Product reliability and warranty: An overview and future research

Abstract

Reliability and warranty are very important in the context of new products. This paper gives an overview of product reliability and warranty and discusses some issues and challenges for future research.

Full text

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Produção, v. 17, n. 3, p. 426-434, Set./Dez. 2007
Confiabilidade e garantia de produto:
visão geral e pesquisas futuras
Resumo
Confiabilidade e garantia são muito importantes no contexto de novos produtos. Este artigo apresenta uma revisão
geral sobre confiabilidade e garantia de produto e discute algumas questões e desafios para pesquisas futuras.
Palavras-chave
Produtos, confiabilidade, garantia, pesquisa.
Abstract
Reliability and warranty are very important in the context of new products. This paper gives an overview of product
reliability and warranty and discusses some issues and challenges for future research.
Key words
Products, reliability, warranty, research.
Product reliability and warranty:
an overview and future research
D.N.P. MURTHY
University of Queensland
INVITED PAPER

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427
Product reliability and warranty: an overview and future research
absence of failures. It is an external property of great interest
to both manufacturer and consumer. Unreliability (or lack of
reliability) conveys the opposite. A more technical defi nition
is the following:
The reliability of a product (system) is the probability
that the product (system) will perform its intended
function for a specifi ed time period when operating
under normal (or stated) environmental conditions.
(BLISCHKE; MURTHY, 2000)
The reliability of a product gets determined by the
decisions made during the pre-production stages (Front-
end, Design, Development) and the production stage
of the product life cycle. Murthy et al. (2007a – c) deal
with reliability decision making during the Front-end (or
Feasibility) and the Design and Development stages of new
product development.
Reliability: different notions
The design reliability depends on reliability
specifi cation at the component level. The reliability of the
produced item can differ from the design reliability due
to assembly errors and component non-conformance. The
reliability of produced items is the “inherent” reliability
of the product. The product needs to be transported
to the market, and often stored for some time, before
it is sold. The reliability at sale for a unit depends on
the mechanical load (resulting from vibrations during
transport), the impact load (resulting from mishandling),
the duration of storage and the storage environment (such
as temperature, humidity etc). As a result, the reliability at
sale can differ from the inherent reliability. Once an item
is sold, it can be either stored for an additional time (if the
unit is used as a spare) or put into operation immediately.
The reliability performance of a unit in fi eld depends on
the length and environment of storage and on several
other operational factors such as the usage intensity
(which determines the load – electrical, mechanical,
thermal, chemical – on the unit), usage mode (whether
used continuously or intermittently) and operating
environment (such as temperature, humidity, vibration,
pollution etc) and in some instance on the human operator.
The reliability performance in operation is often referred
to as “fi eld reliability”. Figure 1 (from MURTHY et al.,
2007d) shows how these different reliability notions are
sequentially linked and the factors that affect them.
Reliability theory
Reliability theory deals with the interdisciplinary use of
probability, statistics and stochastic modelling, combined
with engineering insights into the design and the scientifi c
INTRODUCTION
Since the industrial revolution started new products have
been appearing at an ever increasing pace. The complexity
of the products has increased signifi cantly to meet the ever
increasing needs and expectations of consumers. Products
degrade with age and/or usage and fail when they are
unable to carry out their normal functions. Reliability theory
deals with various issues such as the understanding of the
degradation mechanism, the design of reliable products and
the operation of unreliable products.
Consumers need assurance that the product will perform
satisfactorily over the useful life of the product. In addition,
the legislations are getting more stringent to protect consumer
interests. Manufacturer have responded to these challenges
by offering warranties and extended warranties. A warranty
is a legal contract which requires the manufacturer to either
rectify or compensate for all failures occurring within
the warranty period. There are many different aspects to
warranty and these have been studied by researchers from
many different disciplines.
Offering a warranty results in additional costs (referred
to as warranty servicing costs or simply warranty costs) to
the manufacturer as all failures under warranty need to be
either rectifi ed or compensated by the manufacturer. The
warranty costs depend on the reliability performance of
the product. This in turn depends on several factors some
under the control of the manufacturer (such as the decisions
made during the design and development of the product)
and others under the control of the consumer (such as the
usage intensity, operating environment and maintenance).
The warranty servicing costs vary from 2-10% of the sale
price depending on the product and the manufacturer. As a
result, warranty and product reliability are very important in
the context of new product development.
Both warranty and reliability have received a lot of attention
over the last fi fty years. This paper gives a brief overview of
both reliability and warranty and discusses some new issues
and the challenges for future research. The outline of the paper
is as follows. Section Product Reliability: An Overview deals
with an overview of product reliability and Section Warranty:
An Overview with warranty. In each section we highlight the
important issues and give a historical perspective. Section
New Issues and Challenges: Topics for Future Research
deals with some issues and challenges as part of future
research into reliability and warranty. We conclude with
some comments in Conclusions Section.
PRODUCT RELIABILITY: AN OVERVIEW
Reliability of a product conveys the concept of
dependability, successful operation or performance and the

