REMINDERS

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REMINDERS

• Lecture as usual on Wednesday, 19/9
• No 11am lecture next Friday, 21/9
• Assignment due Monday 8 October
• NB University rules re plagiarism
• Penalties for late submission
• Revision lectures commence Wednesday 17
  October.
• Refer lecture schedule

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Engineering Economics

• System Reliability Considerations
• An Overview

Lecture 8 14 September 2007
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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 illustration and
is not examinable in this subject.
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Design and the Business Process

• A customer need
• Customer calls for tenders.
• Suppliers submit tenders.
• Customer selects successful tender.
• Contract is signed.
• Supplier delivers according to contract terms,
  conditions and technical spec.

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THE TENDER DOCUMENT

• Instructions to Tenderers
• Commercial Terms Conditions
• Price basis (e.g. Tax, FOB, materials/service,
  etc.)
• Terms of payment
• Legal clauses
• Basis for contract
• Technical Specifications
• Functional requirements
• Performance requirements
• Operational and maintenance requirements, etc.
• Appendices (Drawing, Data, etc.)

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EXAMPLE OF A SYSTEM TECHNICAL SPECIFICATION

• Scope
• Requirements
• System Definition
• System Characteristics
• Design and Construction
• Documentation / Data
• Logistics
• Producibility
• Test and Evaluation
• Quality Assurance, OHS Provisions
• Preparation for Delivery

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Cost/benefit considerations

• 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, etc.)

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The Concept of Availability
Reliability
Maintainability
Availability
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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
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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
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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
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System Cost Effectiveness
Cost
System Requirements
System Effectiveness
Capability Performance
Availability Reliability Maintainability
Dependability Reliability Maintainability
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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)
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Costs vs. Reliability (Manufacturer)

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

Costs of Ownership
Price
Consumers Costs
Post-delivery Costs
Reliability
0
1
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The Bath Tub Curve
l
Failure Rate
Time
Burn-In
Useful Life
Wear-Out
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System Operational States
B1
B2
B3
Up
t
Down
A1
A3
A2
Up System up and running Down System under
repair
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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
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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
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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
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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
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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
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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
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Contributors to Unavailability

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

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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

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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

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Types of Redundancy

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

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Active Redundancy
A
Output
Input
Div
B
Divider
Both A and B subsystems are operative at all times
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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.
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Example calculation (illustration purposes
only)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
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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.

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References

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

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Thanks for your attention