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1 © 2024 by ASME
Proceedings of the ASME 2024
International Mechanical Engineering Congress and Exposition
IMECE2024
November 17-21, 2024, Portland, Oregon
IMECE2024- 144013
METHODICAL APPROACH TO INSTANCE-SPECIFIC RELIABILITY MODELING FOR THE
PERPETUAL INNOVATIVE PRODUCT IN THE CIRCULAR FACTORY
Felix Leitenberger
Karlsruhe Institute of
Technology (KIT)
Karlsruhe, Germany
Matthias Dörr
Karlsruhe Institute of
Technology (KIT)
Karlsruhe, Germany
Thomas Gwosch
Karlsruhe Institute of
Technology (KIT)
Karlsruhe, Germany
Sven Matthiesen
Karlsruhe Institute of
Technology (KIT)
Karlsruhe, Germany
ABSTRACT
The Circular Factory reprocesses used products into
current-generation products, aiming for perpetual innovation.
This requires predicting the reliability of a product's components
and subsystems throughout its use life. Each product within the
Circular Factory exhibits unique life cycles and processes,
necessitating instance-specific reliability models.
This study introduces a novel methodical approach for
reliability modeling tailored to the challenges of the Circular
Factory, illustrated through a case study on angle grinders. The
approach consists of four steps: Developing a non-parametric
system reliability model by identifying failure types and
assessing their impact; Generating reference data by sensor-
integrated products and by X-in-the-Loop test benches;
Integrating instance-specific data such as historical loads,
tolerances, and material into reliability models; and validating
these models at both subsystem and system levels to ensure they
accurately reflect expected system reliability. Machine Learning
techniques are proposed to enhance model accuracy and to
challenge instance-specific reliability challenges.
Critical questions emerged from the theoretical case study,
highlighting the necessity for more in-depth investigations.
Future work will involve experimental validation of these
models, continuing the study's contributions to the Circular
Factory paradigm.
Keywords: Product Development, Sustainability,
Reliability, Machine Learning, Uncertainty
1. INTRODUCTION
The Circular Factory is intended to reprocess used products
into products of the current product generation to come closer to
the vision of the perpetual innovative product. Remanufacturing
is a particular focus here. This is intended to contribute to
sustainability. Predicting the reliability of a product's subsystems
and components over its intended use life is essential when
deciding how it should be processed in a Circular Factory. [1]
Reliability is defined as the probability that a component,
subsystem, or system will fulfill a required function under given
conditions over a specified period of time. A failure describes the
cessation of the ability of a component, subsystem, or system to
fulfill a required function. This means that in the context of the
Circular Factory, reliability is not limited to a product's structural
failure but also includes the quality of functional fulfillment
based on the requirements placed on it. Due to the individual life
cycle and the resulting non-deterministic process sequences of
the products within the Circular Factory, each product and its
subsystems and components are unique. The reliability models
must, therefore, be set up individually for each specific instance
and parameterized with a variety of different data from the
Circular Factory. This data contains historical loads, material,
tolerances, etc.
Reliability modeling can be carried out at component,
subsystem, and system level. It is modeled as a time-dependent
probability of failure and thus depicts the uncertainty with. A
failure can, for example, be caused by material fatigue, wear, or
unacceptably high plastic deformation. Depending on the type of
stress, the possible failure types can be derived using classic
approaches to fatigue strength which allow damage to be
calculated and predicted using damage hypotheses. For wear
classical approaches to fatigue strength are not suitable. The
relationships between tolerances and their effects on the Mean-
Time-Between-Failures (MTBF), particularly with regard to
wear behavior, have not yet been sufficiently researched
according to the current state of research [2].
For the calculation of component reliability, the statistical
distribution of stressability and stress is used to make a statement
about the probability of failure. The failure probabilities are
related to the proportion of expected failed products so that the
expected value of the service life is only possible statistically on
the basis of a large number of products using distribution models
but not on an instance-specific basis. For the Circular Factory,
2 © 2024 by ASME
however, the prediction of instance-specific reliability is
required.
System reliability is defined by the failure behavior of the
components of the system (subsystems). Boolean system theory
can be used for simple systems [3]. For systems with complex
structures, there are various methods - for example the successful
path method or the state space method [4]. The consideration of
prior knowledge in reliability assessment is applied, for example,
in [5, 6] for mechanical systems. One area of reliability research
is concerned with the early detection of system failures through
online condition monitoring and predictive maintenance. On the
basis of system data such as vibration data, a condition
assessment and fault prognosis are carried out. The approaches
can be classified as data-driven, model-driven and hybrid
approaches [7]. The approaches often focus on one type of
failure and are therefore only suitable for the requirements of a
Circular Factory to a limited extent.