D.N.P. Murthy
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understanding of the failure mechanisms, to study the
various aspects of reliability. As such, it encompasses the
following topics
1
.
Reliability modelling: Reliability modelling deals with
model building to obtain solutions to problems in predicting,
estimating and optimising the survival or performance of an
unreliable system, the impact of the unreliability, and actions
to mitigate this impact.
Reliability analysis: Reliability analysis can be
divided into two broad categories: (i) Qualitative and (ii)
Quantitative. The former is intended to verify the various
failure modes and causes that contribute to the unreliability
of a product or system. The latter uses real failure data in
conjunction with suitable mathematical models to produce
quantitative estimates of product or system reliability.
Reliability engineering: Reliability engineering
deals with the design and construction of systems and
products, taking into account the unreliability of its parts
and components. It also includes testing and programs to
improve reliability. Good engineering results in a more
reliable end product.
Reliability science: Reliability science is concerned with
the properties of materials and the causes for deterioration
leading to part and component failures. It also deals with the
effect of manufacturing processes (e.g. casting, annealing)
on the reliability of the part or component produced.
Reliability management: Reliability management
deals with the various management issues in the context
of managing the design, manufacture and/or operation of
reliable products and systems. Here the emphasis is on the
business viewpoint, as unreliability has consequences in
cost, time wasted, and, in certain cases, the welfare of an
individual or even the security of a nation.
Historical perspective
Prior to World War II, the notion of reliability was largely
intuitive, subjective and qualitative. The use of actuarial
methods (involving statistical techniques) to estimate
survivorship of railroad equipment began in the early part of
the twentieth century (NELSON, 1982, p. 2). In the late 1930’s,
extreme value theory was used to model fatigue life of materials
and was the forerunner to later probabilistic developments.
A more quantitative (or mathematical) and formal
approach to reliability grew out of the demands of modern
technology and particularly out of the experiences in
the second world war with complex military systems
(BARLOW; PROSCHAN, 1965, p.1). Since the
appearance of this classic book, the theory of reliability
has grown at a very rapid rate, as can be seen by the large
number of books
2
and jounals
3
that have appeared on the
subject.
Barlow (1984) deals with a historical perspective of
mathematical reliability theory up to that time. Similar
perspectives on reliability engineering in electronic
equipment can be found in Coppola (1984); on space
reliability technology in Cohen (1984); on nuclear power
system reliability in Fussel (1984) and on software reliability
in Shooman (1984).
WARRANTY: AN OVERVIEW
A warranty is a manufacturer’s assurance to a buyer that
a product or service is or shall be as represented. It may be
considered to be a contractual agreement between buyer and
manufacturer (or seller) which is entered into upon sale of
the product or service. A warranty may be implicit or it may
be explicitly stated.
Figure 1: Factors influencing field reliability.

