Warranty claims analysis for household appliances produced by ASKO Appliances AB

70 Pages·2013·1.21 MB·English

by  Jonas Erlandsson

Master Thesis in Statistics and Data Mining

Warranty claims analysis for household
appliances produced by ASKO
Appliances AB

Ana Turk
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© Ana Turk
Abstract
The input collected from warranty claims data links customer feedback with product quality.
Results from warranty claim analysis can potentially improve product quality, customer
relationships and positively affect business. However working on warranty claims data
holds many challenges that requires a significant share of time devoted to data cleaning and
data processing.
The purpose of warranty claims analysis is to get the comprehensive overview of the
reliability, costs and quality of household appliances produced by ASKO. While there are
different ways to approach this problem, we will focus on non-parametric and semi-
parametric methods, by using Kaplan-Meier estimators and Cox proportional hazard model
respectively. These kinds of models are time dependent and therefore used for prediction of
household appliance reliability. Even though non-parametric models are quite informative
they cannot handle additional characteristics about observable product hence the semi-
parametric Cox proportional hazard model was proposed. Apart from the reliability analysis,
we will also predict warranty costs with probit model and observe inequality in household
appliances part failures as a part of quality control analysis. Described methods were
selected due to the fact that the warranty claims analysis will be practiced in future by
ASKO’s quality department and therefore straight forward methods with very informative
results are needed.
Acknowledgements
I would like to thank ASKO for providing data and Magnus Älmegran, Antonio Scarlini,
Simon Kumer and Marko Šefer for making this cooperation possible.

I would also like to thank my supervisor Bertil Wegmann for guiding and supporting me
throughout this research. However I would not be able to come so far without a guidance of
all professors in the Statistics and Data Mining department at Linköping University.

Last but not least I would like to thank my family and friends for being there for me and
supporting me on this path. My mom Suzana Turk and dad Karol Turk made this study
possible and I will be always grateful to them for supporting me in all my life decisions. The
one person that always listens and cares about me unconditionally is my sister Ines Turk and
even though I do not say it enough I am really thankful to have you in my life.

LIU-IDA/STAT-A--13/005--SE
Ana Turk
Linköping University
2013-06-17
Table of Contents
Abstract .................................................................................................................................... 3
Acknowledgements .................................................................................................................. 4
Table of Contents ...................................................................................................................... 5
1 Introduction ....................................................................................................................... 1
1.1 Background ................................................................................................................. 2
1.2 Objectives ................................................................................................................... 4
2 Data ................................................................................................................................... 4
2.1 Variables...................................................................................................................... 5
2.2 Raw data ..................................................................................................................... 7
2.3 Secondary data ............................................................................................................ 8
2.4 Univariate analysis ...................................................................................................... 9
3 Methods ........................................................................................................................... 15
3.1 Reliability analysis for a singular failure .................................................................. 16
3.1.1 Reliability function ............................................................................................ 16
3.1.2 Hazard function .................................................................................................. 17
3.1.3 Kaplan-Meier estimator ..................................................................................... 17
3.1.4 Cox proportional hazard model ......................................................................... 18
3.2 Reliability analysis for multiple failures .................................................................. 20
3.2.1 Marginal Cox model for multiple failures ......................................................... 20
3.3 Part failure analysis ................................................................................................... 21
3.3.1 Pareto principle .................................................................................................. 21
3.3.2 Gini coefficient .................................................................................................. 22
3.4 Warranty cost analysis .............................................................................................. 24
3.4.1 Probit model ....................................................................................................... 24
4 Results ............................................................................................................................. 25
4.1 Reliability analysis for a single failure ..................................................................... 25
4.1.1 Testing proportional hazard assumptions ........................................................... 25
4.1.2 Kaplan-Meier estimator ..................................................................................... 27
4.1.3 Cox proportional hazard model ......................................................................... 28
4.2 Reliability analysis for multiple failures .................................................................. 30
4.2.1 Marginal Cox model for multiple failures ......................................................... 30
4.3 Part failure................................................................................................................. 33
4.4 Warranty cost analysis .............................................................................................. 34
4.4.1 Probit model ....................................................................................................... 34
5 Conclusion and discussion .............................................................................................. 35
6 Future work ..................................................................................................................... 39
7 Literature ......................................................................................................................... 41
Appendix A............................................................................................................................. 45
Appendix B............................................................................................................................. 47
Index of Tables
Table 1: Summary of Warranty claims data ................................................................................................................ 7
Table 2: Proportional hazard assumption testing for part failure ...............................................................................26
Table 3: Cox proportional hazard output ....................................................................................................................28
Table 4: Multiple failure marginal Cox model results .................................................................................................30
Table 5: Summary of Backward elimination ...............................................................................................................31
Table 6: Multiple failure marginal Cox model results after the backward elimination ................................................32
Table 7: Model Fit Statistics .......................................................................................................................................32
Table 8: Gini coefficient output ..................................................................................................................................33
Table 9:Probit regression model output .....................................................................................................................34
Table 10: Marginal effect for probit regression model ...............................................................................................35

