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Developing A Warranty Cost Model

Chapter 2: literature review.

2.1. Introduction to Reliability:

The reliability expression may sometimes be unclear in general logic due to the differences in understanding it among customers.

Each customer can define reliability from a different point a view. As an example; a customer may define it as cheap product which has a long guaranteed life cycle period and in the meanwhile works hardly enough. Whereas another customer may define it as a reasonable price product which has a life cycle period and will definitely work as intended. (Institute et al., 1968)

The concept reliability is very clear and understandable in the practical and industrial world.

Reliability of a product, process, or system is the probability that it will perform as specified, and under certain condition, for a specified period of time.(2"Blank, 2004)

Reliability is known as the likelihood of a product, machine or a component, to keep doing its intended task without breaking down under precise conditions for a given period of time. (Yang, 2007) (Yang, 2007)

The above expression holds three significant essentials to ensure the full understanding of reliability:

To know the planned function or task of a product, machine and component.

To know the planned duration specified relating to a product, machine and component.

To know the environment surrounding where the product, machine, and component, suppose to be working at.

Knowing these three essentials conditions will allow us to estimate the product, machine or component reliability capability from the first instance.

2.1.2. Reliability Engineering Studies:

The purpose of reliability engineering studies is to control, or to make sure that a product, machine or component will be reliable under normal operation in a specified studied manner, as well as away from breaking downs. (Smith, 1972)

Reliability engineering studies are science used to minimize the outcome effects and possible behaviour which will result in maximizing reliability.

There are three necessary conditions to achieve the previous statements:

To build a maximum reliability consideration into a product, machine and component, during the design and development stages; this consideration is known to be the most critical point due to its responsibility in inherent reliability.

To cut down production process differences; this will guarantee that the process will not deliberately degrade the inherited reliability.

Once a product is manufactured. A well maintained operation should be commenced; this will prevent the performance degradation and will extend the product life.(Hartman, 2007)

These considerations are presented within a large selection of reliability techniques, as an instance; reliability planning and specification, fault tree analyses, accelerated life testing, degradation testing, reliability verification testing and warranty analysis.(Yang, 2007)

2.1.3. Reliability Main Factors:

To judge on the reliability of any product, there are factors should be known, as an instance:

Intentional usage or application.

Product, machine and component specification.


Customer expectations.

Level of inconvenience caused by product, machine or component breakdown.

2.1.4. Reliability Measurements:

In a view of the fact that reliability is measured by probability or likelihood, any effort to measure it will engage the usage of statistical methods. Therefore statistics are very important tools in relating to reliability studies. (Yang, 2007)

2.1.5. Reliability Formula:

Warranty and reliability share the same patterns for an economic sense to be observed. Reliability has been identified as the likelihood of a product to keep performing its intended task without breaking down.

R= reliability.

P (s): success probability.

N: number of attempted trails.

S: number of success.

F: number of failures.

Reliability mainly presents the successes and failures in a process, where a good economic warranty cost model has high accuracy in reliability prediction.

Design for Reliability: Overview of the Process and Applicable Techniques. 2011. Design for Reliability: Overview of the Process and Applicable Techniques. [ONLINE] Available at: [Accessed 19 March 2011].

2.1.6. Reliability Improvement:

There are many ways by which the reliability can be affected, below are two ways:

Quality is the integration of features and characteristics of a product or a service, to enable us to meet the needs and specific requirements.

Repetition of the same task causing financial and labor waste. (6"Condra, 2001)

2.1.7. Reliability Applications:

Various phases of a power plant such as construction, production and maintenance shall apply the reliability data analysis. Such a data might be (Heyman, 1988)applicable for production planning, benchmarking , trend analysis, plant components improvement, risk issues, RCM , spare parts optimization, Design review , Structural reliability. (Heyman, 1988)

Data on existing units can be effectively useful for benchmarking the unit performance, during RCM, failure preventions, the spare parts optimization.(Heyman, 1988)

2.1.8. Reliability Prediction Science:

It is considered to estimate the effects of the choices made prior the system is built or put into service. Reliability prediction handles the analysing of products with the help of models better than real systems to supply a solid foundation for testing, analysing, planning, manufacturing, and estimating reliability.

