EML 4550: Engineering Design Methods

1. EML 4550: Engineering Design Methods Probability and Statistics in Engineering Design: Reliability, FMEA, FEMCA Class Notes Hyman: Chapter 5

2. System reliability

3. Reliability of Series Systems 0.99 0.85 0.98

4. For constant per-unit failure rates • Per-unit failure rate of series system is constant and equal to the sum of the component failure rates

5. Reliability of Parallel Systems 0.99 0.85 0.98

6. 4 6 5 Example • Find the system reliability of the following combinational system with both serial and parallel arrangements. Assume all sub-systems have a reliability of 0.9 1 2 3

7. For constant per-unit failure rates(example: two systems in parallel) • System does not have constant per-unit failure rate even if components do • System reliability for parallel systems is always greater than the most reliable component • Most systems are not designed in parallel (redundancy) due to cost considerations (unless needed due to safety and life-protection considerations) • Series • Transmission line, Power train • Parallel • Multiple airplane engines, Two headlights

8. Reliability of Large Systems • Most systems are neither parallel nor series, but a hybrid combination • Calculation of overall system reliability, however, is done following the simple principle shown before • Parallel systems are used when extremely high reliability is needed (by use of redundancy)

9. Cost of Reliability Total cost Minimized cost Cost due to design and manufacture Cost  Cost to customer: failed products, reputation, etc.. Reliability 

10. FTA • Fault Tree Analysis • Work from the overall system backwards towards the component level (top down approach) • Identify system fault modes and possible causes • Assign probabilities to each fault mode • Build a ‘tree’ and use it to evaluate overall reliability, availability, etc. • A Fault Tree Analysis Handbook (from US Nuclear Regulatory Commission) • The basic elements of a fault tree in pp. 34-44

11. FMEA and FMECA • Failure Modes and Effects Criticality Analysis • Work from the component level and identify all possible fault modes at the component level (a team effort and bottom-up approach) • Assess criticality of each component fault and its effects on overall system performance • Build a ‘table’ with all fault modes, assign probabilities, severity, determine interactions, possible actions, etc. • Three factors for failure analysis: The severity of a failure (Sev), The probability of occurrence of the failure (Occ), The likelihood of detecting the failure (Det) • RPN (risk priority number)=(Sev)(Occ)(Det): quantify overall risk for a specific failure • Use the table to asses overall reliability (see an example)

12. Step-by-step Procedures • The design is broken down into components with a block diagram showing their interrelations. • Identify functions for each individual components (1st column) • List the potential failure modes (2nd column) • Describe the consequences/effects due to the failure (3rd column); frequently coming from customers, regulation, and/or experienced designers  Use the severity table to determine the numerical value (Sev). • Identify potential causes (root cause analysis, column 6)  Find Occurrence value (Occ) • Determine how one can detect the potential failure (colume 8)  Find detectability (Det) • Calculate the risk priority number (RPN) • Determine the corrective actions to remove potential failures. Assign responsibility to appropriate person(s) for the removal of each failure. • Estimate the RPN after the corrective actions.

13. Implications • Incorporate availability, reliability, and maintainability on the product specification • Prepare a mathematical model to assess system reliability (e.g., FMECA) • Design with reliability and maintainability in mind • Exercise FMECA each time a design change is needed, or to explore incremental improvements to the design that may improve reliability without critically affecting functionality and cost