1 / 36

System Reliability and Availability Estimation Under Uncertainty Tongdan Jin, Ph.D.

System Reliability and Availability Estimation Under Uncertainty Tongdan Jin, Ph.D. Ingram School of Engineering Texas State University, San Marcos, TX tj17@txstate.edu 4/11/2012. Contents. System Reliability Estimation * Variance of reliability estimate * Series, and parallel systems

dannyr
Télécharger la présentation

System Reliability and Availability Estimation Under Uncertainty Tongdan Jin, Ph.D.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. System Reliability and Availability Estimation Under Uncertainty Tongdan Jin, Ph.D. Ingram School of Engineering Texas State University, San Marcos, TX tj17@txstate.edu 4/11/2012

  2. Contents • System Reliability Estimation * Variance of reliability estimate * Series, and parallel systems • Operational Availability * Performance based maintenance/logistics/contracting * Reliability growth or spare parts stocking ? * A unified availability model • Conclusion

  3. 3 Topic One Modeling System Reliability With Uncertain Estimates

  4. Two Components having Same Reliability? Component Test Plan 1 Testing 100 hours Sample n=10, survivals=9 Test Plan 2 Testing 100 hours Sample n=20, survivals=18 Which component is more reliable?

  5. Risk-Averse vs. Risk-Neutral Design system 2 system 1 • = probability density function for reliability estimate • risk-neutral design would always choose system 1 • risk-adverse design might choose system 2 5

  6. Variance of Reliability Estimate Test Plan 1 Testing 100 hours Sample n=10, survivals=9 Test Plan 2 Testing 100 hours Sample n=20, survivals=18 Which component is more reliable? 6

  7. r=0.8 r=0.9 Variance vs. Sample Size n=sample size x=survivals 7

  8. Reliability Variance of Series Systems Component 1 Component 2 k Components in Series 8

  9. Numerical Example Component 1 Component 2 Test Plan 1 Testing 100 hours n1=10, x1=9 n2=20, x2=17 9

  10. Reliability Confidence Estimate Assuming is normally distributed, the lower bound With 90% confidence With 95% confidence 10

  11. Reliability Variance of Parallel System Component 1 Component 2 Where for i=1, and 2 11

  12. Estimates for Reliability and Unreliability n=sample size x=survivals Series System Parallel System 12

  13. Variance of Parallel System k components in parallel Where 13

  14. Numerical Example Component 1 Component 2 Test Plan 1 Testing 100 hours n1=10, x1=9 n2=20, x2=17 14

  15. Reliability Confidence Estimate Assuming is normally distributed, then With 90% confidence With 95% confidence 15

  16. 5 4 1 6 2 3 1 7 4 5 ’ 1’ 2’ 7 Variance Estimation 4 ’ 1’’ 7 7 ’ 1’’ Series-Parallel Systems 16

  17. Compute r and var(r) over Time 17

  18. 18 Topic Two Operational Availability under Performance Based Contract (PBC)

  19. Service Parts Logistics Business • Representing 8-10% of GDP in the US. • US airline industry is $45B on MRO in 2008. • US auto industry is $190B and $73B for parts in 2010. • US DoD maintenance budget $125B and $70B inventory with 6,000 suppliers. • Joint Strike Fighter (F-35): $350B for R/D/P, and $600B for after-production O/M for 30 years. • EU Wind turbine service revenue €3B in 2011 • IBM computing/network servers, etc.

  20. Total Ownership Cost Distribution 20 Cumulative costs over product life Cost ($) 30-40% 50-60% 5% 10-20% Research Development Manufacturing Operation and Support Retirement PBC aims to lower the cost of ownership while ensuring system performance goals Reference DoD 5000, University of Tennessee

  21. Reliability Allocation and Spare Parts Logistics Reliability Allocation Spare Parts Logistics r5 (t) s32 Fleet 1 Fleet 2 Fleet n-1 Fleet n s21 r1(t) s32 r6(t) r8(t) s s22 r2(t) r4(t) s3,n-1 r7(t) s3,n • Scherbrooke (1968, 1992) • Muckstadt (1973) • Graves (1985) • Lee (1987) • Cohen et al. (1990) • Diaz & Fu (1996) • Alfredsson (1997) • Zamperini & Freimer (2005) • Lau & Song (2008) • Kutanoglu et al. (2009) • More ..... • Tillman et al. (1977) • Kuo et al. (1987) • Chen (1992) • Jin & Coit (2001) • Levitin & Lisnianski (2001) • Coit et al. (2004) • Ramirez-Marquez et al. (2004) • Marseguerra, Zio (2005) • Jin & Ozalp (2009) • Ramirez-Marquez & Rocco (2010) • More .....

