultaneously,
constraints when generating solutions.
Considering: each solution as a decision making unit (DMU).
cost type criteria as input for a DMU.
benefit type criteria as output for a DMU.
Proposed optimization method
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Fast non-dominated sorting genetic algorithm (NSGA-II) Step 1: Create a random parent population P0 of size N. Set t = 0.
Step 2: Apply crossover and mutation to 𝑃0 to create offspring population 𝑄0 of size 𝑁.
Step 3: If the stopping criterion is satisfied, stop and return to Pt. Step 4: Set 𝑅𝑡= 𝑃𝑡 ∪ 𝑄𝑡.
Step 5: Identify the non-dominated fronts F1, F2, … , Fk in Rt (using FNDS)
Step 6: For 𝑖 = 1,… , 𝑘 do following steps:
Step 6.1: Calculate crowding distance of the solutions in 𝐹𝑖
Step 6.2: Create 𝑃𝑡+1 as follows:
Case 1: If 𝑃𝑡+1 + 𝐹𝑖 ≤ 𝑁, then set 𝑃𝑡+1 = 𝑃𝑡+1 ∪ 𝐹𝑖 ;
Case 2: If 𝑃𝑡+1 + 𝐹𝑖 > 𝑁, then add the least crowded 𝑁 − 𝑃𝑡+1 solutions from 𝐹𝑖 to 𝑃𝑡+1 Step 7: Use binary tournament selection based on the crowding distance to select parents from Pt+1.
Step 8: Apply crossover and mutation to Pt+1 to create offspring population Qt+1of size N.
Step 9: Set t = t + 1, and go to step 3.
𝑃
𝑄
Parent population
Offspring population
Crossover &
Mutation 𝑅
𝐹1 𝐹2
𝐹3
𝐹𝑘
Fast Non-Dominated Sorting
Population in next
generation 𝐹3
Crowding Distance Sorting
𝐹1 𝐹2
𝐹3 𝑃
Proposed
Optimization Method
(Step 1)
[16-18]
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Proposed
Optimization Method
(Step 2)
Multiple Criteria Decision Making tools: VIKOR
• The name VIKOR is from Serbian:
VIseKriterijumska Optimizacija I Kompromisno Resenje,
• That means:
Multi-criteria Optimization and Compromise Solution.
The basic mechanism: • Calculate the “distance” from each alternative (optimal solution) to a “Positive Ideal
Solution” (PIS) and a “Negative Ideal Solution” (NIS)
• PIS and NIS are defined in “n-dimensional” space, where n represent the number of criterion
(the objective functions of the optimal solutions) in the decision problem.
• The chosen alternative should have the smallest vector distance from the PIS and the greatest
from the NIS.
[19]
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Case study Application of MS MO RGP for next generation dual engine development process
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𝜆3 𝜏 𝐶
Rank 1 20.459 0.030 1223.8
Rank 2 20.459 0.030 1223.8
Rank 3 0.431 2.984 1393.6
Rank 4 0.457 2.970 1307.5
Rank 5 17.211 0.040 1268.8
Rank 6 0.501 2.752 1302.4
Rank 7 0.445 2.684 1389.9
Rank 8 16.214 0.030 1313.9
Rank 9 15.812 0.060 1224.0
Rank 10 0.495 2.591 1379.3
Rank 11 11.783 0.045 2514.3
Rank 12 10.531 0.059 2494.6
Rank 13 10.236 0.074 2514.4
Rank 14 0.317 3.388 2582.9
Rank 15 0.318 3.282 2606.8
Rank 16 5.753 0.160 2471.2
Rank 17 0.318 2.970 2631.2
Rank 18 0.317 2.970 2635.1
Rank 19 0.369 2.749 2609.5
Rank 20 0.528 2.263 2580.1
Rank 21 2.549 0.419 1874.78
Rank 22 2.102 0.508 1924.20
Rank 23 1.587 0.632 1962.61
Rank 24 1.561 0.640 1951.61
Rank 25 2.079 0.655 1924.47
High- ranked optimal solutions
Results : MCDM application
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Conclusions
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Formulate and investigate a multi-stage reliability growth planning model.
Reliability growth planning model is formulated considering multiple objectives.
Considering the percentage of introduced new technology, number of test units, and test time
as decision variables.
Integrate subsystem growth rates within an individual stage into the model.
Applying a multi-objective evolutionary algorithm, called NSGA-II, to find the Pareto
optimal solutions of developed Multi-Objective-Multi-Stage-RGP (MO MS RGP).
Rank the Pareto optimal solutions for solution reduction using an MCDM approach, called
VIKOR.
Future Research:
Considering uncertainty in the parameters of the model
Application and comparison of other MOEAs and MCDM tools
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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.
[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.
[16] Li Z., Mobin M., Keyser T., Multi-objective and multi-stage reliability growth planning in early product development stage, IEEE Transaction on Reliability,
99(1), 1-13, 2016.
[17] Tavana, M., Li, Z., Mobin, M., Komaki, M., & Teymourian, E.. Multi-objective control chart design optimization using NSGA-III and MOPSO enhanced with DEA and TOPSIS. Expert Systems with Applications, 50, 17-39. 2016.
[18] Mobin, M., Li, Z., and Massahi Khoraskani, M. Multi-objective X-bar control chart design by integrating NSGA-II and data envelopment analysis. Proc. 2015 Ind. Syst. Eng. Res. Conf. 2015.
[19] Mobin, M., Dehghanimohammadabadi, M., and Salmon, C. Food product target market prioritization using MCDM approaches. in Proc. the Industrial and Systems Engineering Research Conference (ISERC), Montreal, Canada. 2014.
References
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Biography
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Mohammadsadegh Mobin is a doctoral student in Industrial Engineering and Engineering
Management at Western New England University, MA, USA. He holds a Master degree in Operations
Research (OR) (2011) and a bachelor degree in Industrial Engineering (IE) (2009). He served as a
quality engineer (2006-2012) in different industries. He has published in different journals including:
Expert Systems with Applications and IEEE Transaction on Reliability. He has been the instructor of
“Design and Analysis of Experiments” and “Probability and Statistics”. His research interests lie in
the area of different applications of operations research tools in quality and reliability engineering.
Zhaojun “Steven” Li is an Assistant Professor at the Department of Industrial Engineering and
Engineering Management, Western New England University in Springfield, MA. Dr. Li’s research
interests focus on Reliability, Quality, and Safety Engineering in Product Design, Systems
Engineering and Its Applications in New Product Development, Diagnostics and Prognostics of
Complex Engineered Systems, and Engineering Management. He earned his doctorate in Industrial
Engineering from the University of Washington in 2011. He is an ASQ certified Reliability Engineer,
and Caterpillar Six Sigma Black Belt. Dr. Li’s most recent industry position was a reliability team
lead with Caterpillar Rail Division to support the company’s Tier 4 Locomotive New Four Stroke
Engine and Gas-Diesel Dual Fuel Engine Development.
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THANK YOU
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