Research Papers

Nested Multistate Design for Maximizing Probabilistic Performance in Persistent Observation Campaigns

[+] Author and Article Information
Jeremy S. Agte

Department of Aeronautics and Astronautics,
Air Force Institute of Technology, Dayton, OH 45433
e-mail: jeremy.agte@afit.edu

Nicholas K. Borer

Newport News, VA 23606
e-mail: nick_borer@yahoo.com

1Corresponding author.

Manuscript received March 3, 2015; final manuscript received May 25, 2015; published online November 20, 2015. Assoc. Editor: Ioannis Kougioumtzoglou.

ASME J. Risk Uncertainty Part B 2(1), 011006 (Nov 20, 2015) (9 pages) Paper No: RISK-15-1033; doi: 10.1115/1.4030948 History: Received March 03, 2015; Accepted July 02, 2015

The paper presents a nested multistate methodology for the design of mechanical systems (e.g., a fleet of vehicles) involved in extended campaigns of persistent surveillance. It uses multidisciplinary systems analysis and behavioral-Markov modeling to account for stochastic metrics such as reliability and availability across multiple levels of system performance. The effects of probabilistic failure states at the vehicle level are propagated to mission operations at the campaign level by nesting various layers of Markov and estimated-Markov models. A key attribute is that the designer can then quantify the impact of physical changes in the vehicle, even those physical changes not related to component failure rates, on the predicted chance of maintaining campaign operations above a particular success threshold. The methodology is demonstrated on the design of an unmanned aircraft for an ice surveillance mission requiring omnipresence over Antarctica. Probabilistic results are verified with Monte Carlo analysis and show that even aircraft design parameters not directly related to component failure rates have a significant impact on the number of aircraft lost and missions aborted over the course of the campaign.

Your Session has timed out. Please sign back in to continue.


Agte, J., Borer, N., and de Weck, O., 2012, “Multistate Design Approach to the Analysis of Performance Robustness for a Twin-Engine Aircraft,” J. Airc., 49(3), pp. 781–793. 10.2514/1.C031338
Agte, J., Borer, N., and de Weck, O., 2012, “Design of Long-Endurance Systems With Inherent Robustness to Partial Failures During Operations,” J. Mech. Des., 134(10), p. 100903. 10.1115/1.4007574
Agte, J., and Borer, N., 2012, “Design of Robust Aircraft for Persistent Observation Campaigns Using Nested Multistate Design,” 12th AIAA Aviation Technology, Integration, and Operations Conference and 14th AIAA/ISSM, Indianapolis, IN, September, American Institute of Aeronautics and Astronautics, Reston, VA, AIAA 2012-5452.
Dubbeldam, J., and Redig, F., 2006, “Multilayer Markov Chains With Applications to Polymers in Shear Flow,” J. Stat. Phys., 125(1), pp. 225–243. 10.1007/s10955-006-9166-z
Jin, T., Xing, L., and Yu, Y., 2011, “A Hierarchical Markov Reliability Model for Data Storage Systems With Media Self-Recovery,” Int. J. Reliab. Qual. Saf. Eng., 18(1), pp. 25–41. 10.1142/S0218539311004019
Kemeny, J. G., and Snell, J. L., 1976, Finite Markov Chains, D. Van Nostrand Company, Inc., Princeton, NJ.
Jacobi, M. N., and Goernerup, O., 2007, “A Dual Eigenvector Condition for Strong Lumpability of Markov Chains,” arXiv.org, http://arxiv.org/abs/0710.1986, accessed May 2015.
Abdel-Moneim, A. M., and Leysieffer, F. W., 1982, “Weak Lumpability in Finite Markov Chains,” J. Appl. Probab., 19 (3), pp. 685–691. 10.2307/3213528
Berreto, A. M., and Fragoso, M. D., 2011, “Lumping the States of a Finite Markov Chain Through Stochastic Factorization,” Proceedings of the 18th IFAC Congress, International Federation of Automatic Control, Laxenburg, Austria, pp. 4206–4210.
de Sterck, H., Manteuffel, T. A., McCormick, S. F., Nguyen, Q., and Ruge, J., 2008, “Multilevel Adaptive Aggregation for Markov Chains, With Application to Web Ranking,” SIAM J. Sci. Comput., 30(5), pp. 2235–2262. 10.1137/070685142
Katehakis, M. N., and Smit, L. C., 2012, “A Successive Lumping Procedure for a Class of Markov Chains,” Probab. Eng. Inf.l Sci., 26(4), pp. 483–508. 10.1017/S0269964812000150
Babcock IV, P. S., 1996, “Developing the Two-Fault Tolerant Attitude Control Function for the Space Station Freedom,” 20th International Symposium on Space Technology and Science, Gifu, Japan, May, Kokosi Bunken Insatsusha Company, Tokyo, Japan, Tech. Rep.
Babcock IV, P. S., and Zinchuk, J. J., 1990, “Fault-Tolerant Design Optimization: Application to an Underwater Vehicle Navigation System,” Proceedings of the (1990) Symposium on Autonomous Underwater Vehicle Technology (IEEE/OES), Institute of Electrical and Electronics Engineers, New York, pp. 34–43.
Babcock IV, P. S., Rosch, G., and Zinchuk, J. J., 1991, “An Automated Environment for Optimizing Fault-Tolerant Systems Designs,” Proceedings of the (1991) Annual Reliability and Maintainability Symposium (IEEE), Institute of Electrical and Electronics Engineers, New York, pp. 360–367.
Dominguez-Garcia, A. D., Kassakian, J. G., Schindall, J. E., and Zinchuk, J. J., 2006, “On the Use of Behavioral Models for the Integrated Performance and Reliability Evaluation of Fault-Tolerant Avionics Systems,” IEEE/AIAA Digital Avionics Systems Conference, Portland, Oregon, October, Institute of Electrical and Electronics Engineers, New York, Tech. Rep.
Lisnianski, A., and Levitin, G., 2003, Multi-State System Reliability (Series on Quality, Reliability and Engineering Statistics, Vol. 6), World Scientific, Singapore.
Bhat, U. N., and Miller, G. K., 2002, Elements of Applied Stochastic Processes, John Wiley and Sons, Inc., Hoboken, NJ.
Howard, R. A., 2007, Dynamic Probabilistic Systems: Volume I, Markov Models, Dover Publications, Mineola, NY.
NASA, 2012, “IceBridge: An Airborne Mission for Earth’s Polar Ice,” http://www.nasa.gov/mission_pages/icebridge/, accessed Jun. 2012.
Department of Defense, 2003, “Unmanned Aerial Vehicle Reliability Study,” http://www.uadrones.net/military/research/ acrobat/0302.pdf, accessed Jun. 2012.
Roskam, J., 1971, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, Roskam Aviation and Engineering Corporation, Lawrence, KS.
Grasmeyer, J., 1998, “Stability and Control Derivative Estimation and Engine-Out Analysis,” Virginia Tech, January, VPI-AOE-254.
Moire Inc., 2004, “Cost and Business Model Analysis for Civilian UAV Missions,” Prepared for the National Aeronautics and Space Administration, NASA.
Mettas, A., 2000, “Reliability Allocation and Optimization for Complex Systems,” Proceedings of the Annual IEEE Reliability and Maintainability Symposium, Institute of Electrical and Electronics Engineers, New York.
Nickol, C. L., Guynn, M. D., Kohout, L. L., and Ozoroski, T. A., 2007, “High Altitude Long Endurance UAV Analysis of Alternatives and Technology Requirements Development,” March, NASA/TP-2007-214861.
Tsach, S., Peled, A., Penn, D., and Touitou, D., 2004, “The CAPECON Program: Civil Applications and Economical Effectivity of Potential UAV Configurations,” Proceedings of the 3rd AIAA Unmanned Unlimited Technical Conference, Workshop, and Exhibit, American Institute of Aeronautics and Astronautics, Reston, VA.


