Opportunities for Reliability Studies in ARIES

1. Opportunities for Reliability Studies in ARIES M. S. Tillack ARIES Project Meeting 23-24 April 2009

2. Previous efforts in ARIES focused on design improvements and reliability requirements • Reliability “by design”, e.g. • Minimize joining, locate welds in low radiation environment • Fault-tolerant interfaces (e.g., leaky SiC inserts) • Low pressure LM coolant • Derating (e.g., 90% b) • Maintenance techniques to improve “availability” • Requirements specification via system studies • “R&D needs” often omitted details on reliability growth • Surprisingly, we didn’t describe reliability R&D very well in our TRL exercise • The emphasis was on proof of performance, system integration and environmental relevance

3. Very little R&D have been done to quantify expected reliability, and some have concluded that extensive testing is needed in fusion nuclear devices • Statistical arguments have been used to highlight the possibility of infinitesimal reliability and the need for many long test runs in major facilities • A = Πai • If i is large (like 100,000), then any value of ai much less than unity will cause A to be very small • Confidence levels can be established from the results of testing, depending on the assumed statistics of failure (Weibull, exponential, Poisson, log-normal, …) Requirements for test time have been derived this way.

4. A typical hazard function includes a period of constant (random) failures characterized by an exponential distribution

5. Example of confidence intervals for test data assuming a constant hazard function • Probability density: f(t) = (1/t) exp(–t/t)where t is the (constant) failure rate • Most probable value: = (1/r) Σ(xi)where x is the test time and r is the number of failures • Confidence interval:where a=(1–confidence) • Example case:80% confidence interval (a=0.2): 10,500 ≤ t ≤ 48,000 Example test data (failures in red)

6. Modern “Reliability Engineering” suggests much more can be done now to quantify and improve reliability Elements of reliability engineering: • Reliability program planning • Design for reliability • Failure Modes and Effects Analysis • A formal and systematic approach to identifying potential system failure modes, their causes, and the effects of the failure mode’s occurrence on the system’s operation. • Reliability modeling • “Parts stress modeling” (empirical counting of parts and failure rates) • “Physics of failure approach” (understanding failure mechanisms) • Reliability testing

7. “Physics of Failure” approach to reliability modeling proactively incorporates reliability into the design process by establishing a scientific basis for evaluating new materials, structures & technologies. • Information to plan tests and to determine stress margins are identified. • Failure models are developed and used for new materials and structures as well as existing designs. • This approach involves several steps (Cushing et al, 1993): • Identify potential failure mechanisms (chemical, electrical, physical, mechanical, structural or thermal processes leading to failure), failure sites and failure modes. • Identify the appropriate failure models and their input parameters, including those associated with material characteristics, damage properties, relevant geometry at failure sites, manufacturing flaws and defects, and environmental and operating loads. • Determine the variability for each design parameter when possible. • Compute the effective reliability function. • Accept the design, if the estimated time-dependent reliability function meets or exceeds the required value over the required time period.

8. Stress-Strength Interference Method F(x) • Stress and strength can be measured independently. • Designs can be analyzed and improved to provide more “predictabilty” • Safety factors can be applied to reduce probability of failure. This is highly reminiscent of optics damage threshold statistics Maximum laser fluence Damage fluence “Max of N” Probability Distribution

9. Reliability testing is performed in stages(Dodson and Nolan 2007) • Reliability growth testing: design changes and improvement • Environmental stress screening: eliminate infant mortality failure by subjecting parts to conditions harsher than their operating point • Qualification testing: for “verification” of estimates • Acceptance testing: performed by the manufacturer and/or buyer.E.g., inspection, shake-down testing • In each of these stages, different types of tests can be performed • Sequential testing • Truncated testing (e.g., using exponential probability density) • Accelerated life testing

10. For any reliable technology, the time to gather failure data can become unreasonable Accelerated Testing is used… • To discover failure modes • To predict the normal field life from the high-stress lab life Models are used to transform accelerated test data to normal operating conditions • E.g., linear transformation of time scale • The shape of the failure distribution does not change due to acceleration Example: accelerated testing with exponential probability density • Transform time: to = e te, where te is the time to fail under accelerated conditions • fe(t) = (1/t) exp(–t/t) accererated failure transforms to fo(t) = (1/e) f(t/e) • Transform test data fe(t) = (1/t) exp(–t/t) to A demonstration of accelerated testing: nearly identical slope of failure probability under two different stress conditions

11. Question: Is there work we can do in ARIES to better define reliability R&D needs • Describe a scientific methodology for reliability R&D • Establish a paradigm for treating reliability issues in OFES, akin to our TRL work • Develop a reliability “program plan” specific to fusion • Perform a failure modes and effects analysis, e.g. for a DCLL blanket • Perform reliability modeling • Use the physics of failure approach, rather than parts stress modeling • Develop an R&D plan for reliability testing • Describe stages of testing, opportunities for accelerated testing, details of how materials and component tests should be conducted

12. Conclusions • Reliability is (almost) universally understood to be one of the most critical elements of commercially-viable fusion, yet little has been done to understand and improve reliability. • The field of reliability engineering is mature and can be used to structure a meaningful R&D program. • The ARIES Team has an opportunity to help define R&D needed to establish the credibility of fusion as a viable energy source. • Our Team is the best venue to perform this type of study. Specific research tasks can be envisioned, with several contributors.

13. References • Thomas Stadterman and David Mortin, "Physics of Failure for Making High Reliability a Reality,” U.S. Army Materiel Systems Analysis Activity (AMSAA), http://www.reliasoft.com/newsletter/v4i2/physics.htm • M. Cushing, D. Mortin, T. Stadterman and A. Malhotra, “Comparison of Electronics-Reliability Assessment Approaches,” IEEE Transactions on Reliability, Vol. 42, No. 1, December 1993. • Reliability Engineering, http://en.wikipedia.org/wiki/Reliability_engineering • Bryan Dodson and Dennis Nolan, Reliability Engineering Handbook, QA Publishing, Tucson AZ 1999. • Allisandro Birolini, Reliability Engineering: Theory and Practice, 5th Edition, Springer-Verlag Berlin 2007.

14. Other questions we might address • How do inspection and shakedown testing affect reliability? • E.g., initial crack size is extremely important in crack growth • If modules are stress tested prior to installation and defective ones screened, then how does the reliability improve • How much nuclear testing is really required? • If we understand material properties vs. neutron fluence (including all joints, welds, under all service conditions), then how much risk is involved in extrapolating to full components?