An ideal example of reliability prediction is to predict the system of specified design and specified group of components in an ideal working environment. At the end of the prediction the reliability of the same system should be tested in a different surroundings from those which data and prediction were obtained from earlier.(3"Blischke and Murthy, 2000)

Reliability prediction procedure is attempted at the very first steps of improving a program to hold up the design procedure. Commencing a reliability prediction helps in supplying clear demands of reliability enhancement within the improvement stage, and the knowledge of the possibilities of failure of the equipment in its operation life.

The advantage of applying reliability prediction, machinery designs are able to develop, money is saved rather than spending on poor designs and time is preserved concerning testing.

A widely used way for prediction the reliability of machinery is based on database usage, however this way is not probable due to variety types of failure rates which dramatically happen to similar products.(Geitner and Bloch, 2006)

2.1.9. Objective of Reliability Prediction:

The importance of reliability prediction lies down under several points:

The reliability prediction should be implemented as an assurance program in different sections of a plant.

Repairing decisions are taken when and where problems appear.(Kececioglu, 2002)

2.1.10. Taxonomy Related to Reliability:

Availability: It can be defined as the probability that the component will function at any random time.

Mean time to failure (MTTF): The time that elapses until a failure occurs.

Mean time between failures (MTBF): It is the average time between failures. It is used for repairable systems.

Failure Rate: The failure rate in a time interval which is the probability that a failure per unit time occurs in the interval given.

Hazard Function: The failure rate limit as the interval approaches zero.(Pham, 2006)

2.2. Reliability Centred Maintenance:

The word maintenance from the engineering point of view is: to take the necessary action to maintain or restore equipment and machinery, or system to determine the practical requirement to achieve maximum validity. This includes corrective maintenance, preventive maintenance, and predictive maintenance.

What is maintenance? Definition and Meaning. 2011. What is maintenance? Definition and Meaning. [ONLINE] Available at: [Accessed 19 March 2011].

Reliability centred maintenance or (RCM) can be expressed as an advanced study into maintenance, which joins the maintenance of interactive applications, preventive, predictive, and proactive, as well as the formation of plans to make the most of the life of the product, and also to ensure proper function for the product, machine and component at the lowest possible cost.

Introduction to Reliability Centered Maintenance (RCM) Part 1. 2011. Introduction to Reliability Centered Maintenance (RCM) Part 1. [ONLINE] Available at: [Accessed 19 March 2011].

2.2.1. Preventive Maintenance:

Preventive maintenance is the programme of planned maintenance, which aims to prevent the collapse and failure. The main objective of preventive maintenance is to prevent the failure of equipment before it happen. It is designed to maintain and improve equipment reliability by replacing worn components before they fail in practice. Preventive maintenance activities include equipment checks and repairs, partial or complete checks at fixed intervals, oil changes, and lubrication and so on.

In addition, workers can record equipment deterioration so they know when to replace or repair defective parts before they cause system failure. It would be an ideal preventive maintenance program to prevent all equipment failure before it happens.

Preventive Maintenance. 2011. Preventive Maintenance. [ONLINE] Available at: [Accessed 19 March 2011].

2.2.2. Predictive Maintenance:

Techniques help to determine the status of equipments in service in order to predict when you must perform maintenance.

This approach offers cost savings over routine preventive maintenance.

What Is Predictive Maintenance?. 2011. What Is Predictive Maintenance?. [ONLINE] Available at: [Accessed 19 March 2011].

2.2.3. Terms and Goals of Using Reliability Cantered Maintenance:

The majority of maintenance organizations classify the goals of using (RCM) by the below listed steps:

Scheduling the tasks by its priority.

Consider the safety prospective.

To be familiar with the machinery capabilities; each type of machinery will have different performance type.

Knowing the failure causes; to recognize when the right moment to reduce it is.

Using skilled staff; to help out in scheduling priorities.

