EML4550 2007 1

EML 4550: Engineering Design Methods

Probability and Statistics in Engineering Design:Reliability, FMEA, FEMCA

Class NotesHyman: Chapter 5

EML4550 2007 2

System reliability

EML4550 -- 2007

Reliability of Series Systems

ns RRRR ...21

n

iis RR

1

0.99 0.85 0.98

825.0sR

EML4550 -- 2007

For constant per-unit failure rates

i

tsystem

tsystem

ti

eR

eR

e)t(Ri

i

Per-unit failure rate of series system is constant and equal to the sum of the component failure rates

EML4550 -- 2007

Reliability of Parallel Systems

n

nss

RRRFFFFR

1...111

11

21

21

n

iis RR

1110.99

0.85

0.98

99997.0sR

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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

4

56

889.0)9.0)(99.0)(999.0(]9.0[)1.0)(1.0(1)1.0)(1.0)(1.0(1

)1)(1(1)1)(1)(1(1))()((

654321

654321

RRRRRRRRRRs

EML4550 -- 2007

For constant per-unit failure rates(example: two systems in parallel)

ttt

system

ttsystem

2121

21

eeeR

e1e11R

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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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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Cost of Reliability

Cos

t

Reliability

Cost due to design and manufacture

Cost to customer:failed products, reputation, etc..

Total costMinimized cost

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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

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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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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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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

EML4550 -- 2007

EML4550 -- 2007