How do you know how long your design is going to last?

Is there any way we can predict how long it will work?

Why do Reliability Engineers get paid so much?

2

By the end of this chapter, you should: Have a familiarity with the basic principles of probability

and understand how they apply to reliability theory. Understand the mathematical definition and meaning of

failure rate, reliability, and mean time to failure. Understand how to determine the reliability of a

component. Understand how to derate the power of electronic

components for use under different operating temperatures.

Understand how to determine the reliability of different system configurations.

3

Definitions Experiment

Event

Event Space

4

What is an axiom?

2 of the 3 axioms

5

What is a random variable (RV)?

What is a PDF?

Math Definition

6

Normal Density

7

pX(x)

x

2

2

1

2

1)(

x

X exp

Uniform Density

8

bxaab

xpX

,1

)(

a b

1/(b-a)

pX(x)

x

Reliability (defn)

Failure Rate

9

10

t

service lifetime / constant failure rateburn-in wear-out

electrical devices

mechanicaldevices

(t)

See the book for derivation of R(t). If the failure rate is constant, then R(t) = ?

11

What factors influence the failure rate?

12

Low Frequency FET, Appendix C.

How would you find each of these?

13

hours 10failures 6EQATb

14

VI = 0 or 5V

Vcc = 5V

RB = 10k

RC = 100

2N3904

VO = 5V or 0V

= VI VO

IC

IB

15

Junction, TJ

Case, TC

Ambient, TA

JC

CA

16

TJ

TC

TA

JC

CA

PD

17

Junction, TJ

Case, TC

Ambient, TA

JC

CSHeat Sink, TS

SA

thermalconductive

paste

18

TJ

TC

TA

JC

SA

CSTS

PD

19

TA, oC

slopes = -1JA mW/ oC

with heat sink

without heat sink

PD,max, mW

So far, we have only looked at a single device.

We are interested in collection of devices into a system!

For example

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VI = 0 or 5V

Vcc = 5V

RB = 10k

RC = 100

2N3904

VO = 5V or 0V

= VI VO

IC

IB

Def’n (Series System) =

We model this as

21

S1 S2 Sn

...

Definition: Redundancy

Definition: Parallel System

22

23

S1

S2

Sn

.

.

.

24

S2

S3

S4

S1

Probability Review◦ Random Variables

◦ PDFs and CDFs

◦ Mean and Variance

Reliability Estimation◦ Failure rate and the bathtub curve

◦ Reliability & MTTF

◦ Application to single components (MIL-SPEC)

System Reliability◦ Series systems

◦ Parallel systems

◦ Combination systems

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