Practicing preventative tasks; to help in knowing the machinery status.

Disposing and replacing the damaged components; to ensure the effectiveness of the other related parts.

Standards must be identified for each step mentioned above.

It is important that the steps are done by the same staff who are responsible of the function and operation of the plant.(Tweeddale, 2003)

The conditions to develop a sufficient (RCM) program depend on the success of using the observation and statistical methods, because sometimes both methods depend on each other.

2.3. Failure Mode and Effects Analysis:

Mechanical failures are introduced as any significant changes regarding size, shape or material characteristics in a system.

The first and main responsibility of any mechanical designer is to make sure that the design produced is capable of doing its function properly, meets the designated life time and most important is to be competitive in the market.

Estimating and identifying all possible modes of failure which may restrict the functionality of the design will ensure the success in designing.

The designer must be familiar with the variety collection of failure modes presented in the work sites as well as the circumstances leading to it, so the designer becomes ready to prevent failure from occurring once again.

The designer should preferably have an on hand experience to investigate predictable failures in a professional manner, thus failures could be prevented in future. It is clear that the failure analysis, prediction, and preventative are significant to be known to every designer.(5"Collins, 1993)

The term behind the failure can be known as the failure to meet some specific performance measurements. Different between definitions terms such as defects, malfunction, fault and reject are usually vital in comparing causes of failures, as well as in the categorizing and analyzing of provided information.

The different between the terminologies is mainly to define the types of failure, reasons, and level of failure. For any introduced definition of failures there are no doubts in introducing reliability. Because the failure is the absent of the specification and so changes in performance capabilities occur. (Smith, 2005)

The estimation of the data could be done by two methods, first by using history data; this will enable us to have a look at similar machinery which may had experienced identical problems, warranty data, and customer feedback.

Second method is conducted, by using several mathematical methods, models and simulations. Dealing with (FMEA) does not always mean that one way is better or more accurate than the other; both of the methods can be used if applied correctly.

The proper way in commencing (FMEA) will result is providing helpful data which can help in reducing the hazards relating to work load in a system, product and service.

The (FMEA) is one of the most efficient ways considered in preventative maintenance. The (FMEA) will help in having knowledge about what is suitable correction tasks should be done to keep failures away from happening.

An effective and successful (FMEA) system could be recognized by meeting these objectives, first recognize the known and possible failures modes, and then reasons of failures. Schedule the failures modes according to the highest risk level, and finally follow up the work done to ensure the correction of the failure.(Stamatis, 2003)

2.3.1. When and Where To Use Failure Mode and Effects Analysis:

The (FMEA) procedure is extensively used in different stages, regarding product designing and manufacturing processes. It offers a well organized structure and an easy way to communicate amongst the team of manufacturers. It can be used as well in developing services which will help production process.(McDermott et al., 1996)

Traditional failure modes and effects analysis (FMEA) are mainly used models in warranty cost among other models in the automobile industry. (Majeske, 2003)

An essential term to inherent reliability into a product or system is by recognizing the failure causes, and making sure they are removed or that their likelihood of happening once again is low.

This thought can be done by conducting tests, or logically by using models. Failure mode and effects analysis is a planned way in clarifying the origin of failures modes, and it is considered to be a sufficient reliability schedule, especially it links to reliability development throughout design stage.(7"Denson, 2006)

2.4.4. Hazard and Operability Study (HAZOP):

Risk analysis is an orderly and systematic method for Examination system and risk management. In particular, are often used as a risk and operating Technique to identify potential hazards in the system and identify interoperability problems.

It assumes that events are caused by the risk of design or operating intentions. This approach is a unique feature of risk and vulnerability to treatment methodology that helps to stimulate the imagination of the team Members when exploring potential deviations. Figure (2) shows a sample of HAZOP system.(Organisation and Safety, 1988)

Figure (1) a sample of HAZOP system

Hazard & Operability Studies (Hazops) - 1 of 2. 2011. Hazard & Operability Studies (Hazops) - 1 of 2. [ONLINE] Available at: [Accessed 19 March 2011].