Index of Figures
Figure 1: Data for one-dimensional non-renewing warranty (Blischke et.al., 2011) .................................................... 5
Figure 2: Data for analysis .......................................................................................................................................... 6
Figure 3: The distribution of a life time for Dishwashers ............................................................................................. 9
Figure 4: The distribution of a life time for washing machines ...................................................................................10
Figure 5: The distribution of a life time for tumble dryers ..........................................................................................11
Figure 6: Bar chart presenting the percentage of failures for dishwashers, washing machines and tumble dryers. ....12
Figure 7: Bar chart presenting extreme number of failures for dishwashers, washing machines and tumble dryers. .12
Figure 8: Line plot of cumulative average costs regarding the number of failures for Dishwashers, Washing machines
and Tumble dryers ............................................................................................................................................13
Figure 9: Bar chart of 10 most frequent part failures .................................................................................................14
Figure 10: Pareto rule applied to part failures within warranty period .......................................................................22
Figure 11: A modified Lorenz curve for part failure analysis .......................................................................................23
Figure 12: Kaplan-Meier curves for testing the proportionality of explanatory variables ...........................................26
Figure 13: Kaplan-Meier survival curves estimates for Washing machines, Tumble dryers and Dishwashers .............27
Figure 14: Predicted survival curve based on Cox PH model for dishwashers .............................................................29
Figure 18: Lorenz curve presenting the inequality of the part failure distribution ......................................................33
1 Introduction
Survival analysis plays an important role in medicine data and biostatistics but its
characteristics can be applied to the field of warranty analysis as well, where it is mostly
known as reliability analysis. Both fields focus on the lifetime of observable units but
instead of for example survival of bacteria we observe the reliability of household
appliances.
Reliability of a product is related to the dependability, successful operation or performance
and the absence of a failure (Blischke et.al, 2011). Considering the life cycle of the product
we can observe different stages of its reliability. It starts with design reliability, inherent
reliability, reliability at sale and once the product is sold we can observe field reliability
(Blischke et.al, 2011). We will focus on field reliability where performance of a product will
be evaluated regarding different factors (model type, severity of failures and working
power).
What makes reliability analysis special is data censoring since additional information about
the item future can be incorporated in different models. Lifetime of each item is observed
for a certain period of time and after that if no failures are reported it becomes censored.
The observable lifetime period can either be censored after the last noted failure of specific
household appliance or after the warranty time expires in case when no failures are
presented.
There are many reasons that impel us to explore the field of warranty analysis. This problem
concerns the marketing (sales), economic (cost), engineering (design) and operational
(servicing) aspects of a company (Murthy and Djamaludin, 2002). An important segment of
warranty claims analysis is repair costs hence, cost analysis will be presented hereafter.

Pareto analysis will be applied as a part of statistical quality control. With the aim of
identifying a few of the most important quality problems we can use different methods that
focus on part failure inequality. These quality issues correspond to the parts of household
appliances that cause the most failures and are therefore most frequently presented in
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warranty claims data.
The purpose of this thesis is to find appropriate models for warranty claims data where the
reliability of household appliances, quality control and the costs of warranty claims are
evaluated.
This thesis is divided in six parts. In the first part we describe the background of warranty
analysis and shortly present the ASKO company. The thesis objectives will be specified in
the first part as well. In the second part we present the characteristics and issues of warranty
data and present the data used for the further analysis. In the third part we present the
methods that will be used for analysis. Results are presented in the fourth part. After that,
the conclusion including evaluation of the methods used will be presented in the fifth part.
Future work will be presented in the final sixth part of this thesis.
1.1 Background
Warranty is defined as a contractual obligation of a manufacturer in selling a product to
ensure the product functions properly during the warranty period (Blischke et al., 2011).
Customers need assurance that a product will perform satisfactory over its designed useful
life (Blischke et al., 2011).

Processing and analysing warranty claims data will be in special benefit for ASKO since
they are dealing with the warranty claims on a daily basis. ASKO is an internationally
oriented Swedish company with long tradition in production of household appliances.
General warranty policy in ASKO is two year non-renewing warranty. For this time period
ASKO replaces or repairs the defected parts and finances the labour needed. Two years
warranty policy considered in this thesis is only eligible for ASKO’s distributors. Even
though the warranty period for customers can be longer and it is usually up to 5 years long,
all the additional warranty expenses after two years become a distributor’s responsibility.

ASKO’s warranty policy only depends on the time, not for instance mileage or usage as it is
common for automotive industry. Therefore we can refer to our data as one dimensional
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data. Another characteristic of our warranty policy is that it is non-renewing which means
that the warranty term does not begin anew on replacement or repair of a failed item
(Blischke et al., 2011).

Warranty analysis is beneficial for a company because it can give a better overview of the
product quality. Through the reengineering of management processes and the application of
a suitable warranty model, it is possible to (Diaz et al., 2010):
• Improve sales of extended warranties and additional related products.
• Improve quality by improving the information flow about product defects and their
sources.
• Improve customer relationships.
• Reduce expenses related to warranty claims and data processing.
• Better management and control over the warranty costs.
• Reduce invalid expenses and other warranty costs.

Moreover the ability to predict and estimate failures for warranty period makes it possible to
appropriately size the necessary resources and consequently optimize the costs (Patankar et
al., 1995). The optimal warranty time should be considered in terms of the relationship
between the price and the warranty policy (Kotler, 1976; Peterson, 1970).

Product performance depends on the reliability of the product, which in turn, depends on
decisions made during its design, development and production (Blischke et al., 2011).
Therefore we will focus on the problem of product reliability that conveys the concept of
dependability, successful operation or performance and the absence of failures. It is an
external property of great interest to both manufacturer and consumer (Blischke et al.,
2011). The main purpose of warranty analysis is therefore customer satisfaction and product
reliability.

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