Chapter 8

Design for Reliability

8.1 Reliability Specification

8.2 Reliability Allocation
8.3 Design Methods

C. Ebeling, Intro to Reliability & Maintainability

Chapter 8 Engineering, 2nd ed. Waveland Press, Inc. Copyright © 1
2010
 8.1 Reliability Specification
The Reliability Design Process
Specify Reliability Allocate Reliability
Goals to components

Implement Design
System Effectiveness Methods
Life Cycle Costs

Failure Analysis
(FMEA/FMECA)

System Safety yes goals no

Analysis(FTA) achieved
?

Safety Goals yes Ready for

achieved? production
no

Chapter 8 2
 Reliability Activities & Product Life Cycle
Development Conceptual & Detailed Design, Production & Product Use &

Phase Preliminary Development & Manufacture Support

Design Prototyping

Specification Design Methods Acceptance test Preventive &

Allocation Failure Analysis Quality Control Predictive

Design Methods Growth Testing Burn-in & Screen Maintenance

Safety Analysis Testing Modifications

Parts Replacement

Chapter 8 3
 System Effectiveness

System Effectiveness

Operational Mission Design

Readiness Availability Adequacy

Reliability Maintainability
Reliability

Chapter 8 4
 Life Cycle Cost Categories
Acquisition Costs Operations and Support Costs Phase-out

Research and Development Operations Salvage value

Managem ent Facilities Disposal Costs

Engineering Operators

Design and Prototyping Consum ables (energy & fuel)

Engineering Design Unavailable time or downtime

Fabrication Support

Testing & evaluation Repair resources

Production Supply resources

Manufacturing repairables

Plant facilities & overhead expendables

Marketing & Distribution tools, test & spt equip

Failure Costs

Training

Technical Data

Chapter 8 5
 Life Cycle Cost

LCC = Acquisition Costs + Operations Costs + Failure Cost

+ Support Costs - Net Salvage Value

where Net Salvage Value = Salvage Value - Disposal Cost

Discount Monetary Values

Chapter 8 6
 8.2 Reliability Allocation
In general: h(R1(t), R2(t), ... , Rn(t)) ≥ R*(t)

where Ri(t) is the reliability at time t of the ith component,

and R*(t) is the system reliability goal at time t.

or g(MTTF1 , MTTF2 , ..., MTTFn ) ≥ MTTF*

n
For series related components: ∏ R (t ) ≥ R * (t )
i =1
i

Chapter 8 7
 Exponential Case

∏e
i =1
−λit
≥ R * (t )

∑λ
i =1
i ≤ λs

Chapter 8 8
 ARINC Method
Assume components are in series, are independent, and
have constant failure rates.
new λi = wi λ *
λi
wi = n
i = 1, 2,..., n ; since
∑λ
i =1
i

n n n
λi λ * λ* n

∑ new λ =∑ w λ = ∑
i i
*
n
= n ∑λ i =λ *

i =1 i =1 i =1
∑ λi
i =1
∑ λi
i =1
i =1

Chapter 8 9
 AGREE Method
t = system operating time
R*(t) = system reliability goal at time t
n = number of components
ni = the number of modules within component i
N = total number of modules in system = Σ ni
ti = the operating time of the ith component, ti <= t
λ i = the failure rate of the ith component
wi = the probability the system will fail given component i has failed

Allocating an equal share of the reliability to each module

results in component i’ s contribution to the system reliability
ni
being
[ R * ( t )] N
Chapter 8 10
 AGREE Method
ni
− λ i ti
wi (1 − e ) =1- [ R * ( t )] N

1 1 − R * (t ) ni / N
λ i = − ln(1 − )
ti wi
n
note that ∏ei =1
− λ i ti
≤ R * (t )

Chapter 8 11
 AGREE Method - Example
Component Import Index (wi) Oper hrs (ti) Nbr of modules -ni
Receiver .8 1000 25
Antenna 1 1000 15
Transmitter .7 500 23
Power Supply 1 1000 70

The total module count is 133. If the system reliability goal is .99,
then the reliability to be allocated to the ith component is .99ni /133 .

