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RELIABILITY: AN INTER-DISCIPLINARY PERSPECTIVE
Professor Pra Murthy
The University of Queensland, Australia
and NTNU, Norway
Divergent disciplines, specialities, sub-, sub-disc. Convergent goals, problems, tasks.
DISCIPLINE ORIENTED GROWTH
A
B
1MISSION ORIENTED GROWTH
2
3
5
4
Disciplinary branching effect Interdisciplinary crystallisationeffect
Knowledge growth as combination of disciplinary branching and interdisciplinary crystallisation
PRODUCT RELIABILITY
RELIABILITY
Reliability of a product (system) conveys the concept of dependability, successful operation or performance and the absence of failures. Unreliability (or lack of reliability) conveys the opposite.
PRODUCT RELIABILITY
• Determined by technical decisions made by the manufacturer during the design and manufacturing stages
• Affected by usage mode, environment and maintenance actions of the buyer
• Impact both the manufacturer and the buyer in terms of costs
PRODUCT RELIABILITY
• Buyers need assurance that the product will perform satisfactorily
• Warranty and Post-sale support provide this assurance
• Offering warranty costs extra money to manufacturer but also serves as a signal to promote the product
MATERIAL
PRODUCTRELIABILITY
MANUFACTURE
DESIGN
QUALITYCONTROL
WARRANTY COST
PROFITS
SALES
MANUFACTURER’S PERSPECTIVE
RELIABILITY THEORY
Deals with the interdisciplinary use of probability, statistics and stochastic modelling, combined with engineering insights into the design and the scientific understanding of the failure mechanisms, to study the various aspects of reliability.
RELIABILITY THEORY
It encompasses issues such as
• reliability modelling,
• reliability analysis and optimisation
• reliability engineering,
• reliability science,
• reliability technology and
• reliability management.
LIFE CYCLE PERSPECTIVE
Time
Rel
iab
ility
Feasibility
Design
Develop-ment
Pre-production
Production
Deterioration
Cost of maintenance
Growth
Replace/discard
Life of item
Design limit
Desiredperformance
FOR MORE DETAILS….
• Blischke, W.R. and Murthy, D.N.P. (2002), Reliability, Wiley, New York [Covers the different aspects of reliability in an integrated manner]
• Blischke, W.R. and Murthy, D.N.P. (eds) (2004), Case Studies in Reliability and Maintenance, Wiley, New York [Collection of 25 cases studies]
RELIABILITY SCIENCE
S-N CURVES
P-S-N CURVES
EMPIRICAL DISTRIBUTION FUNCTIONS
FAILURE MODELLING
• Two distributions used extensively -- Weibull and lognornal
• Effect of stress: Scaling relationships - several different formulations
• Comparison of model with data -- different plots
• Weibull model and data do not match all the plots
NEW RESEARCH
• Other Weibull models: Mixture and competing risks -- same story
• Need to look at more complex distributions
• Uncertainty in the scaling relationship - to reflect variability in the component
• Better understanding of the physics of failure
RELIABILITY MODELLING
HAZARD FUNCTION
t1 tf
Slope Slope
r(t)
HAZARD FUNCTION
t
r(t)
NEW CHALLENGES
Distributed systems [water, sewerage, gas, rail networks]
Extend failure concepts from lumped to distributed systems -- failure occurrence given by a two-dimensional intensity function (t,x)
Imperfect knowledge of system condition
2-D FAILURES
• T: Age and X: usage at failure
• Failure distribution F(t,x)
• Failures are points on a 2-D plane
• Analysis with different types of repairs -- minimal, imperfect [affect the hazard function r(t,x) differently]
• Comparison with the 1-D case
STATISTICAL INFERENCE
PROBABILITY / STATISTICS
DATA MODEL
PROBABILITY
STATISTICAL INFERENCE
WEIBULL MODELS
• A large number of models have been derived from the two-parameter Weibull distribution [See, Weibull Models, D.N.P. Murthy, M Xie and R. Jiang, Wiley, 2003 (December)]
• Several new topics in model selection (to model data sets), analysis, estimation and validation
CHALLENGING TOPICS
• Data collection with information uncertainty
• Design of Experiment
• Combining data from different sources
• Model validation with small incomplete data sets
• Estimation for 2-D models
MAINTENANCE
MAINTENANCE
Need for an integrated approach as failures are influenced by– Design– Operations – Maintenance
A framework to integrate these must take into account the interaction between technology and commercial factors.
Equipment State
Equipment Degradation
Operational
Maintenance Production
Process
StrategicDesign/Upgrade
Expansion/Growth
Technology
Commercial
Operational Strategic
Strategic Operational
AN APPLICATION
Draglines used in open cut mining
Optimal bucket load based on (i) building a reliability model and (ii) optimising the annual yield
For details: See Townson, P., Murthy, D.N.P. and Gurgenci, H. in the Case Studies in Reliability and Maintenance.
IMPACT OF TECHNOLOGY
Systems are getting more complex
Maintenance requires specialist skills and equipment
It is not often not economical for businesses to carry out in-house maintenance.
Out-sourcing of maintenance is an option
MAINTENANCE OUT-SOURCING
Maintenance provided either by
- Original Equipment Manufacturer (OEM)
- A external Third Party
Involves a Maintenance Service Contract
MAINTENANCE SERVICE CONTRACTS
Two different viewpoints
- Agent (providing the maintenance service)
- Customer (owner of the system and recipient of the maintenance service)
Different objectives or goals
GAME THEORETIC FORMULATION
The agent needs to take into account the optimal actions of the buyer in deciding on the optimal contracts (price, terms etc)
STACKELBERG game situation with the agent as the leader and the customer as the follower.
WARRANTY SERVICING
WARRANTY CONCEPT
• Contractual agreement (at the time of sale) which requires the manufacturer to fix any problem with the product within the warranty period
• Establishes -- Buyer responsibility, Limitations, Seller liability
• Nearly all products are sold with some form of warranty
FOR MORE DETAILS...
• Blischke, W.R. and Murthy, D.N.P. (1994), Warranty Cost Analysis, Marcel Dekker, New York
• Blischke, W.R. and Murthy, D.N.P. (1996), Product Warranty Handbook, Marcel Dekker, New York
• Several review papers
WARRANTY SERVICING
• Warranty servicing costs money. This varies from 0.5 - 7% of the sale price depending on the product and the manufacturer
• Manufacturers need to service warranty in an efficient manner to ensure customer satisfaction and loyalty
WARRANTY LOGISTICS
• Deals with the different logistical issues to service warranty in an effective manner
• Need to differentiate between strategic and operational issues
• Service is usually carried out by an agent
• An area for lot of new research
Number of sales
Warranty terms
Product reliability
Warrantyclaims
Warrantyservice
Satisfiedcustomer
Inventorylocation
Product usage
Repaircapacity
Servicelevel
Provisioning ofproducts/spares
WARRANTY LOGISTICS
STRATEGIC PROBLEMS
• Optimal Number and location of warehouses (multi-echelon)
• Optimal transportation of components (mode, frequency)
• Optimal inventory levels
• Optimal repair capacity at different service centres
SERVICING STRATEGIES
• Optimal repair versus repair strategies
– Based on repair limit
– Based on age at failure
• These lead to interesting point process stochastic optimisation problems
SERVICE CENTRE
• Owned by the manufacturer
• Independent of manufacturer: An agent carries out the warranty servicing under a contract with the manufacturer
• This raises a whole range of new issues
• The Principal - Agent (or Agency) Theory deals with such problems