In summary, no models exist to date that take into account
the different types of data and failure mechanisms, in particular,
the consideration of the instance-specific shape (geometry and
material), into account. In relation to the requirements of
reliability assessment in the Circular Factory, this means that no
instance-specific statement can be made. There is therefore a
lack of methods for reliability assessment and prognosis that take
into account the individual shape of a product instance. In
addition, there is no method that enables a reliability assessment
at the component and system level by using available data and
knowledge about wear and failure mechanisms, their
dependencies on external influencing factors and the associated
uncertainties [8].
The research gap is that the current reliability models and
methods have not been applied to the complexity and challenges
in the context of the perpetual innovative product in the Circular
Factory.
2. MATERIALS AND METHODS
This study introduces a novel methodical approach that aims
to overcome the challenges of instance-specific reliability
modeling for the perpetual innovative product in the Circular
Factory.
An application is described through a theoretical case study
on angle grinders. Angle grinders are ideal for this study because
of their widespread use in both professional and domestic
settings and their susceptibility to varied types of failures. As a
failure type the vibration in the system is in focus. Depending on
the usage time and load profile, the wear occurring in the gearbox
results in a geometric change of the gear profile (see Figure 1).
This can lead to higher tooth excitation and therefore stronger
vibrations in the angle grinder. The quality of functional
fulfillment thus changes over the usage time. A failure is
detected if the vibrations exceed the permissible working
regulations. This makes clear that reliability is not limited to a
product's structural failure, e.g. wear in this case, but also
includes the quality of functional fulfillment.
FIGURE 1: WEAR IN THE BEVEL GEAR [9]
3. METHODICAL APPROACH TO
INSTANCE-SPECIFIC RELIABILITY MODELING
The methodical approach is divided into four steps, which are
illustrated in Figure 2.
FIGURE 2: METHODICAL APPROACH TO INSTANCE-
SPECIFIC RELIABILITY MODELING
The individual steps of the methodological approach are
described in detail below.
3.1 STEP 1: Structure of non-parametric reliability
models
This step requires a thorough identification and evaluation
of relevant failure types and the development of a comprehensive
reliability structure. This structure is essential to understand how
the failure behavior of critical subsystems influences the
product's MTBF. To achieve this, state-of-the-art failure analysis
methods such as the Ishikawa diagram and the Design Structure
Matrix (DSM) are employed. These methods enable a systematic
exploration of failure causes and possible interactions between
the subsytems. The Ishikawa diagram, or fishbone diagram,
helps in visually organizing potential causes of failure into
categories and subcategories. The Design Structure Matrix, on
the other hand, is utilized to analyze the complex interactions
between various subsystems of the product. DSM is instrumental
in identifying and assessing the dependencies and feedback
loops that could contribute to system failures. By mapping out
these interactions, the DSM helps in pinpointing critical
components or subsystems that significantly impact the product's
reliability and MTBF.
Structure of non-parametric
reliability models
Generation of reference data
Integration of instance-specific
data into reliability models
Validation of reliability models
3 © 2024 by ASME
Furthermore, a detailed categorization system is established
to enhance the failure analysis process. This system includes:
• Failure Type: Identifying whether the failure is
mechanical, electrical, software-related, or due to
external factors.
• Affected Subsystem: Determining which parts of the
product are most impacted by the failure.
• Measured Variable: Documenting the specific variables
that are affected by the failure, such as temperature,
pressure, or load capacity.
• Reason of Failure: Analyzing the root causes, which
could range from material fatigue to improper usage or
environmental conditions.
• Frequency of Failure: Monitoring how often each type
of failure occurs, which helps in prioritizing the issues
that need immediate attention.
• Criticality: Assessing the severity and potential impact
of the failure on overall system performance.
Using the example of an angle grinder, one failure type is
excessive vibration, typically caused by wear and degradation in
the bevel gear. This issue impacts all other components, with
particular focus on bearings, the motor, and the housing.
Vibration levels are measured using acceleration sensors placed
within the system. The reason for this failure is the operation of
the angle grinder beyond permissible working regulations, which
can potentially lead to user harm. The frequency of this failure
type is high, as it is a progressive effect that occurs over the
operational lifespan of the tool. Despite its high frequency, the
criticality of this failure is considered medium, as it does not
immediately render the overall system inoperative but can
progressively degrade performance and safety.