Chapter 8 12
 AGREE Method - Example
Component Failure Rate MTTF Reliability System Rel

Receiver 2.362 x 10-6 423,369 .99764 .99811

Antenna 1.1335 x 10-6 882,227 .99887 .99887
Transmitter 4.9676 x 10-6 201,303 .99752 .99826
Power Supply 5.2896 x 10-6 189,048 .99472 .99472
System 1.3753 x 10-5 72,713 .98879 .99

From the above table, the probability

of a component failure is 1-.98879 while
the probability of a system failure is 1-.99.

Chapter 8 13
 Redundancy
starter
R2
motor chassis
R4
R1

R3

R* = R1 x R’ x R4
R’

R’ = 1 - (1 - R2 ) (1 - R3 ) = R2 + R3 - R2 R3
R '− R3
R2 = or R’ = 2 R - R2
1 − R3
with solution R = 1 - (1 - R’ ).5

Chapter 8 14
 8.3 Design Methods

Parts and Material Selection

Derating
Stress-Strength Analysis
Complexity
Choice of Technology
Redundancy

Chapter 8 15
 Material Selection
Structure MATERIALS Material
atomic bonding SCIENCE Properties MATERIALS
crystal structure yield strength ENGINEERING
defect structure hardness
microstructure fatigue life
creep
Service Manufacturing
Performance Process
Stresses casting
corrosion
temperature
machining (cutting)
MANUFACTURING
radiation ENGINEERING joining
vibration heat treatment
R(t) assembly
Chapter 8 16
 Design Methods
Parts and Material Selection
Tensile Strength
Hardness
Impact Value
Fatigue Life
Creep
Property of Materials

Ceramics

Composites

Chapter 8 17
 Material Selection

Metals Ceramics Polymers

strong strong weak
stiff stiff compliant
tough brittle durable
electrically electrically electrically
conducting insulating insulating
high thermal low thermal temperature
conductivity conductivity sensitive

Chapter 8 18
 Tensile strength
Tensile strength measures the force required to pull something
such as rope, wire, or a structural beam to the point where it
breaks.
Specifically, the maximum amount of stress that it can be subjected
to before failure
Yield strength - The stress a material can withstand without
permanent deformation.
Ultimate strength - The maximum stress a material can withstand.
Breaking strength - The stress coordinate on the stress-strain curve at
the point of rupture.
Compressive strength is the capacity of a material to withstand
axially directed pushing forces. When the limit of compressive
strength is reached, materials are crushed. Concrete can be
made to have high compressive strength.

Chapter 8 19
 Parts and Material Selection
Tensile Strength
stress ultimate strength
(lbs/in2)
yield strength
X
breaking strength

slope = E

modulus of elasticity (lbs/in2)

Hooke’s Law: Stress = E x Strain strain (in/in)

Chapter 8 20
 Another Stress-Strain
Curve

Chapter 8 21
 Hardness

resistance of material
to the penetration of an
indenter - used in
analyzing service wear.

Brinell - Bhn (kg/mm2)

Rockwell - R
Vickers - Vhn

Chapter 8 22
 Fatigue
• The progressive, localized, and permanent structural
damage that occurs when a material is subjected to
cyclic or fluctuating strains at nominal stresses that
have maximum values less than the static yield
strength of the material.
• The resulting stress may be below the ultimate tensile
stress, or even the yield stress of the material, yet still cause
catastrophic failure.
• In high-cycle fatigue situations, materials
performance is commonly characterized by an S-N
curve. This is a graph of the magnitude of a cyclical
stress (S) against the cycles to failure (N).

Chapter 8 23
 Parts and Material Selection
Fatigue Life

stress - S
(lbs/in2) steel

endurance
limit

nbr of cycles - N
S-N Curve: N = c S-m where c, m > 0
Chapter 8 24
 Creep
• The tendency of a material to move or to deform
permanently to relieve stresses.
• Material deformation occurs as a result of long term
exposure to levels of stress that are below the yield
or ultimate strength of the material.
• Creep is more severe in materials that are subjected
to heat for long periods and near melting point.
• The rate of damage is a function of the material
properties and the exposure time, exposure
temperature and the applied load (stress).