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429
Product reliability and warranty: an overview and future research
Warranty classification
There are many different types warranty policies and
a classifi cation of these can be found in Blischke and
Murthy (1994 and 1996). They can be divided into different
categories as indicated below.
• Involving reliability improvement or not
• Single item or group of items (cumulative warranty)
• One-dimensional (limit on age) or two-dimensional
(limits on age and usage)
• Renewing or non-renewing
• Base or extended
Base warranties
Base warranty is integral to the sale and is factored into
the sale price. Most standard products are sold with one of
the following two warranty policies.
1-D Free Replacement Warranty (FRW) policy
The manufacturer agrees to repair or provide replacements
for failed items free of charge up to a time W (the warranty
period) from the time of the initial purchase. The warranty
expires at time W after purchase.
1-D Pro-Rata Rebate Warranty (PRW) policy
The manufacturer agrees to refund a fraction of the
purchase price should the item fail before time W (the
warranty period) from the time of the initial purchase. The
buyer is not constrained to buy a replacement item. The
refund depends on the age of the item at failure (X) and it
can be either linear or a non-linear function of (W – X), the
remaining time in the warranty period and the sale price.
2-D Free Replacement Warranty (FRW) policy
The manufacturer agrees to repair or provide a replacement
for failed items free of charge up to a time W or up to a usage
U, whichever occurs fi rst, from the time of the initial purchase.
W is called the warranty period and U the usage limit. The
warranty region is a rectangle in a 2-dimensional plane with
age along one axis and usage along the other axis.
Cumulative warranties
Cumulative warranties are for items are sold as a single
lot of n items and the warranty refers to the lot as a whole.
The policies are conceptually straightforward extensions of
the non-renewing free replacement and pro-rata warranties
discussed previously. Let X
i
denote the service life of item
i, i = 1, 2, ... and
.
Cumulative FRW policy (GUIN, 1984)
A lot of n items is warranted for a total (aggregate)
period of nW. The n items in the lot are used one at a
time. If Sn < nW, free replacement items are supplied, also
one at a time, until the fi rst instant when the total lifetimes
of all failed items plus the service time of the item then in
use is at least nW.
Reliability Improvement Warranties
Reliability Improvement Warranty (RIW) policies are
offered with complex systems intended for long use. The
basic idea is to extend the notion of a basic consumer
warranty (usually the FRW) to include guarantees on the
reliability of the item and not just on its immediate or short-
term performance. These often include a guaranteed MTBF
as a part of the warranty contract.
Reliability Improvement Warranty policy (GANDARA ;
RICH, 1975)
The manufacturer agrees to repair or provide replacements
free of charge for any failed parts or units until time W
after purchase. In addition, the manufacturer guarantees
the MTBF of the purchased equipment to be at least M. If
the computed MTBF is less than M, the manufacturer will
provide, at no cost to the buyer, (1) engineering analysis
to determine the cause of failure to meet the guaranteed
MTBF requirement, (2) Engineering Change Proposals,
(3) modifi cation of all existing units in accordance with
approved engineering changes, and (4) consignment spares
for buyer use until such time as it is shown that the MTBF
is at least M.
Extended warranties
The base warranty is integral to the sale and as such
factored into the sale price and the customer does not pay
anything extra. Extended warranties are optional which
customers purchase by paying an extra amount. These are
offered by several parties – manufacturers, retailers and
independent agencies such as insurance companies etc.
Warranty costs
There are several different notions of warranty costs.
These include (i) warranty cost per unit, (ii) warranty
cost over some interval (for example, product life cycle)
and (iii) warranty costs per unit time (warranty cost
rate). As mentioned earlier, the warranty costs depend
on product reliability and the product usage. Figure 2 is
simplified characterisation for determining the warranty
cost per unit. Blischke and Murthy (1994) discuss the
expected warranty costs for a wide variety of warranty
policies.
The warranty cost as a fraction of the sale price can
vary from 1 – 10% depending on the product and the
manufacturer. The total warranty costs for General Motors
and Ford were over 4 billion dollars each for 2006. Through
proper servicing logistics, these costs can be reduced.

