Identification of factors that differentiate motor vehicles that have experienced wear or failure of brake system components during the warranty service period

The paper focuses on issues related to selected automotive brakes with the aim of applying the proposed methodology to other structural systems of this type. The main aim of the paper is to identify the factors that differentiate the course of wear and occurrence of a fault in brake system components of passenger cars and light commercial vehicles during the warranty service period. The following methods were used in this study: systematic literature review, process analysis, and descriptive and inferential statistics, including analysis of variance and multiple classification analysis. As a result of an analysis of 295 brake system repairs, six differentiating factors that allowed for ex post analysis of the repairs were identified. An analysis of the interaction of these factors made it possible to distinguish three groups of motor vehicles depending on the cause of failure of the braking system. Based on the data generated in the warranty process, it is possible to determine the factors that differentiate the occurrence of a fault and the course of brake disc and pad wear. Highlights Abstract

The study reproduced the actual process of diag-• nosis and repair of the brake system An analysis of the operation process was carried • out using the process mining method The identified factors that differentiate the course • of brake disc wear and failure were vehicle type, body type, vehicle make, and vehicle model.
Groups of factors that differentiate the vehicles • reported for brake system failure and wear were identified.
Identification of factors that differentiate motor vehicles that have experienced wear or failure of brake system components during the warranty service period

Introduction
As a result of dynamic technological and technical development, attempts are made to find material and construction solutions that have a positive and direct influence on the economic, environmental [5], design, and production aspects related to motor vehicles. They are aimed at developing solutions that reduce CO 2 emissions [12] and fuel consumption [18], and replace internal combustion engines with electric units [11,15]. There is a noticeable trend of improving such performance parameters in motor vehicles as acceleration and maximum speed. As a result, this requires modification of current solutions and the design of new active and passive safety systems, with a clear emphasis on the design of the brake system. Assuming that the effectiveness of the brake system in motor vehicles has a significant effect on the speed of vehicles at the time of a collision and, as a result, on the consequences of the accident, this system should be indicated as one of the most important structural assemblies of vehicles [19]. According to a report on the statistics of road accidents caused by vehicle defect factors in the UK in 2018 (1,443 accidents), as many as 36.10% of the defects were related to the brake system [8]. The statistics presented provide the basis for discussions between representatives of the research community and the business community concerning the design of structural solutions for the brake system based on the acquisition and analysis of data generated in the process of the use of vehicles [19].
A systematic literature review identified a research gap related the small number of publications that identify factors differentiating vehicles with wear or failure of brake system components. Efforts to find the factors that differentiate vehicles in which brake discs and pads have become worn out or faulty are particularly important during the first few years of vehicle use. This concerns anticipation of the costs related to safety, selection of subcontractors, indication of warranty costs, and determination of the extent and frequency of brake system checks and inspections. Attempts to analyze the wear of brake system components are found in the literature. In publication [19], the results of studies presented thus far were extended to include an assessment of the impact of vehicle operating conditions on the brake system wear. The present paper adopts a similar approach, which consists in measuring the thickness of the brake system mechanism components (brake discs and brake pads) at Authorized Service Stations (in Polish, ASO). The measurements were made in real operating conditions when symptoms of malfunction were indicated by the user, which may indicate wear or a fault of the brake system components. The study considered interventions during the first four years of vehicle use (the period of the manufacturer's warranty, extended warranty, and service under additional vehicle maintenance packages). It should be emphasized that the ex post analysis of events in the warranty process related to the wear of brake systems provides important knowledge on the failure rate, the wear rate, selection and determination of subcontractor participation in warranty costs, estimation of future costs, calculation of vehicle value, but also estimation of the value of additional service packages. Hence, from the perspective of the outlined problems, it is important to identify the factors which may have impact on the accelerated wear of brake systems and their faults.
The main research objective of this paper is identification of factors that differentiate the course of wear and the occurrence of failure in major components of brake system, such as the disc and the pads used in two types of motor vehicles: passenger cars and commercial vehicles produced by two manufacturers, X and Y 1 . Two partial objectives were assigned for the work: reconstruction of the brake mechanism diagnosis process at the level of the authorized passenger car service stations and reconstruction of the car operation process in the context of assessment of the wear of the examined safety system using the process mining method.