2.3.2. Failure Prevention:

Failures are predictable, sooner or later all products, machines and component will experience failure due to many reasons.(Yang, 2007)

In any engineering system failures are expected. The effects of failures differentiate from little inconvenience costs to financial drops. Failures happen due to various factors, such as:

Bad engineering design.

Manufacturing process errors.

Insufficient testing.

Human mistakes.

Poor maintenance.


In order to reduce failures or breakdowns in any engineering systems, there are some methods should be followed:

Identify the cause and the way the failure happened.

Identify how many times do the failure tends to repeat.

Reliability handles the failure concepts in details via different statistical approaches. Whereas safety tries to study, specify, measure, determine, and analyze the failure.(Verma et al., 2010)

2.4. Introduction to Hazard:

The accurate understanding of hazard is appreciated due to its criticality. It supplies us with the base foundation of a system safety.

Hazard analysis is conducted to identify hazards consequences, and hazard main factors, As well as to determine the risks facing the system.

To carry out hazard analysis in a proper manner, it is essential to recognize what causes hazards and how to define hazards. Understanding the hazard character is an important issue to improve the skills needed to identify potential hazards and their results in a system design.(Ericson, 2005)

2.4.1. Hazard Analysis:

This analysis involves describing the complete process first, and then collecting the answers for a set of systematic questions. The purpose is to identify how exactly the deviations from the design can arise.  These deviations are further assessed by any negative effect of their consequences on the safe and efficient operation of the plant.  The assessment would provide a basis for any action to be taken to cure this situation.

From an engineering point of view, hazard analysis process is the best tool for analyzing reliability data. It can be used to make conclusions about the reliability of a component. (1"2002)

2.4.2. Survival Analysis:

Survival function, also known as a reliability function of the survivors, is a property of any random variable that maps a set of events, usually associated with failure of some system.

2.4.3. Hazard Rate Function:

Hazard rate function can be obtained by an equation which assumes a constant hazard rate.

2.4.5. Bathtub Curve:

Figure (2) illustrates the bathtub curve which demonstrates the product failure rate against time.

Any product cycle life can be divided into three separate durations:

The first duration (early life): This duration where the failure probability is decreased to minimum. . It what happens in the early life of most new products, sometimes the first period is mentioned as the mortality period.

The second duration (normal life or useful life): This is represented in the graph by a flat line. Failures and breakdowns happen randomly within this duration. In this period the failure rate tends to become somehow constant. During this period the lowest failure rate is observed, so it is the most appropriate time to make reliability predictions.

The third duration (wear out): this begins where the slope starts to rise till the end. This typically happen to products when they get old, thus the failure rate increases. Wear out is usually caused by break down due to various reasons such as physical wear and stress.(speaks, 2005)

Figure (2) a bathtub curve.

A Brief Introduction to Reliability. 2011. A Brief Introduction to Reliability. [ONLINE] Available at: [Accessed 19 March 2011].

2.5. Statistical Models for Life Data:

Statistical models for life data such as weibull distribution, survival analysis and warranty help in producing high accuracy in prediction.

The automobile manufacturing having relied heavily on warranty interval in its warranty provision inclines more in reliability and therefore seek such analysis. (Ward and Christer, 2005)

2.5.1. Weibull Distribution:

The weibull distribution is named after a Swedish professor Waloddi Weibull. He explained the ability to use the weibull distribution in small sizes measurements and it is easiness to supply an accurate model for a broad data sets.

At the beginning of his exploring weibull distribution he faced some obstacles and doubts form his colleagues. However, the weibull distribution has ended now to be widely practised in reliability.(8"Dodson, 2006)

A reason for the wide spread of the weibull distribution is that it has a large different shapes, which makes it easy to fit any data. Also, it is perfect to show the weakest connection of a product. For example, if a system has more than one part, the weibull distribution will present each failure time of each part at the same distribution no matter how insignificant they are .(Nelson, 2003)

Figure (3) is a sample of weibull a distribution plot.

Figure (3) a sample of weibull distribution plot.

