1. System Performance Definitions and Application of Failure, Reliability, Resilience and Vulnerability KlaraGunnarsen, Cornelius Zeller, Matthias Ganghofner and Justin Kotzebue

2. To evaluate the performance of a system, different indices are used to show the sustainability of a system. Failure - Reliability - Resilience - Vulnerability System performance

3. Definitions used for system performance analysis • Failure • Reliability • Resilience • Vulnerability • Sustainability • Case study • Scenario • Customised equations • Sustainability analysis • Conclusion Overview

4. Failure: • Needs to be defined for a system • Identifies when a system cannot fulfill its intended functions • Is always in relation to time • May be easily defined or complex with a combination of different parameters. Failure (Manohar & Gupta 2005)

5. Reliability Ris the probability that a system will fulfill its intended function for a specific time period and under given conditions. It is the probability of satisfaction or the counter probability of failure F. R(t) = 1 – F(t) Reliability (Hashimoto et al., 1982)

6. Resilience is the ability of a system to recover. Resilience is the probability P of a system Sto re-enter a non-failure state NF after a period of failure F. Resilience (Hashimoto et al., 1982)

7. Vulnerability is the probability of a hazardous event multiplied by the impact of the event. In other words it is the measure of the likely damage a failure event may cause. If reliability is very high a system will be less vulnerable as the probability of a hazardous event is low. Vulnerability (Ajamiet al. 2008)

8. Reliability-Resilience-Vulnerability: R-R-V modelling In order to analyze the System Performance we multiply these three interrelating components to achieve system sustainability System Performance Analysis (Ajamiet al. 2008)

9. Water reservoir concept Case – Shasta Lake, California (http://www.dailyventure.com/photo/Shasta-Dam-and-Shasta-Lake)

10. Fresh water supply • Area prone to droughts • Supply should always meet demand • Management strategies have to be evaluated in which restrictions on water outflow may be necessary  Drawing of reservoir Case - Environment (Ajamiet al. 2008)

11. In this case, failure state is when demand coverage Xtcannot meet demand Ct. • Ztdefines the system performance • Wdescribes the transition between a failure and non-failure state Case - Failure (Ajamiet al. 2008)

12. Reliability is calculated by the sum of monthly demand coverage Xt in relation to the sum of the total monthly demand Ci. CR =1: supply meets the demand Case - Reliability (Ajamiet al. 2008)

13. Resilience is the relation between the number of months where the system is in transition between a failure and non-failure state Wtand number of total months where supply does not meet the demand. T is the total amount of months. The closer to 1, thefasteritrecovers! Case - Resilience (Ajamiet al. 2008)

14. Vulnerability of a water supply system shows the maximum shortfall of water [m3] accrued during failure periods.  Case - Vulnerability (Ajamiet al. 2008)

15. For the relative vulnerability we use the deficit volume Cv and divide it with the total supply in the failure state period. Case - Vulnerability (Ajamiet al. 2008)

16. System sustainability (S): The closer to 1 the more sustainable Case – System Performance Analysis (Ajamiet al. 2008)

17. 5% buffer-zone coefficient: • Less reliable than other scenarios, • More resilient during drought • 20% buffer-zone coefficient: • High reliability of meeting demand • Less vulnerable • Less resilient during drought • Chosen scenario: Combination  5% during drought, 20% at all other times Case - results (Ajamiet al. 2008)

18. Performance analysis proved to be a good tool to use for choosing management strategies for a water supply system. Some argue that vulnerability can be left out of the sustainability equation as it is inversely related to reliability. We think not, as the relationship is non-linear. Conclusion (Kjeldsen& Rosbjerg 2004)

19. Ajami, N.K., Hornberger, G.M. , Sunding D. L. (2008): Sustainable water resource management under hydrological uncertainty. [online] WATER RESOURCES RESEARCH, VOL. 44, W11406, doi:10.1029/2007WR006736, 2008 Available at http://www.google.at/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDYQFjAA&url=http%3A%2F%2Fare.berkeley.edu%2F~sunding%2FSustainableMngmtWater.pdf&ei=ccprU-eXCJGh7Abzw4GQBg&usg=AFQjCNEo4aKE4Nd15xQ_Rl8ADByAh_wsoA&sig2=bSv_lnS7dGxj1DKavKXhmA&bvm=bv.66330100,d.ZGU Accessed at 01-05-2014 Hashimoto, T., Loucks, D. P. & Stedinger, J. (1982) Reliability, resilience and vulnerability for water resources system performance evaluation. Water Resour. Res. 18(1), 14–20. [onine] Available at http://onlinelibrary.wiley.com/doi/10.1029/WR018i001p00014/abstract Accessed on 01-05-2014 Manohar, C. S. & S. Gupta 2005: Modeling and Evaluation of Structural Reliability: Current Status and Future Directions. [online] Recent Advances in Structural Engineering. Universities Press (India) Private Limited. Chapter 4, p. 90- 168. ISBN 81 7371 493 2. Available at: http://books.google.dk/books?id=BVTOZpv9FHAC&pg=PA101&lpg=PA101&dq=first+order+reliability+model+g(x)&source=bl&ots=yVPoIo8lh5&sig=LLL71u0OAfqlmlOAkhk9QLA0v8M&hl=da&sa=X&ei=iQRoU5GhLpKh7Aa4_ICwCw&ved=0CC0Q6AEwAQ#v=onepage&q=first%20order%20reliability%20model%20g(x)&f=false Rodding Kjeldsen, T. & Rosbjerg, D. (2004): Choice of reliability, resilience and vulnerability estimators for risk assessments of water resources systems / Choixd’estimateurs de fiabilité, de résilience et de vulnérabilité pour les analyses de risque de systèmes de ressources en eau, [online] Hydrological Sciences Journal, 49:5, -767. Available at: http://www.tandfonline.com/doi/abs/10.1623/hysj.49.5.755.55136#.U2vDu7FpT4c Accessed on 02-05-2014 References