IEEE TRANSACTIONS ON RELIABILITY, VOL. 61, NO. 3, SEPTEMBER 2012
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Estimating Mean Residual Life for a Case Study of
Rail Wagon Bearings
Alireza Ghasemi and Melinda R. Hodkiewicz
Abstract—This paper develops a prognostics model to estimate
the Mean Residual Life of Rail Wagon Bearings within certain confidence intervals. The prognostics model is constructed using a Proportional Hazards approach, informed by imperfect data from a
bearing acoustic monitoring system, and a failure database. The
model supports prediction within a defined maintenance planning
window from the time of receipt of the latest acoustic condition
monitoring information. We use the model to decide whether to
replace a bearing, or leave it until collection of the next condition
monitoring indicators. The model is tested on a limited number of
cases, and demonstrates good predictive capability. Opportunities
to improve the performance of the model are identified, and the
processes necessary and time required to build the model are described. Lessons learned from dealing with real field data will assist
those interested in using prognostics to support maintenance planning activities.
Probability of getting condition indicator value
while the equipment is in state ; an element
of the observation probability matrix
Index Terms—Acoustic monitoring, condition monitoring, imperfect information, prognostics, proportional hazards model.
The hazard function of the proportional hazards
model at time while the system state is
Current value of the indirect indicator of the
system’s degradation state
History of the indirect indicator values up to
time
Probability of going from state to state
between two consecutive observations
(inspections), knowing that the equipment has
not failed during that interval; an element of the
transition matrix
Baseline hazard function
ABBREVIATIONS
MRL
Mean Residual Life
PH
Model Proportional Hazards Model
HMM
Hidden Markov Model
CBM
Condition Based Maintenance
MLE
Maximum Likelihood Estimation
CI
Confidence Interval
State effect function
Conditional probability distribution of the
equipment’s state at observation moment ,
Probability of being in state at observation
where
is an element
moment ,
of the vector
Equipment’s state conditional probability
distribution history up to time
Survival function at time when the history of
the indicator values up to time is
NOMENCLATURE
Failure time of the equipment
Observation interval
Probability distribution function of the
time-to-failure at time when the history of the
indicator values up to time is
Equipment’s degradation state at time
Conditional reliability at observation moment
for a period of , knowing that the state is
Equipment’s degradation state after the -th
observation interval;
Manuscript received February 06, 2012; revised April 10, 2012; accepted
April 11, 2012. Date of publication July 31, 2012; date of current version August 28, 2012. This work was supported by Australian Government Endeavour
Post-Doctoral Fellowship Award. Associate Editor: E. Zio.
A. Ghasemi is with Department of Industrial Engineering, Dalhousie University, Halifax, NS B3H 4R2 Canada (e-mail: alireza.ghasemi@dal.ca).
M. R. Hodkiewicz is with University of Western Australia, M050, Crawley,
WA 6009 Australia (e-mail: Melinda.Hodkiewicz@uwa.edu.au).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TR.2012.2209251
0018-9529/$31.00 © 2012 IEEE
Conditional mean sojourn time at period
knowing that the state is
Conditional reliability of the equipment for a
period of , at observation moment , while
the conditional probability distribution of the
equipment’s state is
Mean residual life at observation moment
while the state is
Mean residual life at observation moment
while the conditional probability distribution of
the equipment’s state is
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IEEE TRANSACTIONS ON RELIABILITY, VOL. 61, NO. 3, SEPTEMBER 2012
I. INTRODUCTION
II. LITERATURE REVIEW
HIS RESEARCH project develops a prognostics algorithm to determine the Mean Residual Life (MRL) of rail
wagon bearings for use in maintenance planning. While the development of prognostic algorithms is a well-established field,
academically successful implementations by industry have only
had limited success [1]. The ability of those responsible for asset
maintenance planning to 1) perform the prognostic modeling,
and 2) deliver the outputs to those responsible for the maintenance action via existing business systems as a routine part
of the maintenance cycle, is dependent on a number of factors.
These factors include the availability of appropriate condition
indicators, skilled modeling personnel (in house or contracted),
appropriate computing and data exchange infrastructure, and a
disciplined work management processes. This list is in addition
to the organizational processes involved in managing a routine
condition-monitoring program cost-effectively [2].
The rail industry uses a variety of monitoring tools to assess
the condition of the rail wagon bearings. These tools include,
but are not limited to, thermal (hot bearing detection and hot
wheel detection), acoustic (rail bearing acoustic monitor), and
weight-based techniques (wheel impact detector). These tools
provide condition indicators to be used for diagnosis. Diagnostic
interpretations and synthesis of the different indicators is generally done by rail staff, is predominantly intuitive, and success
is correlated with the experience of personnel familiar with the
equipment. One of the main challenges is the number of bearings monitored. In this case study, there are tens of thousands of
rail car wheel bearing assemblies in service.