Guidelines for Burn-in Justification and Burn-in Time Determination. 2011. Guidelines for Burn-in Justification and Burn-in Time Determination. [ONLINE] Available at: [Accessed 19 March 2011].

2.5.2. Kaplan Meier Survival Estimator:

The Kaplan Meier estimator is named after Edward L. Kaplan and Paul Meier. It estimates the survival function. In engineering this method is used to measure the time until failure of different products, machine and components.

Kaplan EL, Meier P. J Am Stat Assoc 1958; 53:457-81. [Cited by: McKenzie S, et al. JOP. J Pancreas (Online) 2010 Jul 5; 11(4):341-347. (Reference 14)]. 2011. Kaplan EL, Meier P. J Am Stat Assoc 1958; 53:457-81. [Cited by: McKenzie S, et al. JOP. J Pancreas (Online) 2010 Jul 5; 11(4):341-347. (Reference 14)]. [ONLINE] Available at: [Accessed 19 March 2011]. Formulation:


t (1) < t (2) <... < t (n) – ordered failure and censoring data; E = k, if k < n and E = n, if k = n; dj = number of failures at t (i)

2.5.3. Exponential Distribution:

This is the most commonly used distribution in reliability, and is often used to predict the probability of survival to time (t) figure (4) shows a sample of exponential distribution graph.(9"Dovich, 1990)

Figure (4) a standard exponential distribution graph

Continuous Random Variables: The Exponential Distribution. 2011. Continuous Random Variables: The Exponential Distribution. [ONLINE] Available at: [Accessed 19 March 2011]. Formulation:

The probability density function is:


Mean time to failure =

Or, where

2.5.4. Disadvantages and Advantages of Statistical Method:

Cost; studying and analyzing a quantity of data of different products within a system are an expensive job.

The results revealed are not sufficient enough to build an understanding of the type of maintenance needed in this particular situation.

The only disadvantage of the observation method appear is when applying it carelessly and without keeping record of founding’s, this will result in mixing up different judgements.(4"Chalifoux and Baird, 1999)

2.6. Introduction to Warranty:

Warranty is a provision for a seller to provide assurance to a buyer that the product will perform as implied. (Zhou and Tang, 2008)

Warranty brings confidence to the buyer; automotive vehicles like any other automated system consider warranty to a buyer. (Wu and Li, 2007)

Unlike the quality loss function which assumes a fixed target and accounts for immediate issues, warranty loss occurs during the customer use. (Zhou and Tang, 2008)

In automotive industry, data is tracked and analyzed regularly (Zhou and Tang, 2008). The interval can be evaluated on the basis of their costs.

The effect of warranty especially in the context of the interval, affects the performance of the company especially if the number of returns on warranty is high. (Wu and Li, 2007)

Neglecting the fact that warranty cost is a result of conflict between the customer expectation and the performance of the product, the interval of the warranty liability disturbs the economic sense of warranty. (Wu and Li, 2007)

Warranty costs have in many companies been positioned as operational costs. (Ward and Christer, 2005)

The impact of warranty in the whole business performance has challenged vehicle manufacturers to develop vehicles that are less costly to repair (Metric: Warranty $s) and are more reliable within a longer period of time. (Metric: annual failure rates, AFR)

For this purpose to be done, warranty cost models that make the impact of reliability on cost and costs associated with repair of specific failure modes should be economically healthy. (Wu and Li, 2007)

2.6.1. Warranty Probability:

The ratio as Pw is termed as the warranty probability (Ward and Christer, 2005). The warranty probability is the ratio of the number of complaints N against the total number of products Tp.


Another factor that is important in warranty cost analysis is the complaint factor. (Ward and Christer, 2005)

The complaint factor is the ratio of the actual number of complaints and the potential number of complaints where the actual number of complaints is the number of actual complaints fixed. (Ward and Christer, 2005)

The method for calculating the warranty probability depends on product performance and customer expectations. (Wang et al., 2010)

The distance of performance is a function of the warranty interval. (Ward and Christer, 2005)

It is supposed that as time passes, the distance of performance increases, this is the common feature referred to as mileage.