Grahic Jump Location
Fig. 1

Markov chain formulation for a generic three-element system. Each state is characterized by performance, GKs, and the probability, PKs, that the system finds itself in that particular state of performance at time t. The failure levels (FL) indicate the total number of failures the system has experienced within the corresponding level’s set of system states. λ are component failure rates.

Grahic Jump Location
Fig. 2

Nested reliability analysis procedure

Grahic Jump Location
Fig. 6

Main effect of maximum engine power on campaign availability

Grahic Jump Location
Fig. 7

Main effect of wing sweep on total vehicles lost

Grahic Jump Location
Fig. 4

SEM—sortie equivalent states are N = nominal; D = degraded; A = sortie abort; L = loss of vehicle

Grahic Jump Location
Fig. 3

VMM—vehicle component failure rates are λA = failure rate of component A, 1/500  h; λB = failure rate of component B, 1/500  h; λC = failure rate of component C, 1/200  h; λD = failure rate of component D, 1/300  h

Grahic Jump Location
Fig. 8

Tradespace of life-cycle cost and campaign availability showing effect of manipulation of component failure rates for geometry optimized for nominal performance (shaded diamonds), manipulation of design variables with fixed component failure rates (open diamonds), and concurrent multistate manipulation of both parameters (black diamonds)

Grahic Jump Location
Fig. 5

CEM—CEM rates come from SEM: λNDCEM=λNDSEM=1/198.2  h; λDFCEM=λNDASEM+λNDLSEM=1/141.7  h; λNFCEM=2  ptλNASEM+λNLSEM=1/1566  h; μDNCEM=f(MTTF); μFNCEM=1/346  h

Grahic Jump Location
Fig. 9

Life-cycle cost comparison of baseline and multistate solutions. Stratifications in data produced by varying x are due to the fact that design geometry can only affect availability through system performance, thus changes occur through step transitions as system performance crosses a threshold (e.g., from abort to degraded). Component failure rates, on the other hand, affect availability through transition probabilities in a continuous fashion, thus data are not stratified.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Articles from Part A: Civil Engineering
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In