The structure of the non-parametric reliability model can be
effectively designed using a reliability block diagram (RBD).
This diagrammatic approach is particularly useful for visually
representing the interconnections and dependencies of various
components within a system. By organizing the system into
blocks that represent different subsystems or components, the
RBD allows for a clear visualization of how each part contributes
to overall system reliability. In constructing the RBD, each block
within the diagram corresponds to a specific component or
subsystem, and the configuration of these blocks illustrates the
flow of operational functionality throughout the system.
It is also necessary to initially describe how the reliability of
each subsystem and the overall system will be mathematically
defined. The Weibull Distribution can be useful for most failure
types on subsystem level due to its flexibility in modeling
various life behaviors, such as aging and early failures. It is
particularly effective in reliability engineering due to its ability
to model different failure rates. For the system level, Bayesian
Neural Network (BNN) can be used to capture the complex and
probabilistic relationships between subsystems and other
variables affecting the system's reliability. This neural network
models the system as a whole, considering both direct and
indirect influences on system performance and functional
fulfillment. The BNN should be designed to incorporate prior
knowledge and uncertainty inherent in system reliability data. It
uses Bayesian inference to update the model’s understanding as
new data is obtained, making it robust in handling real-world
variabilities.
All the used methods can be replaced by different state-of-
the-art methods as long as they contribute to create the structure
of the non-parametric reliability models.
3.2 STEP 2: Generation of reference data
Products in a Circular Factory setting often undergo
complex interactions due to varied operational histories and
remanufacturing cycles. Reference data helps in understanding
how these interactions affect the product's functionality and
reliability. Reference data is indispensable for developing robust,
accurate, and instance-specific reliability models. Instance-
specific modeling requires detailed and precise data to predict
the functional fulfillment of each unique component or
subsystem. The use of advanced Machine Learning techniques
in reliability modeling requires substantial, high-quality datasets.
Reference data provides the necessary volume and variety of
data needed for these computational techniques to identify
patterns, train algorithms, and test hypotheses about product
behavior under various conditions. Therefore, it is essential to
first analyze which loads need to be measured during the usage
phase. For capturing the loads on subsystems, sensors already
present in the product can be utilized, or additional sensors may
need to be integrated into future generation products.
Consequently, the integration of sensors represents a potential
requirement for products of a new generation.
In the context of an angle grinder, sensors that measure
current, voltage, temperature, acceleration, forces, and
deformations can be utilized [10]. Figure 3 shows the different
sensor types and positions. Due to the limited installation space,
the use of soft sensors makes sense. Those soft sensors can be
based on Deep Learning methods [11]. An application of angle
grinders to predict tool forces has already been shown [12].
Alternatively, the use of sensor-integrated machine elements is
also conceivable. There are initial concepts and implementations
for gearboxes, clutches, bearings, and fasteners, which are
particularly interesting for application in angle grinders [13].
FIGURE 3: MEASURED VARIABLES AND POSITIONS OF A
SENSOR-INTEGRATED ANGLE GRINDER [14]
4 © 2024 by ASME
For the valid determination of the MTBF and especially for
assessing the uncertainty of reference data, data collection must
be reproducibly conducted in endurance tests. The test bench
must be capable of consistently applying previously determined
loads on both the subsystem and the entire system level of the
product. Furthermore, the interactions with other subsystems of
the product must be equivalently represented under similar load
conditions.
The load-equivalent representation of interactions is
facilitated in the X-in-the-Loop approach through the integration
of virtual models with mechatronic components using coupling
systems. This setup allows for a dynamic and realistic simulation
of the product's operational conditions, enhancing the accuracy
and relevance of the testing process. X-in-the-Loop test benches
can therefore be used to gather reference data that are crucial for
the parametrization of the reliability models. In the context of the
angle grinder, X-in-the-Loop test benches apply dynamic forces
and loads on the power train of the angle grinder. Such a test
bench for the system test has already been shown in studies [15].
The setup for subsystem tests has also been shown. For example,
a test bench has already been used to demonstrate the
relationship between the design parameters and radial vibrations
of angle grinders [16].
To collect a sufficiently large amount of reference data for
the parameterization of the reliability model in the Circular
Factory with manageable effort, methods for efficient data
collection and processing need to be used. One method includes
automated test specification, execution, and evaluation aimed at
efficiently collecting reference data. Automated test
specification is designed to cover the same test space (test
coverage) more efficiently than traditional methods like
statistical experiment design (Design of Experiments), without
intervention by the test engineer. Artificial Intelligence
approaches, such as genetic algorithms, are utilized to allow
changes in test specifications based on test evaluations. The
classification into relevant test cases can be illustrated using the
example of an angle grinder by identifying its use cases.