In motor vehicles the time age of the car has been consistently assumed to be a factor representing its use. (Manna et al. 2008)

Despite the fact that mileage can be determined, the correlation between mileage and age of the car is strong and positive. (Manna et al. 2008)

Since vehicles manufacturing designs and model change with time, the automobile industry prefer attaching warranty to age of the vehicle rather than calibrated mileage.

Warranty is a key factor in bringing confidence to a buyer. The higher the warranty time, the more the confidence is the buyer. (Manna et al. 2008)

2.6.2. Warranty Distribution Analysis:

Feedback from warranty returns provides a solid basis in determining use failure distribution. (Murthy, and Blischke, 2006)

The time interval as a factor contributes significantly to predictions. The warranty intervals are the most solid factor that can be used in assessing the failures prediction.

By maintaining warranty and assessing failures for a longer period of time, more knowledge on the performance especially for automated systems is achieved. (Murthy, and Blischke, 2006)

Reasons for carrying out warranty data analysis are the following:

Forecasting warranty claims.

To determine risk assessment and monitoring.

Reliability assessment.(1"2002)

2.6.3. Reduction strategies for cost drivers

There are two factors that have been identified as primary warranty cost drivers. The number of occurrence of an event which can be noticed by the analysing failure rate and the cost of the process are the identified cost drivers. (Attardi et al., 2005)

The strategies employable for reduction of costs are by reducing the factors. (Attardi et al., 2005)

2.6.4. Cost model in product development

The cost model has been used in product development in making economic sense of organizational existence. (Karim and Suzuki, 2005)

Through its impact in influence of decision making by providing design alternatives that come handy in warranty cost, the model establishment should be in advisory of the product development through calculation of estimates of product total warranty cost. (Aldridge, and Dustin, 2006)

Difference in warranty costs based on design alternatives provides a short projection of the optimized design that maintains both customer confidence through warranty and economic advantage to the organization. (Attardi et al., 2005)

Identification of necessary product features, capabilities and diagnostic tools that are required in automobile projected warranty savings for the warranty intervals is achievable through the cost model in product development. (Aldridge, and Dustin, 2006)

Under the foundation of the cost model, the risk involved in the warranty interval can be evaluated by analyzing the risk involved in an extension of warranty in automobiles. (Aldridge, and Dustin, 2006)

It should be taken into consideration that the cost model economic impact is dependent on the period of warranty especially with automobiles that are known to wear and tear. (Karim and Suzuki, 2005)

Chapter 3: case study (from notes given by doctor)


Field data in the automotive industry often comes in two types, the first is grouped data expressed by months in service. The second is ungrouped data available from company owned but customer operated fleets and expressed as miles to failure.

In many scenarios, data which comes from late stages have a greater importance over the former because of the following reasons:

Mileage is more objective measure of the component life than time in service.

There are types of failures are not tracked by the warranty system.

The complexity of censoring mechanism in relating to reliability analysis of grouped warranty data.

Therefore, this theoretical case study will focus on the analysing of ungrouped mileage data which is not represented by time in service, because it comes from the company owned fleets.

Aim and objective:

To discuss a procedure to estimate the censoring mileage and the reliability function for a component of interest (e.g.: battery).


Table 1 shows a format of failure data from a customer operated fleet. The vehicle mileage is reported only at failure or service events.


failed / serviced comopnent

failure / service mileage





fuel pump



brake pads



front wipers



head lamp



clutch disks



front wipers









front struts









door lock



fuel pump









head lamp



front struts









brake pads



brake pads



clutch disks






head lamp



front struts






door lock



clutch disks






fron wipers



clutch disks



brake pads



front wipers


Table 1 illustrates an example of failure data collection

If every line in the previous table had experienced a failure mileage of the same type if component (in this case, battery) it would be considered a complete data set.

Censored data set appears when only encounter a few failures of a given component within the sample of vehicles.

Singly censored on the right means

Chapter 4 case study (real life)

Chapter 5 discussion and conclusion

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