D.N.P. Murthy
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Murthy et al (2004) deals with warranty logistics. One
particular issue is the choice between repair versus replace
for a failed item under warranty. Murthy and Jack (2007a)
deal with this topic.
Extended warranties are similar to outsourcing of
maintenance and this topic is examined in Murthy and Jack
(2007b).
Issues in warranty
Because of the diversity of purpose and application,
product warranty has received the attention of researchers
from many diverse disciplines
4
. As a result, warranty
issues have been considered from the following different
perspectives
• Historical: origin and use of the notion
• Legal: court action, dispute resolution, product liability
• Legislative: Magnusson-Moss Act; Federal Trade
Commission, Warranty requirements in government
acquisition (particularly military) and TREAD Act in the
USA and the latest EU legislation
• Economic: market equilibrium, social welfare
• Behavioral: buyer reaction, influence on purchase
decision, perceived role of warranty, claims behavior
• Consumerist: product information, consumer protection
• Engineering: design, manufacturing, quality control,
testing
• Statistics: data acquisition and analysis, data-based
reliability analysis
• Operations Research: cost modeling, optimization
• Accounting: tracking of costs, time of accrual
• Marketing: assessment of consumer attitudes, assessment
of the marketplace, use of warranty as a marketing tool,
warranty and sales
• Management: integration of many of the previous items,
determination of warranty policy, warranty servicing
decisions
• Societal: public policy issues
As a consequence, the literature on warranty is very large.
Blischke and Murthy (1996) deal with these issues in detail.
Administration of warranties in the context of government
acquisition is discussed in Brenan (1994) and Murthy and
Blischke (2005) deal with warranty management in the
context of new product development.
Historical perspective
The origin of the word warranty is interesting. In a study
of the origin and history of the concept, Loomba (1996)
states:
“The words warranty and guarantee, known to linguists
as “doublets,” are derived from same original source but
traveling to today’s English language by different routes.
The origins of the word warranty can be traced back to the
Old North French word warant and warantie, to the Old High
German word werento meaning “protector”. During the
Middle Ages, the original expressions used included hoc ex
condicione, warrantizavit, promisit, and sub tali plevina.”
The earliest record of warranty can be found in the
Babylonian and Assyrian tablets of the twenty-fi rst century
B.C. Since then it has evolved over time and in many
Figure 2: Simple characterisation for warranty cost analysis.

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431
Product reliability and warranty: an overview and future research
different societies. Some of the key milestones in this
evolution were:
i. Roman laws of the fi fth century B.C.,
ii. Bavarian laws at the start of the Christian era,
iii. Jewish commercial laws of the second century A.D.,
iv. Hindu religious laws of the fi fth century,
v. Islamic laws of the eighth century,
vi. Egyptian formularies of a slightly later period,
vii. Scattered Russian codes of the early tenth century,
and
viii. The customs of the church rule of medieval times and
customs of the English borough.
The start of the Industrial Revolution in the sixteenth
century brought a major change to manufacturing.
Components were produced by different businesses and
often no single entity was responsible for the product as a
whole. Until the fi rst half of the nineteenth century, caveat
emptor was the rule and sellers rarely offered any sort
of formal warranty on their goods. In the late nineteenth
century, warranties were treated as standardized contracts
with extremely limited scope
5
.
During the twentieth century, consumer movements
have had an impact on warranty. There have been three
consumer movements and these are discussed in Blischke
and Murthy (1996). The third consumer movement began
after the end of World War II and gained momentum
in the 1960s. Because of growing concerns for buyers’
protection, the notion of express warranty was augmented
by another concept, “implied warranty,” which basically
states that a product must be capable of performing its
intended function when used properly and under normal
operating conditions. By 1952, every state in the United
States except Louisiana adopted what is termed the
Uniform Commercial Code (UCC). Several forms of
legislation have been enacted during the past few decades
to regulate warranties on various products, the most notable
such legislation being the Magnuson-Moss Warranty-
Federal Trade Commission Improvement Act of 1975 and
the TREAD Act of 1999
6
.
NEW ISSUES AND CHALLENGES: TOPICS FOR
FUTURE RESEARCH
A framework to study warranty and reliability is given in
Figure 3 (from MURTHY; BLISCHKE, 2005). Some of the
new issues are the following:
• Outsourcing of design: Here the some component designs
are outsourced. If items are not designed properly, it can
result in high warranty claims and signifi cantly impact
the bottom line of the manufacturer.
• Outsourcing of component manufacture: The warranty
costs to the manufacturer of the product can increase
signifi cantly if the fraction on nonconforming components
is high. There is a trend towards the manufacturer passing
on these costs to the component suppliers.
• Warranty servicing: Here the warranty servicing is
carried out by an independent agent under a contract.
Poor servicing affects customer satisfaction and in turn,
the reputation of the product and the manufacturer. Also,
Figure 3: Framework for study of reliability and warranty.