Chapter 8 25
 Parts and Material Selection - Creep
ε = ε 0 (1 + β t 1/ 3 ) e kt
strain Failure
Failure

high temperature

moderate temperature

time

Chapter 8 26
 Failure modes
Failure Mode Material Property
gross yielding yield strength
buckling compressive strength
creep creep rate
brittle fracture impact energy
Low cycle fatigue ductility
high cycle fatigue fatigue properties
corrosion electrochemical potential
wear hardness
thermal fatigue coefficient of expansion

Chapter 8 27
 Material Failure Mechanisms

Overstress Failures Wear-out Failures

brittle fracture corrosion
ductile fracture dendritic growth
(electrolytic process)
yield
interdiffusion
buckling
fatigue crack
large elastic
propagation
deformation
diffusion (molecular
thermal breakdown migration)
radiation
creep
adhesive wear
Chapter 8 28
 Derating
Derating Curve

3000
Failure Rate (E-07 per hr)

2500

2000

1500

1000

500

0
0 20 40 60 80
Ambient Temperature (degrees cent.)

0.3 0.5 0.9

(applied voltage) / (rated voltage)

Chapter 8 29
 More Derating
F s I F L I Fv I F cI F TI
.7

λ=λ G J G J G J G J G J
4 .69 .54 .67 3

Hs K H L K H v K Hc K HT K
Failure Rate of a gear: s
b
d d s s

λ b = base failure rate specified by the manufacturer

s = operating speed
sd = design speed
L = operating load
Ld = design load
v = viscosity of lubricant used
vs = viscosity of specification lubricant
c = concentration of contaminants
cs =standard contamination level
T = operating temperature
Ts = specification temperature

Chapter 8 30
 Stress-Strength Analysis
• Concerned when abnormal loads are possible
• Probabilistic compare the magnitude of the stress with the
design strength.
• Use physical models
• Major categories of stress
• electrical
• thermal
• mechanical
• chemical Looking for strength to
cope with the stress!
• Two design approaches
• select parts with sufficient strength against max load
• protect part against excessive stresses

Chapter 8 31
 Stress - Strength Analysis
Lognormal Distribution
Safety Factor = Y/X
0.6

e 0.5
r
lu
i
a 0.4
F
f
o
y
ti 0.3
li
b
a 0.2
b
o
r
P
0.1

0
1 2 3 4 5 6 7 8 9 10
Safety Factor

denom= 0.8 denom= 1 denom= 1.2

⎛ ln S F ⎞ m
R =Φ⎜ ⎟ w h ere S F = y
⎜ s y2 + sx2 ⎟ mx
⎝ ⎠

Chapter 8 32
 Stress Protection
Electronic Circuit Boards
Stress Failure Mode Design activity

high temperature insulation deteriorates dissipate heat, use fans,

increase conductor size
thermal shock mechanical damage shielding

mechanical shock component and mechanical design - use

connector damage of mountings
vibration early wearout, mechanical design
connector failure
humidity corrosion sealing, use of silica gel

dust increased contact sealing

resistance
biological effects decayed insulation chemical protection
material

Chapter 8 33
 Redundancy

R edundancy

A ctive Standby

Parallel K out of N Failures Sw itching

in Standby Failures
Load Sharing M ultiple
U nits in
Standby

C om bined A ctive/Standby

Chapter 8 34
 Redundancy

Advantages Disadvantages
Quickest way to ⌦ Sensors and switching
improve reliability may increase cost and
May be cheapest vs. reduce reliability
cost of redesign ⌦ May exceed size, weight
May be the only or power constraints
solution if specified ⌦ Increases
reliability is beyond the maintainability
state of the art requirements

Chapter 8 35
 Conclusion
As an engineer, I can
assure you that these
design methods work.

Chapter 8 36