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