  22. A 4-Step Performance-Based Contracting Step 1 Performance Outcome Step 2 Performance Measures Step 3 Performance Criteria Step 4 Performance Compensation System availability, MTBF, MTTR, Mean downtime, logistics response time Mini availability, max failure rate, max repair waiting time, max cost per unit time System readiness, operational reliability, assurance of spare parts supply Cost plus incentive fee, cost plus award fee, linear reward, exponential reward 22

  23. Five Performance Measures by US DoD • Operational availability (OA) • Inherent reliability or mission reliability (MR) • Logistics response time (e.g. MTTR, LDT) • Cost per unit usage (CUU) • Logistics footprint 23

  24. Interactions of Five Performance Measures MTBF=Mean Time Between Failures MTTR=Mean Time to Repair MLDT=Mean Logistics Delay Time Mission Reliability (MR) Operational Availability(OA) Cost Per Unit Usage (CUU) Logistics Footprint (LF) Logistics Response Time (LRT) 24

  25. Evolution of Sustainment/Maintenane Solution CM=>{Warranty, MBC} PM=>{MBC} CBM=>{Warranty, MBC} PBM/PBL=>{PBC} CM Total Ownership Cost PM CBM PBM PBC aims to lower the cost of ownership while ensuring system performance (e.g. reliability and availability). Note: PBM=performance-based maintenance 25

  26. Integrating Manufacturing with Service Emergency Repair OEM for design and manufacturing Repair Center Local spares stocking System fleet N(t) Supplier or OEM Customer Emergency Repair OEM for design and manufacturing Local spares stocking Repair Center System fleet N(t) Supplier or OEM Customer

  27. Availability and Variable Fleet Size Variable Fleet Size • Availability Semiconductor Industry • MTBF=100 hours, MDT=5 hours • MTBF=200 hours, MDT=10 hours Wind Power Industry 27

  28. Performance Measures and Drivers Inherent Reliability () MTBF OEM Controlled Maintenance Schedule () Operational Availability (Ao) MTTR Logistics Support (s, ts, tr) MLDT System Fleet (n, ) Customer Controlled 28

  29. A Unified Operational Availability Model Ref: Jin & Wang (2011)

  30. =0.5, n=50, tr=60 days Ao=0.8 Ao=0.95 Trading Reliability with Spares Stocking (II) Note: here lambda=alpha in previous slide 30

  31. Trading Reliability with Spares Stocking (I) =0.5, n=50, tr=30 days Ao=0.8 Ao=0.95 31

  32. Trading Reliability and Spares Stocking (III) =0.8, n=50, tr=30 days Ao=0.8 Ao=0.95 32

  33. Key Terminologies Variance of reliability estimate Variance propagation Series/parallel reduction Unbiased estimate Operational availability Mean downtime Mean time to repair Mean logistics delay time Mean time between failures Mean time to failure Performance based logistics/contracting/maintenance Performance measure Performance criteria Material based contracting 33

  34. Conclusion Variance is a simple, yet accurate metric to gauge the reliability uncertainty Estimating the reliability variance for series, parallel and mixed series-parallel systems PBC aims to guarantee the system performance while lowering the cost of ownership PBC incentivizes the OEM/3PL to maximize the profit by optimizing the development, production and logistics delivery.

  35. References Reliability Estimation D. W. Coit, “System reliability confidence intervals for complex systems with estimated component reliability,” IEEE Transactions on Reliability, vol. 46, no. 4, 1997, pp. 487-493. J. E. Ramirez-Marquez, and W. Jiang, “An improved confidence bounds for system reliability,” IEEE Transactions on Reliability, vol. 55, no. 1, 2006, pp. 26-36. E. Borgonov, “A new uncertainty measure”, Reliability Engineering and System Safety, vo;. 92, pp. 771-784, 2007. T. Jin, D. Coit, "Unbiased variance estimates for system reliability estimate using block decompositions," IEEE Transactions on Reliability , vol. 57, 2008, pp.458-464. H. Guo, T. Jin, A. Mettas, “Designing reliability demonstration test for one-shot systems under zero component failures," IEEE Transactions on Reliability , vol. 60, no. 1, 2011, pp. 286-294 Availability Estimation Huang, H.-Z., H.J. Liu, D.N.P. Murthy. 2007. Optimal reliability, warranty and price for new products. IIE Transactions, vol. 39, no. 8, pp. 819-827. Kang, K., M. McDonald. 2010. Impact of logistics on readiness and life cycle cost: a design of experiments approach, Proceedings of Winter Simulation Conference. pp. 1336-1346. Kim, S.H., M.A. Cohen, S. Netessine. 2007. Performance contracting in after-sales service supply chains. Management Science, vol. 53, pp. 1843-1858. Nowicki, D., U.D. Kumar, H.J. Steudel, D. Verma. 2008. Spares provisioning under performance-based logistics contract: profit-centric approach. The Journal of the Operational Research Society. vol. 59, no. 3, 2008, pp. 342-352. Öner, K.B., G.P. Kiesmüller, G.J. van Houtum. 2010. Optimization of component reliability in the design phase of capital goods. European Journal of Operational Research, vol. 205, no. 3, pp. 615-624. T. Jin, P. Wang, “Planning performance based contracts considering reliability and uncertaint system usage,” Journal of the Operational Research Society , 2012 (forthcoming) Jin, T., Y. Tian, “Optimizing reliability and service parts logistics for a time-varying installed base,” European Journal of Operational Research, vol. 218, no. 1, 2012, pp. 152-162 35

  36. For Questions E-mail to tj17@txstate.edu 36

More Related