D.N.P. Murthy
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Produção, v. 17, n. 3, p. 426-434, Set./Dez. 2007
there are potential problems of over-servicing, fraudulent
claims etc.
• Flexible (base and extended) warranties: This is to meet
the varying usage and risk profi les of consumers.
We now briefl y discuss some potential topics for future
research.
Warranty servicing and game theory
Murthy and Ashgharizadeh (1999) deal with
maintenance outsourcing as a Stackelberg game
formulation. Here the service agent (providing the
maintenance) is the leader and the owner of the product
(and customer for the maintenance service) is the follower.
The service agent provides a set of service options A
i
(
θ
i
), 1
≤ i ≤ n, and the customer chooses the best option to optimize
the customer’s goal. This generates the optimal response
function A*(
θ
1
,
θ
2
,...,
θ
n
) as shown in Figure 4. Using this,
the service agent then optimally selects the decision
variables to maximize the goals of the service agent.
As mentioned earlier, extended warranties are closely
related to maintenance out-souring. The study of warranty
servicing from a game theoretic viewpoint is an interesting
topic for future research.
Warranty management and agency theory
The framework in Figure 3 indicates three cases involving
two parties – manufacturer and an external party. These
are: (i) External design houses, (ii) external component
suppliers and, (iii) independent warranty service agents. The
manufacturer delegates tasks to an external party and the
goals (or objectives) of the two are different.
Agency theory deals with the relationship that exists
between two parties (a principal and an agent) where the
principal delegates work to the agent who performs that
work and a contract defi nes the relationship. Agency theory
is concerned with resolving two problems that can occur in
agency relationships.
The fi rst problem arises when the two parties have
confl icting goals and it is diffi cult or expensive for the
principal to verify the actual actions of the agent and whether
the agent has behaved properly or not. The second problem
involves the risk sharing that takes place when the principal
and agent have different attitudes to risk (due to various
uncertainties).
According to Eisenhardt (1989), the focus of the Agency
theory is on determining the optimal contract, behaviour
versus outcome, between the principal and the agent.
Agency theory has also been applied in many different
disciplines. For an overview, see Acekere (1993). The
different issues involved are indicated in Figure 5 and
discussed briefl y.
Moral hazard: Moral hazard refers to lack of effort (or
shirking) on the part of the agent. The agent does not put
in the agreed-upon effort because the objectives of the two
parties are different and the principal cannot assess the level
of effort that the agent has actually used.
Adverse selection: Adverse selection refers to any
misrepresentation of ability by the agent and the principal
is unable to completely verify this before deciding to hire
the agent.
Information: To counteract adverse selection, the
principal can invest in getting information about the agent’s
ability. One way of getting the desired information is by
contacting people for whom the agent has provided service
in the past.
Monitoring: The principal can counteract the moral
hazard problem by monitoring the actions of the agent.
Monitoring provides information about the agent’s actual
actions.
Information asymmetry: There are several uncertainties
that affect the overall outcome of the relationship. The two
parties, in general, will have different information to make
an assessment of these uncertainties and will also differ in
terms of other information.
Risk: This results from the different uncertainties that
affect the outcome of the relationship. The risk attitude of the
two parties, in general, will differ for a variety of reasons. A
Figure 4: Stackelberg game formulation.