In recent years, there has been increased expectation of availability for rail systems, and hence on rail cars, with little spare
capacity in the system for unplanned failures. This requirement
has increased pressure of the rail staff to ensure that incipient
failures are detected, correctly diagnosed, and that interventions
are scheduled to minimize risk of unplanned failure, and hence
disruption to the trains’ schedule.
The aim of the project is to develop and test a prognostics
model to identify bearings that are going to fail in a specific
schedule window (15 pass-bys) so they can plan maintenance
intervention. A pass-by is defined as the action of the train
passing by a specific point in the rail network. This pass-by
definition will allow maintenance planners to schedule the rail
cars on which these bearings are mounted to be brought into the
maintenance facility in a planned way. This approach reduces
the risk of unplanned rail bearing failures, which can result in
derailment or expensive repairs if the failure is in an isolated
location with associated impacts on train schedule compliance.
The challenge with this project is that the data come from a
number of systems that have evolved separately, have different
coding to identify the assets, and possess the usual issues with
maintenance data quality [3]–[5]. This report describes the steps
involved in developing the prognostics model, the technical and
organizational assistance and barriers, the data requirements,
and the factors that impact on confidence in the results.
Condition monitoring is the act of observing and collecting
information concerning the degradation condition of equipment to schedule maintenance actions prior to failure. Data
concerning one or more indicators of degradation are collected
periodically to establish a diagnosis of the equipment’s condition, and a prognosis for future performance. A combination
of human expertise, signal processing, and modeling is used
through this process.
Considerable work has been done in the last 20 years to develop models to assist with the prognosis processes [6]–[8]. Jardine et al. [6] explains that the approaches to prognosis fall into
three main categories: statistical approaches, artificial intelligent approaches, and model-based approaches.
Statistical approaches are usually applied to predict the
chance that a machine operates without failure up to a future
time, given the current machine condition, and past operational
profile. These approaches require considerable data and information on historical performance. A well-used statistical
approach for prognostics with condition monitoring data is
proportional hazards (PH) modeling. PH Models have been
used to address many practical (e.g. [9]–[11]) and theoretical
or experimental (e.g. [12]–[14]) health monitoring and prognostics problems.
Artificial intelligence approaches, also known as data-driven
approaches, are derived directly from routine condition monitoring (CM) data (e.g. temperature, vibration, oil debris, current,
etc.). These methods predict the selected features that correlate
with the failure progression based on the learning or training
process. In general, data-driven approaches adopt a one-step
or multi-step ahead prediction technique to predict the future
state. Several data-driven prognosis methods have been developed and published [15]–[17] and [12]. A main drawback of
data-driven approaches is their dependency on the quality of
the monitored data, and there is limited physical understanding
usually provided. Realistically, information may contain noise
due to errors of measurement, of interpretation, or due to the
limited accuracy of the measurement’s instruments, and it may
not reveal the exact state of the equipment. The information is,
however, stochastically correlated with the degradation state. In
this case, the information collected may be referring to more
than one possible state with different probabilities. This category of condition monitoring is referred to as “Indirect Monitoring” [18], “Partial Observation” [19], or Imperfect Observation [20]. This imperfection of information limits the application
of data-driven and statistical approaches in many cases.
Model-based approaches (also known as physics-based
approaches) assume that accurate mathematical or physical
models are available, and provide a technically comprehensive
approach that has been used traditionally to understand failure
mode progression, e.g. the crack propagation model. The drawback of this approach is its specificity, which means it can only
be applied to specific types of components and failure modes
limiting its flexibility.
A common challenge with all of these approaches is the
reliance for development or validation or both, on historical
field failure and operational context data. Field data are rarely
T
GHASEMI AND HODKIEWICZ: ESTIMATING MEAN RESIDUAL LIFE FOR A CASE STUDY OF RAIL WAGON BEARINGS
“clean,” often suffering from the effects of environmental conditions and other factors. Field data often come as a by-product
of maintenance records, and are not originally aimed to help
reliability practitioners. The data collected are usually the
times of events which may be the failure or replacement of
components. These data have to be matched with the condition
monitoring data gathered throughout the equipment’s life. This
task is usually a challenge, as the data for condition monitoring
and failures are usually stored in separate systems, data arrives
at different times, and the data may not always be structured in
the same data hierarchy. Hence, considerable time and expert
input are often required to create a common database of failure
and health data for a specific asset or component.
This paper is concerned with prognostics of mechanical rotating components. It is focused on the identification of potential for a catastrophic failure, or the occurrence of bearing faults
such as cup or ball defects. It draws on two important developments that have enhanced the survival analysis method: 1) construction of a survival curve from censored data, derived from
a nonparametric method introduced by Kaplan and Meier [21],
and 2) construction of the degradation curve using a Proportional Hazard Models, introduced by Cox [22], [23], with censored data to estimate the survival function, and investigate the
effect of covariates on the failure time distribution. However,
one of the main on-going challenges with the use of the PH
Model is that field data are assumed to be perfect, and can be
directly used as the covariates of the PH Model. In [9]–[28],
the authors are fortunate to have “perfect” data, or have assumed that the data are perfect, and reflects the exact condition
of the system state. This assumption has allowed them to use the
data directly in the PH Model. Where field data have not been
available, researchers have used simulated or laboratory experimental data [13], [29].