Consumer-grade sensors can be employed for this purpose, with
the data being analyzed using machine-learning techniques. [17]
The second method involves accelerating the pace of test bench
experiments. This is achieved by utilizing models from current
research that are relevant to the specific type of failure, where
acceleration of load is possible [18]. Traditional models used for
accelerating tests include the Coffin-Manson model or the
Basquin equation, as these models describe the relationships
well. With successful development and implementation of this
method, the testing effort can be significantly reduced.
3.3 STEP 3: Integration of instance-specific data into
reliability models
Data from different sources are integrated into the reliability
models, ensuring that each subsystem’s and component's unique
history and predicted future use are accurately reflected.
Historical load curves are essential for understanding the actual
loads and operational conditions that a product has undergone.
Integrating these curves helps to establish baseline performance
metrics and identify patterns or anomalies in usage. This data can
be used to simulate similar conditions in reliability tests,
ensuring that models accurately reflect the functional fulfillment
experienced by the product over time. A data-driven, intelligent
approach is proposed, employing Machine Learning algorithms
to analyze historical usage data. Incorporating predicted load
data allows the models to predict future loads and their impact
on the product. By simulating future conditions, the models can
predict the product function. Material models provide detailed
information about the materials used in each component,
including their properties such as strength, durability, and fatigue
life. Integrating this data helps to tailor the reliability models to
the specific materials used, considering how they respond to
environmental stresses and operational loads. Functional models
describe how each component or subsystem contributes to the
overall functionality of the product. By integrating these models,
reliability models can not only predict when a component might
fail but also how such a failure impacts the product’s
performance and functionality. This integration is essential for
understanding the cascading effects of component failures within
complex systems. If several failure types are relevant for a
subsystem, the individual parameterized models are merged. To
do this, the failure types must be statistically accumulated and
interactions, if necessary, parameterized.
3.4 STEP 4: Validation of reliability models
The validation of the reliability models ensures that the
models are robust, accurate, and capable of guiding decision-
making processes in the Circular Factory. This step starts with
verifying the models at the subsystem level and assessing their
accuracy and predictive capabilities. The verification of the
reliability models at the subsystem level is conducted
experimentally using tests on the X-in-the-Loop test bench.
Initially, a sensitivity analysis is performed to define the scope
of investigation with specified loads for each subsystem. It is
important to note that the MTBF is reported with a degree of
uncertainty. Statistical experimental design is employed based
on the failure-critical parameters and the expected variability.
This involves estimating the required duration of tests and
determining the number of test repetitions based on the estimated
variability. The levels of parameters for varying the load level
and types of loads are set considering the results from the
sensitivity analysis.
Verification at the subsystem level is then carried out by
comparing the statistical evaluation of the test results with the
predicted MTBF. This step ensures that the reliability models
accurately reflect the operational performance of the subsystems
under varied stress conditions, enhancing the reliability of
predictions and supporting effective maintenance and design
optimization strategies.
Validation is followed on the system level, ensuring the
reliability models accurately represent the entire system's
expected performance under operational conditions. The
execution of the tests is conducted according to the test plan until
failure occurs. The experimental data are analyzed using
statistical methods. The validation of the reliability models at the
5 © 2024 by ASME
system level is carried out by comparing the results from the tests
with the predicted system reliability. During this process, it is
also examined whether the uncertainty indicated by the
prediction of system reliability corresponds to the variability of
the MTBF observed during the tests. This step is crucial to ensure
that the models are not only predictive but also accurate in
estimating the reliability and expected lifespan of the system
under realistic operational conditions. This validation helps to
fine-tune the models, improving their precision and
trustworthiness in the prediction of system reliability in the
context of the Circular Factory.
4. DISCUSSION
It is crucial to underline that the methodical approach is
demonstrated through a theoretical case study centered on angle
grinders. This approach, while comprehensive in its current
form, primarily serves as a concept that captures the complexity
of reliability modeling within the context of a Circular Factory.
To ensure that our approach is not only theoretically sound but
also practically viable, a series of experimental validations is
planned for the future. These experimental validations are
essential to assess the real-world applicability and effectiveness
of the reliability model.
As we explored the application of a novel methodical
approach to reliability modeling within a Circular Factory
setting, several intriguing questions emerged. These questions
not only highlight the complexities involved in modeling the
reliability of remanufactured products but also underscore the
potential limitations of our current methodologies and the
necessity for ongoing research.