Produção, v. 17, n. 3, p. 426-434, Set./Dez. 2007
433
Product reliability and warranty: an overview and future research
problem arises when this disagreement is over the allocation
of risk between the two parties.
Costs: There are various kinds of costs for both parties.
Some of these depend on the outcome (which is infl uenced
by uncertainties) but also in acquiring information,
monitoring and the administration of the contract. The heart
of the principal-agent theory is the trade-off between (i)
the cost of monitoring the actions of the agent and (ii) the
cost of measuring the outcomes of the relationship and the
transferring of risk to the agent.
Contract: The design of the contract that takes into
account the issues discussed above is the challenge that lies
at the heart of the principal-agent relationship.
The literature on Agency theory is vast. Bulk of them deal
with study of various issues using static models. The study
of out-sourcing of (i) design, component manufacturing and
(iii) warranty servicing using Agency theory require dynamic
model formulations. In addition, RIW will be important in
the context of design outsourcing and cumulative warranties
in the context of component outsourcing. There is lot of
scope for new research in this area.
Flexible warranties
One can defi ne several different notions of fl exibility in
warranties. A key issue with each notion is the pricing of
the warranty. These needs to take into account the response
function of consumers. A simple model for fl exible warranty
is proposed in Jack and Murthy (1977) and there is scope for
lot more new research.
Figure 5: Issues in agency theory.
Reliability modelling and warranty
cost analysis
As discussed in Section Product Reability: an overview,
there are several different notions of reliability – design
reliability, inherent reliability and fi eld reliability. One
needs to build models that link inherent reliability to design
reliability and the affecting factors and similarly for the link
between fi eld reliability and inherent reliability. Murthy
and Jiang (2007) deals with one such model formulation
involving Weibull distributions.
The warranty cost analysis based on fi eld reliability then
allows one to assess the impact of these affecting factors on
the warranty costs and optimal cost effective strategies to
reduce this impact.
Analysis of warranty data
Warranty data (for products sold with either one- or
two-dimensional warranties) provide useful information to
estimate fi eld, inherent and design reliabilities. The literature
deals mainly with fi eld reliability estimation under different
scenarios (see, KARIM; SUZUKI, 2005). The extension
of these to estimate inherent and design reliabilities is a
potential topic for new research.
CONCLUSIONS
In this paper we have discussed some new issues and
challenges in the areas of reliability and warranty and
suggested some topics for research in the future.

D.N.P. Murthy
434
Produção, v. 17, n. 3, p. 426-434, Set./Dez. 2007
D.N.P. Murthy
Division of Mechanical Engineering
The University of Queensland, Brisbane Q 4072 – Australia
Email : p.murthy@uq.edu.au
 About the author
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MURTHY, D. N. P.; OSTERAS, T.; RAUSAND,
M. Reliability design – I: An integrated
approach, 2007a, under review for
publication
MURTHY, D. N. P.; OSTERAS, T.; RAUSAND,
M. Product Reliability – Specifications and
Performance, under preparation for
publication by Springer Verlag, London,
2007d.
MURTHY, D. N. P.; SOLEM, O.; ROREN,
T. Product Warranty logistics: Issues and
challenges, Euro. Jr. Oper. Res., 156, 110-
126, 2004.
MURTHY, D. N. P.; VIRTANEN, S.;
HAGMARK, P. E. Reliability design – II:
Linking product reliability to business
objectives, 2007b, under review for
publication
MURTHY, D. N. P.; XIE, M.; JIANG, R.
Weibull Models, Wiley, New York, 2003.
SALEH, J. H.; MARAIS, K. Highlights from
the early (and pre-) history of reliability
engineering, Reliability Engineering and
System Safety, v. 91, p. 249-256, 2006.
SHOOMAN, M. L. Software reliability: A
historical perspective, IEEE Transasctions
on Reliability, v. 33, p. 48-55, 1984.
THOMAS, M. U.; RAO, S. S. Warranty
economic decision models: A summary
and some suggested directions for future
research, Operations Research, v. 47, p.
807-820, 1999.
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20, p. 523-534, 1911.
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References
1. Blischke and Murthy (2000) deal with
all the different issues in an integrated
manner.
2. Some books deal with one issue (for
example, estimation, accelerated testing
etc) in detail and others deal with more
than one issue.
3. These include the following: IEEE
Transactions on Reliability, Reliability
Engineering & System Safety,
Microelectronics Reliability, Quality and
Reliability Engineering, International
Journal of Reliability and Applications and
International Journal of Quality, Reliability
and Management. Papers on reliability can
also be found in Operational Research,
Statistics, Engineering and other journals.
4. See Djamaludin et al (1996) for a
bibliography listing over 1500 papers
through 1996. Reviews of the more re-
cent literature on warranty can be found
in Thomas and Rao (1999) and Murthy
and Djamaludin (2002).
5. Vance (1911) discusses the history
of the development of the warranty in
Insurance Law.
6. An excellent discussion of express
and implied warranties, the Magnuson-
Moss Act and related issues may be
found in “A Businesspersons Guide to
Federal Warranty Law,” available at
http://www.ftc. gov/bcp/conline/buspubs/
warranty.htm
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Notes