The process of diagnosis and verification of brake systems in the tested group of motor vehicles
The main functions of the brake system include slowing and stopping a motor vehicle, maintaining its speed when driving down a hill, and parking [2]. The design of the brake systems of contemporary passenger cars is characterized by the use of disc and drum brakes [17]. Disc brakes are widely used in many types of vehicles ranging from light motorcycles, through passenger cars and trucks, to trains [20]. Increasingly, they are installed by car manufacturers on both the front and rear axles. This is particularly noticeable in sports cars [e.g., 6]. The main advantage associated with the use of this component in the design of automotive brake systems, as opposed to drum brakes, is better heat dissipation [16]. In the design and operation of vehicles that reach significantly higher acceleration values and maximum speeds, the vehicle user aspect must be considered. It should be considered in the context of damage to the components of the brake system associated with the driving style characterized by intense and repeated braking in short time intervals, resulting in the inability of the brake discs to cool nominally. As a result, the possibility to dissipate the accumulated thermal energy may be limited, i.e., the braking mechanism may reach a state of dysfunction due to the conversion of the vehicle's kinetic energy into thermal energy of a significant value 1 The names of companies and authorized service station chains had to be anonymized for publication purposes. [4,14]. This condition has a significant impact on the effectiveness of the brake system [13].
Based on an analysis of the warranty claims and repair documentation at authorized service stations, the range of possible measurements (diagnosis) of the brake system mechanism components on a stationary stand was reconstructed (Fig. 1).
The visual inspection of the brake system components, the measurements of brake disc thickness, and the measurements of the curvature of their working zones at a specified radius of the disc in the studied group of units were performed in accordance with the requirements specified in the car manufacturer's technical documentation. The inspection was performed with qualified and trained technicians at authorized service stations of the X and Y car brands. An example of a measuring tool that enables measurement of the curvature of brake discs to determine the deformation level is shown in Figure 2.   Figure 3A shows the measurement tool while Figure 3B shows how to measure the thickness of a disc mounted on the front axle of a passenger car at an authorized service station. The maximum values of the measurement sensor indications ("maximum deformations") and the minimum values determined during the brake disc thickness measurements, compared to the limit value of this parameter mentioned in the technical documents, are recorded in the measurement cards.  Figure 4 shows a summary, compiled from service records, of the interventions associated with repair or replacement of the components of a front axle disc brake mechanism. At this point, it is important to emphasize that the catalogue of interventions presented concerned incidents identified in the first four years of motor vehicle use. Figure 5 shows the process of brake system components diagnosis, reconstructed from the available analysis of repair documentation for Fig. 1. Methods of assessing the measurement of brake system mechanism components on a stationary stand the studied group of vehicles. The sequence of steps was reconstructed primarily on the basis of repairs related to thickness measurement and deformation due to thermal loading.
As shown in Figure 5, in the first stage of the diagnosis process, the actions intended to identify the issues reported by the customer are the same in the studied group of repairs. Only a visual assessment of the condition of the front axle disc brake components can indicate the need for diagnosis or actions consisting in a direct contact with the technical department of the motor vehicle importer, the vehicle manufacturer, or the component manufacturer.

