REMINDERS

1
REMINDERS

• Final management lecture next Wednesday
• No lectures next Friday
• Assignment due Monday 10 October, 2pm
• NB University rules re plagiarism
• Penalties for late submission
• Revision lectures commence Wednesday 19
  October.

2
Assignment some possible companiesStatus update

• BHP-Billiton
• Alcoa
• Woodside
• Coles-Myer
• Woolworths
• David Jones
• Fosters Group
• Qantas
• Virgin Blue
• Patrick Corporation
• Orica
• Wesfarmers
• Coca Cola Amitil
• Cochlear

• Telstra
• Hutchison
• Optus (Singtel)
• Telecom NZ
• PowerTel
• ERG
• CSL
• Fairfax
• Newscorp
• PBL
• Tabcorp
• Pacific Brands
• CBA
• ANZ

3
Engineering Economics

• System Reliability Considerations
• An Overview

Lecture 8 16 September 2005
4
Objectives
The aim of this lecture is to highlight the
relationship between cost and reliability and
reinforce the concept of Engineering
Economics. The mathematical representation is
intended only for the purpose of demonstration
and is not examinable in this subject.
5
Introduction

• The cost of a system (or a piece of equipment) is
  directly proportional to its reliability.
• The fee for providing a service is also directly
  proportional to the level of service.
• Telecommunication service providers are bound by
  a Service Level Agreement (SLA).
• An SLA documents service parameters that can be
  reasonably measured (availability, Response Time,
  Channel Bandwidth, BER, etc.)

6
The Concept of Availability
Reliability
Maintainability
Availability
7
Reliability
Reliability is the probability that a device or a
system will operate without failure for a given
period and under given operating conditions.
R(t) e-lt
8
Maintainability
Maintainability is the probability that a device
or a system that has failed will be restored to
operation effectiveness within a given time.
M(t) 1 - e-mt
9
Availability
Availability is the proportion of the system
Up-Time to the total time (Up Down) over a
long period.
Up-Time Up-Time Down-Time
A
10
System Cost Effectiveness
Cost
System Requirements
System Effectiveness
Capability Performance
Availability Reliability Maintainability
Dependability Reliability Maintainability
11
Capability A measure of the ability of a product
to satisfy given requirements (A measure of
Quality - no time dependency)
Availability A measure of the ability of a
product to complete a mission without excessive
down time (Depends on Reliability and
Maintainability)
Dependability A measure of the ability of a
product to commence and complete a mission
without failure (Depends on Reliability and
Maintainability)
12
Costs vs. Reliability (Manufacturer)

Costs of Providing Product
Manufacturers Costs
Post-delivery Costs
Pre-delivery Costs
Reliability
0
1
13
Costs vs. Reliability (Consumer)

Costs of Ownership
Price
Consumers Costs
Post-delivery Costs
Reliability
0
1
14
The Bath Tub Curve
l
Failure Rate
Time
Burn-In
Useful Life
Wear-Out
15
System Operational States
B1
B2
B3
Up
t
Down
A1
A3
A2
Up System up and running Down System under
repair
16
Mean Time To Fail (MTTF)
MTTF is defined as the mean time of the
occurrence of the first failure after entering
service.
B1 B2 B3 3
MTTF
B1
B2
B3
Up
t
Down
A1
A3
A2
17
Mean Time Between Failure (MTBF)
MTBF is defined as the mean time between
successive failures.
(A1 B1) (A2 B2) (A3 B3) 3
MTBF
B1
B2
B3
Up
t
Down
A1
A3
A2
18
Mean Time To Repair (MTTR)
MTTR is defined as the mean time of restoring a
device or system to operation condition.
A1 A2 A3 3
MTTR
B1
B2
B3
Up
t
Down
A1
A3
A2
19
Availability
Availability is defined as
Up-Time Up-Time Down-Time
A
Availability is normally expressed in terms of
MTBF and MTTR as
MTBF MTBF MTTR
A
20
Reliability/Maintainability Measures
Reliability R(t)
(Failure Rate) l 1 / MTBF R(t) e-lt
Maintainability M(t)
(Maintenance Rate) m 1 / MTTR M(t) 1 - e-mt
21
Failure Rate (l)
Failure rate l(t) is a function of time, it
is constant during the Useful Life of the
device or system. If a piece of equipment has a
failure rate l(t), its probability of survival
from time 0 to t, or reliability R(t), is given
by
If the failure rate l(t) is constant, the
expression reduces to
22
Contributors to Unavailability

