1. EML 4550: Engineering Design Methods
Probability and Statistics
in Engineering Design:
Reliability, FMEA, FEMCA
Class Notes
Hyman: Chapter 5
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2. System reliability
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3. Reliability of Series Systems
0.99
0.85
0.98
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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
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5. Reliability of Parallel Systems
0.99
0.85
0.98
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6. 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 4 5 6 2 3
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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
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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)
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9. Cost of Reliability Cost  Reliability  Total cost Minimized cost
Cost due to design
and manufacture
Cost 
Cost to customer:
failed products, reputation, etc..
Reliability 
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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
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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)
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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.
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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
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14. EML

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