Research sample
The empirical research was conducted in the period of 2018 to 2020 on a sample of 295 cars. The warranty repairs were performed in the years 2014˗2018 at Authorized Service Stations. The study comprised a group of seven B-segment car models, manufactured by companies X and Y. The vehicles were homogenous in terms of their installed disc brake mechanism. This means that brake mechanism from the same manufacturer, with the same design and the same dimensions of brake discs, were installed in the studied group of vehicles. Most units in the studied group were diesel-powered (278 cars) with an engine capacity of 1,600 ccm3 (288 cars), and with a manual gearbox (287 cars). All car repairs were divided into two groups according to the reason of malfunction: wear (133 cars) and fault (162 cars). Figure 6 presents the structure of the analyzed vehicles with respect to the brand (X or Y) and the installed motor.
An attempt was made to analyze the repairs concerning brake discs and pads installed on the front axle in the studied group of motor vehicles in which malfunctions of the brake system components were identified during 4-year service performed at the manufacturer's expense. Figure 7 shows a photograph of the studied group of brake discs and pads.
It is important to emphasize that, in addition to the components shown in the figure, the disc brake assembly consists of the following main components: the backing layer, the backing plate, the shim, and the brake caliper [17]. Detailed characteristics of the elements are provided in [17]. Table 1 shows the detailed characteristics of the studied brake discs.
In the group of identified repairs, the average value of brake disc thickness was 24.08 mm ± 1.06 mm (for brake discs mounted on the right side of the motor ve- hicle) and 24.11 mm ± 1.00 mm (for brake discs mounted on the left side of the aforementioned vehicles).
In the analyzed group of cars, the procedure for measuring the thickness of brake system components was started with measurement of brake discs. If the disc thickness was found to be below the minimum value, the friction pad thickness was not measured or was not recorded. The component was taken out of service and replaced with a new one. Of the 295 cases studied, friction pad thickness measurement was recorded in 91 cases, that is 31%.

Operational process mining of the studied group of vehicles
In this part of the study, in order to reconstruct the process of operation of the studied vehicles, the process mining method was applied using the Celonis Snap software. The use of the process mining method was justified by the possibility of a reconstruction of the real vehicle operation process, divided into brake discs and pads wear and faults. Examples of the use of this method are described in detail in [3,7].
The process mining resulted in verification of 297 cases (repairs) and 1,493 actions in the studied group of repairs. Two cases were rejected in a further analysis because the repair was not approved by the manufacturer. At this stage of the process analysis, all recorded cases were included (N=297). Figure 8 shows the course of the operation process of the studied group of vehicles for the adopted group of interventions related to the front axle brake system. Figure 8A shows the median throughput time, from which it can be seen that the median time between sale of the vehicle and replacement of the brake discs and pads, due to a fault or wear, is 481 days after purchase and 525 days after vehicle manufacture. In contrast, the values of the arithmetic mean in the studied group are the following: from the sale of the vehicle to repair is 507 days and from the date of manufacture is 569 days. The average repair time was 6 days. As an extension of earlier data, Figure 9 shows the result of the mining of the studied process with a breakdown of the causes of intervention: wear (9A) versus fault (9B).
As can be seen in Figure 9, in the studied group of repairs, the first report of a brake system defect (concerning brake pads and discs mounted on the front axle) occurred within a period of 669 days for a fault and 372 days for wear from the date of sale. It should be emphasized that the long time, respectively 7 and 8 days, from the day the defect was reported to the settlement of the repair with the manufac-turer's warranty department. In the course of the empirical research, factors affecting the duration of the warranty process were identified. In the case of repairs related to replacement of discs and pads, for both types of interventions the following were qualified: lack of availability of spare parts at the ASS warehouse (due to a change in rules of spare parts availability resulting from their generally available distribution from the warehouses of car manufacturers or distributors associated with the car manufacturer), prolonged warranty procedure in the case of interventions related to the brake system (exceeding 14 working days), and immediate contact of the vehicle user with the service center after a fault has occurred without earlier agreeing on the date of the repair, which increased the load on the work schedule of the ASS staff. In summary, the use of the process mining method, for selected types of faults, can provide information on parts storage and estimation of warranty costs for selected models and types of faults.