• Equipment failure
• Primary power failure
• Transmission medium failure
• Maintenance and human errors
• Unlocated

23
Maintainability Consideration

• Notification of failure
• Fault diagnostic (remote / site visit )
• Fault identification / isolation
• Obtaining the necessary parts
• Repairs / faulty component replacement
• Functional testing / verification
• Putting system into service

24
System Life Cycle Stages

• Requirement Analysis Formulation
• System Specification (Function Performance)
• System Equipment Design
• Equipment Manufacturing
• Network System Engineering
• Transportation (delivery to sites)
• Installation Commissioning
• Operation, Administration, and Maintenance
• System Retirement

25
Types of Redundancy

• Active Redundancy
• Load Sharing
• Route Diversity
• Frequency Diversity
• Space Diversity
• Standby Redundancy
• Hot Standby
• Warm Standby

26
Active Redundancy
A
Output
Input
Div
B
Divider
Both A and B subsystems are operative at all times
27
Standby Redundancy
A
SW
Output
Input
B
Switch
Standby
The standby unit is not operative until a
failure-sensing device senses a failure in
subsystem A and switches operation to subsystem
B, either automatically or through manual
selection.
28
Output Switching
A
Output
Input
C
Div
B
Divider
Combiner
The type of Combiner depends on the actual
system, technology, signal, and so on. Can be a
very complex device.
29
Element/Component Duplication
A1
B1
Input
Output
A2
B2
30
System Duplication
A1
A2
A3
Output
Input
CE
CE
B1
B2
B3
CE Common Element
31
Series System
A1
A2
An
Input
Output
Rs p1 . p2 . pn
For identical elements
Rs pn
Rs Probability of system survival pi
Probability of component survival
32
Parallel System
A
Output
Input
B
Additive Rule
Rs p1 p2 - p1 p2
Multiplicative Rule
Fs q1 q2
q1 1 - p1 q2 1 - p2
Rs 1 - Fs
Rs 1 - q1 q2 qm
33
Series / Parallel System
A1
A2
Input
Output
C
B1
B2
34
System with Repairs
Let MTBF q and system MTBF qs
For Active Redundancy (Parallel or duplicated
system)
qs ( 3l m )/ ( 2l2 )
qs m / 2l2 MTBF2 / 2 MTTR
For Standby Redundancy
qs ( 2l m )/ (l2 )
qs m / l2 MTBF2 / MTTR
35
System without Repairs
For systems without repairs, m 0
For Active Redundancy
qs ( 3l m )/ ( 2l2 )
qs 3l / ( 2l2 ) 3 / ( 2l )
qs (3/2) q where q 1/l qs 1.5 MTBF
For Standby Redundancy
qs ( 2l m )/ (l2 )
qs 2l/ l2 2/ l
qs 2q where q 1/l qs 2 MTBF
36
Example - SLA Terms

• Helpdesk - Business Hours, 24 x 7, etc.
• Bandwidth - ADSL 256/64 kbps, 512/128 kbps
• Availability - 99.99 , 99.97, 99.0, etc.
• Response Time - 8 hrs, 4 hrs, 2 hrs, etc.
• Coverage - Monday-Friday, 24 x 7, etc.

37
Transistor Amplifier Failure Rate
lR1
lR2
lT1
lRC
lRE
lCE
lAC
lRS
lCB
lRL
lCO
lPS
38
Radio Link Availability
Radio Path Availability depends on the link Fade
Margin (/dB)
Tx
Tx
I/P
I/P
Radio Path
BR
BR
Rx
Rx
O/P
O/P
O/P
I/P
lP
lB
lA
lA
lT
lR
lB
One-Way Availability
39
References

• Blanchard, Benjamin S., Fabrycky, Wolter J.,
  Systems Engineering and Analysis, Prentice-Hall,
  Inc.

40
Thanks for your attention
41
REMINDERS

• Final management lecture next Wednesday
• No lectures next Friday
• Assignment due Monday 10 October, 2pm
• NB University rules re plagiarism
• Penalties for late submission
• Revision lectures commence Wednesday 19
  October.