STEP 1: Structure of non-parametric reliability models
• How do the Ishikawa diagram and DSM complement
each other in identifying and evaluating failure types,
and what are the specific advantages and limitations of
each method in the context of reliability analysis for
complex systems like angle grinders?
• In what ways can the RBD be optimized to more
accurately reflect the interactions within a system,
particularly in systems with high variability in
operational conditions, such as those experienced by
angle grinders?
• How does the integration of Weibull distributions at the
subsystem level improve the predictive accuracy of the
reliability model, and what are the key parameters and
data requirements for effectively utilizing Weibull
distributions in modeling various life behaviors?
• What are the specific benefits of using a BNN at the
system level to model the complex and probabilistic
relationships between subsystems, and how does the
incorporation of prior knowledge and Bayesian
inference enhance the model’s robustness in handling
real-world variabilities?
STEP 2: Generation of reference data
• How do the interactions between remanufactured
components and new components influence the overall
reliability and functionality of products in a Circular
Factory, and what methods can be used to model these
interactions accurately?
• Given the reliance on advanced Machine Learning
techniques in reliability modeling, what specific data
challenges arise when using these methods in the
Circular Factory context, particularly regarding data
quality and volume?
• What are the key factors that determine the choice of
sensors for capturing load data on subsystems, and how
does the integration of additional sensors into future-
generation products impact the accuracy and
granularity of the data collected?
• How does the X-in-the-Loop approach enhance the
representation of load-equivalent interactions and real-
world conditions during testing?
• Considering the need for efficient data collection and
processing in the Circular Factory, how effective are
automated test specification and accelerated testing
methods in reducing the time and cost associated with
reliability testing, and what are their limitations in
practical applications?
STEP 3: Integration of instance-specific data into reliability
models
• How do Machine Learning algorithms enhance the
accuracy of predicting future load conditions based on
historical usage data, and what are the challenges in
training these models to handle diverse and non-
standard data sets?
• What methodologies are employed to integrate and
synthesize data from different sources (historical loads,
material properties, functional performance) to develop
a cohesive and accurate reliability model, and how is
data integrity ensured during this process?
• How effectively do the reliability models incorporate
and predict the cascading effects of component failures
within complex systems, and what advanced modeling
techniques are used to simulate these interactions?
• When merging parameterized models for different
failure types within a subsystem, what statistical
methods are used to accumulate and parameterize these
failures, and how are potential interactions between
different failure modes handled?
STEP 4: Validation of reliability models
• How does the variability in the MTBF observed during
experimental tests compare to the predicted uncertainty
in system reliability, and what implications does this
have for model accuracy and reliability prediction?
• In what ways can the process of statistical experimental
design be optimized to better reflect real-world
6 © 2024 by ASME
operational conditions and improve the predictive
capabilities of the reliability models at both subsystem
and system levels?
• How do the outcomes of the X-in-the-Loop test bench
experiments influence subsequent iterations of model
development, particularly in terms of parameter
adjustment and model validation?
• What are the challenges and limitations encountered
during the verification and validation of reliability
models in the Circular Factory, and how can these be
addressed to enhance the models’ effectiveness in
guiding maintenance and design optimization
strategies?
We outlined the critical questions that arose from our theoretical
case study, setting the stage for future research studies. These
inquiries will probe deeper into the unresolved aspects of
reliability modeling, seeking to refine our understanding and
enhance the practical application of these models in a real-world
Circular Factory environment. By addressing these questions, we
aim to pave the way for more approaches that can more
accurately predict product function and system reliability.
5. CONCLUSION
In conclusion, this study describes a novel methodical approach
to instance-specific reliability modeling in the context of the
Circular Factory, which focuses on remanufacturing. The
approach consists of four critical steps: developing a non-
parametric system reliability model, generating reference data
through sensor integration and X-in-the-Loop test benches,
incorporating instance-specific data, and validating the models
at both subsystem and system levels. An application is described
through a theoretical case study on angle grinders. Future work
will involve experimental validation of these models to solidify
their contributions to the Circular Factory paradigm.
ACKNOWLEDGEMENTS
This research was funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation)
in the collaborative research center (CRC) 1574 “Circular
Factory for the Perpetual Product” with the project ID
471687386. While preparing this work, the authors used AI tools
such as deepl.com and grammarly.com to improve readability
and language. After utilizing these tools, the authors reviewed
and edited the content as necessary. The authors take full
responsibility for the publication’s content. All authors have read
and agreed to the published version of the manuscript.
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