Characteristics of the studied vehicles
The database of the car repairs concerning the studied brake system components was prepared using the warranty repair database reconstructed on the basis of repair orders.    9. The course of the operation process in the studied repair group *Process mining was performed for 135 repairs due to a wear ( Figure  9A) and 162 repairs due to fault ( Figure 9B). Source: prepared by the authors based on the completed study using the Celonis SNAP software. Table 2 shows the characteristics of the variables in the relational database that was developed, on the basis of which the statistical analyses discussed in the next chapter of the paper were performed.
Using the collected empirical data, an attempt was made to conduct a statistical analysis of the factors that characterize the vehicles reported to the service center due to a fault or wear of the brake system. Seven factors were identified whose distributions were analyzed in the groups of vehicles in which, during the warranty period, brake discs and pads wear occurred and in the group of vehicles with faults: Vehicle counted in months of vehicle use, calculated as the difference between the date the car was reported for service and the date of manufacture.
The structure of the sample is shown in Table 3. The hypothesis was put forward that the distributions of the above variables differ in the group of cars in which a fault occurred and the group of cars in which the brake system elements were worn out. Both groups were analyzed separately and the hypothesis was verified by appropriate statistical tests.
Identification of the regularities that characterize the vehicles reported for service due to brake disc wear or fault should start with identification of the distributions of the variables that describe the ve-hicles. These variables can be numerical (e.g., mileage, vehicle age, brake disc thickness, etc.) or non-numerical (e.g., car model, gearbox type, etc.). In the case of the numerical variables, the choice of the method of further analysis depends on the type of distribution of the respective variable [9].
When the variables have a normal distribution, the analysis can be carried out using parametric methods, while for other types of statistical distributions (often skewed ones) non-parametric methods are required. The assumption of equality of the empirical distribution with the normal distribution is verified with one of the normality tests. In the present study, the Kolmogorov-Smirnov normality test with a Lilliefors correction was used [1]. Since distributions of all analyzed characteristics were not normal, the evaluation of the differences in the distributions of the numerical variables was obtained  using the non-parametric Mann-Whitney test (when two distributions were compared) and the non-parametric Kruskal-Wallis ANOVA test (when more than two distributions of variables were compared).
In the case of non-numeric variables (e.g., vehicle brand, vehicle model, engine type, etc.), it is important to analyze the frequency of attributes of these variables in the sample. In the case of a variable with a large number of minor attributes, it is necessary to combine them into homogeneous and sufficiently numerous groups. Dichotomous variables whose attributes are very minor cannot be used in further analysis. For non-numeric variables on a nominal scale, an analysis of association can be carried out using multiple correspondence analysis.

Reason of malfunction and characteristics of the repaired vehicles
In the sample, the malfunction of the front brake system components (brake pads and discs) was reported in 133 vehicles due to wear and in 162 vehicles due to failure. Tables 4 and 5 show the descriptive statistics of the variables presented in Tables 1 and 2 that characterize the repaired vehicles. Repairs were divided into repairs due to a fault (Table 4) and due to wear ( Table 5). All of these variables were quantitative. The hypotheses of the normality of their distributions were verified at the next stage. Results are shown in Table 6.
All the variables except for friction pad thickness have a distributions other than the normal distribution (Table 6). Therefore, in the further part of the study, non-parametric tests were used to analyze the properties of the distributions as well as correlation between variables and to test the hypotheses that the sample of cars repaired due to fault and the sample of cars repaired due to wear come from the same distribution. For the reason that non-parametric tests do not require the assumption that variables are normally distributed, they were used in this study.
The correlation between the variables was examined using the Spearman's rank correlation coefficient separately for the vehicles in the fault group (Table 7) and the wear group (Table 8).   In the case of the vehicles in the fault group, most of the variables are statistically significantly correlated. However, in the case of the vehicles in the wear group, only the age and mileage of the vehicle and the thickness of the left and right discs are significantly positively correlated. In the case of the correlation between age and mileage, it should be noted that the strength of the correlation is much lower than for the vehicles in the fault group. Figure 10 shows the distribution of vehicle mileage by year of operation and reason for vehicle servicing.
To verify whether differences in distributions of the variables in the wear and fault groups were significant, the Mann-Whitney test was used. The results are shown in Table 9. As can be seen from the data in Table 9, all the examined distributions are statistically significantly different. The distributions of the variables in both groups (wear and fault) are shown using box-plots in Figure 11.
As can be seen in Figure 11, when comparing the data on the service interventions and dividing them into the wear and fault groups, it was noted that the reports related to faults involve a lower mileage than those related to wear (Figure 11b). This means that faults occur much earlier (Figure 11a). It should also be noted that vehicles reported for wear had smaller disc thickness (right and left) than those reported for fault (Figures 11c and 11d). A similar effect is seen in the thickness of the friction pads (Figure 11e).

Factors that differentiate the serviced vehicles 4.2.1. Factor I: vehicle type
As discussed in the previous subsection, the distributions of the variables describing the serviced vehicles were statistically significantly different in the group of vehicles with brake system wear and in the group of vehicles with a fault. In order to identify the characteristics of the vehicles in each of these groups, an attempt was made to analyze the variation in the intensity of use of the brake system measured by disc thickness and deformation. Analyses were performed on the groups of vehicles distinguished according to the identified factors (brand; model; type of motor vehicle; engine; gearbox type; engine type and capacity).
First, the focus was on the variable defining the type of the studied vehicle. Based on the collected empirical data, two types of vehicles (car_type) were distinguished: passenger cars and commercial vehicles. Tables 10 and 11 show the results of the non-parametric analysis of the differences between distributions of the variables that describe the condition of the brake system in commercial vehicles and passen-   ger cars, separately for vehicles reported due to wear (Table 10) and due to a fault (Table 11).
Among the vehicles reported due to a fault, passenger cars had thicker right-hand brake discs than commercial vehicles. The remaining variables were not statistically significantly different in the passenger car and commercial vehicle groups. The distributions of the thickness of the right brake discs in both groups of vehicles are shown in Figure 12.
An analogous analysis was completed for the group of vehicles serviced due to wear of a brake system. The results are shown in Table  11. In the group of vehicles reported due to wear, there were no sta-tistically significant differences in the distributions of the analyzed variables.

Factor II: car body
As a second factor, the following three groups of car bodies were distinguished:  To test whether the variables describing the vehicles have the same distributions in the identified three groups, a non-parametric analysis of variance (Kruskal Wallis ANOVA) was applied. The test results for the group of vehicles reported due to wear of braking system components are shown in Table 12.
In the vehicles reported due to wear, at least in one group (by vehicle type) the thickness of the right disc is different from those in the other groups. Pairwise tests (post-hoc analysis) were conducted for this variable to determine the groups with differences (Table 13).
Of the pairs analyzed, a statistically significant difference was found only for the Group I -Group III pair. This means that the thickness of the right brake disc in the vehicles reported due to wear was higher in Group III (crossover, etc.) than in Group I (van/minibus). Groups I (van/minibus) and II (van) have no statistically significant differences.
The distributions of right disc thickness in the three groups analyzed are shown in Figure 13.
An analogous analysis was made for the group of vehicles reported due to brake system fault. The results of the non-parametric analysis of variance are shown in Table 14.   As a result, no statistically significant differences were identified in the distributions of the analyzed variables in the group of vehicles reported due to a fault.

Factor III: Vehicle brand
Another factor analyzed was the vehicle brand. Two vehicle brands were analyzed. Due to the need to anonymize them, they are referred to as X and Y. The sample included 126 motor vehicles of brand X and 169 motor vehicles of brand Y. To verify the hypotheses that vehicles repaired due to brake system wear (Table 15) and due to a fault (Table 16) have the same distributions, the Mann-Whitney U test was applied. Results are presented in Table 15 for the wear group and in Table 16 for the fault group.
The distributions of variables describing the intensity of use of motor vehicles of brands X and Y serviced due to wear are not significantly statistically different. However, in the group of motor vehicles serviced due to a fault, cars of brand X had higher mileage (Table 16 and Figure 14).  Because in the studied sample, the majority were vehicles with 1,600 cm 3 diesel engines and manual gearboxes (cf. Table 3), it was not possible to investigate the relationship between such factors as gearbox type, engine capacity, and engine type and brake system malfunction.

Multidimensional analysis of the diversity of vehicles
A multiple correspondence analysis was used to detect and represent the relationships between the studied variables. This analysis enables graphical representation of simultaneous occurrence of categories of the analyzed variables. The variables used in the correspondence analysis should be on a nominal scale or at most on an ordinal scale. The analysis covered following variables, which in univariate analyses were significantly correlated with the reason for the vehicle being reported for servicing: vehicle age, vehicle mileage, vehicle type (commercial vehicle/passenger car), and vehicle brand. The first two of these variables were measured on a ratio scale and, therefore, they were converted to an ordinal scale in the first step. Vehicle age was presented in years of use, while the mileage was dichotomized into groups: up to 39,850 km and over 39,850 km. The dichotomization was performed using the C&RT exhaustive partitioning method to maximize the discriminatory power of the mileage variable when predicting the value of fault type variable. The Gini coefficient was used as a measure of goodness of fit in the discrimination procedure.
The most popular form of presentation of the results of the correspondence analysis is presentation of the points that describe the levels of the variables in a two-dimensional distribution of eigenvalues. Usually, the first two eigenvalues that explain the largest percentage of inertia are presented. Interpretation of the graph consists in observing the position of the points representing the attributes of each variable relative to other points and relative to the center of the coordinate system. Classification methods can be used to identify groups of related points (those nearest to each other) [10]. Ward's method of hierarchical classification is used in the present paper. Three groups marked with red rectangles in the graph were identified ( Figure 15).
As shown in Figure 15, the vehicles were classified into the following groups: Group one • -vehicles that were reported due to wear. These are also vehicles with mileage over 39,850 km, in their second or third year of use. These are X brand commercial vehicles. Group two • -vehicles that were reported due to a fault. These are Y brand passenger cars with mileage up to 39,850 km and in the first year of use. Group three • -cars reported in the 4th and 5th year of use. The large distance of the two points constituting this group from the others indicates that there is no interaction with any of the other analyzed variables and their levels.
At this point, it is important to emphasize that the vehicles reported due to a fault were in the first year of use with low mileage (up to 39,850 km). At the same time, the thickness of the brake discs and friction pads in these vehicles was greater than in the vehicles reported due to wear (cf . Tables 4 and 5). Based on the results of the multiple correspondence analysis, it can also be concluded that reports of fault are involved with passenger cars of the Y brand. In contrast, the vehicles reported for wear were in their third or, more rarely, second year of use and had higher mileage. These were X brand commercial vehicles. In the commercial vehicles, the brake disc thickness was smaller than in passenger cars, which is related to the previous observations.

Conclusions
The approach presented herein to the identification and analysis of the factors that differentiate the course of wear and the occurrence of faults in brake system components in motor vehicles with the use of statistical methods is an original solution. It can be applied by both researchers studying similar problems and by organizations operating in the automotive sector.
As a result of the empirical process, three generalizing conclusions were formulated: Vehicles reported for service due to brake system wear or fault 1.
have different characteristics. Their identification makes it possible to predict which vehicles and at what time of use will be reported due to malfunction of the brake system. The distributions of analyzed variables that describe the intensity of use of vehicles are not normal, hence in their analysis it is necessary to use non-parametric measures. In particular, quartiles should be used in describing the central tendency rather than measures based on the arithmetic mean. The use of multiple correspondence analysis makes it possible to study of relationships between the factors that characterize the intensity of use of the vehicles. The results presented herein may have a positive impact on 2.
the efficiency and effectiveness of activities associated with the diagnosis and repairs of brake systems in motor vehicles. Moreover, the results obtained, in the utilitarian space, can provide new knowledge to car manufacturers regarding an analysis of the quality of the components and parts ordered as well as the selection of subcontractors (Original Equipment Manufacturers -OEM).
The study outlines an area for improvement in the production 3.
processes, selection of parts manufacturers, and diagnosis and repair of the described brake system components, in the context of the prediction of the costs related to parts wear and faults.
The relationship between such characteristics of the studied 4.
motor vehicles as vehicle type, body type, vehicle brand and model and the cause and time of reporting of a malfunction of brake system components was demonstrated.
At this point, it is necessary to outline the limitations of the empirical procedure carried out. First is a focus on a four-year service period of the studied group of vehicles. Second, possible errors exist in the measurement of the thickness and deformation of the studied group of brake system components, which were beyond the authors' control. The authors outline new directions of research that focus on broadening the study by an attempt to enlarge the list of factors that differentiate the brake system components by adding variables describing the steering system and the vehicle suspension. Additionally, the sample size and the observation period should be increased, taking into consideration repairs carried out in the warranty period, as well as paid repairs.