In the PH Model process, it is often necessary to describe the
behavior of the covariates. Early work on this area was done by
[30], who used a non-homogenous discrete Markov process to
predict future development of covariates, and failure times. This
work results in the failure model containing two sub models: one
distribution model with covariates, and the second a degradation model representing the behavior of covariates with respect
to various health states. Further developments combining PH
Models and HMM include [31], and [32]. The issues of determining the health state relative to other states, or as an overall
health level, was explored in [33].
The combination of PH Model and HMM can also be used to
address the imperfect observation problem, and to manage one
of the challenges in the time-dependent PH Model, which is the
inclusion of only the latest condition monitoring information in
the model. This technique was demonstrated in and tested on
simulated data in [20]. This paper extends the work by testing
the model proposed in [20] using imperfect acoustic data from
condition monitoring, and failure and repair data for rail wagon
bearings from maintenance databases in a heavy haulage rail
system.
There is very little published work on the prognostics of
bearing failure in heavy haulage rail wagons using either or
both vibration and acoustics as condition indicators. There have
been developments in systems to measure different condition
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Fig. 1. Key phases in the model development and testing.
indices including acoustic emission [34], [35], and work has
been done to diagnose relevant faults [36], [37]. Work to understand failure distributions for rail wagon bearings is reported
in [38]. This paper therefore contributes both data and a model
for prognostics specifically for rail wagon bearings.
The paper is organized as follows. Section III describes the
mathematics underpinning the development of the model, the
identification and preparation of the performance and failure
data, and the modeling approach to estimating residual life.
Section IV presents the results including the challenges faced
with “real” data, and the outcome of testing a replacement
policy based on a specified maintenance planning window.
Section V discusses the results of the parameter estimation,
importance of bearing type, model performance and confidence, and recommendations for dealing with “real” data from
multiple systems. The conclusions are presented in Section VI.
III. APPROACH
This section describes the two phases of the project: 1) model
development and parameter estimation, and 2) use of the model
to estimate mean residual life. The main phases in this development are shown in Fig. 1.
A. Proportional Hazards Models
The prognostics model is based on the PH Model proposed
by Cox [22], but assumes that the condition monitoring is indirect; i.e., at each observation moment, an indicator value of
the underlying degradation state is available. Observations are
collected at a constant (or a near constant) interval . In this
study,
represents the degradation state of the equipment at
time , which will be used as the diagnostic covariate in the PH
Model, and is a value from the set of all the possible indicator
values
. In other words, the set of indicator
values is discretized into a finite set of
possible values. The
equipment’s condition is described as follows.
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IEEE TRANSACTIONS ON RELIABILITY, VOL. 61, NO. 3, SEPTEMBER 2012
• The equipment has a finite, known number of degradation
states .
is the set of all possible degradation states.
• The degradation state transition is modeled by a HMM.
The transition matrix is
, where
is the probability of going from
state to state ,
during one observation interval,
knowing that the equipment does not fail before the end of
the interval.
• The value of the indicator is stochastically related to the
equipment’s state through the observation probability matrix,
,
,
.
is
the probability of getting the indicator value , while the
equipment is in degradation state .
• The indicator is collected periodically at fixed or near fixed
intervals .
• Failure is not a degradation state. It is a non-working or
dangerous condition of the equipment that can happen at
any time, while the system is in any degradation state.
To deal with unobservable degradation states, a new transition rule is introduced. This rule allows for all observations from
the last renewal moment up to current moment to be included
when calculating the conditional probability of being in degradation state at the th observation moment [39]:
history into the state conditional probability distribution history
,
,
,
, up
to time , accordingly. The elements of
are calculated by
(1) and (2) at corresponding observation moments, when a new
indicator value is available [39].
By assuming that the equipment’s unobservable degradation
state transition follows a stationary Markov Process, the transition probability at time
, from state to state , knowing
that the equipment has survived at least until the next observation moment, is
The survival function of the assumed model is [40]
where
(3)
The conditional probability distribution of the equipment’s
degradation state at period is
defined as
is the PH Model’s hazard function at time while
and
the equipment’s degradation state is .
Based on the MLE, one adopts an estimate of the unknown
set of parameters , i.e. , which gives the maximum of
the expected likelihood of the available information [29],
. The likelihood
of the set of parameters is defined by
(1)
where
meaning that the equipment is in its best possible state at period
zero. After obtaining an indicator value via an inspection at
an observation moment, the prior conditional probability
is
updated to
. By using Bayes’ formula, and knowing that
the indicator has occurred at the
-st observation moment,
is determined as
The method of MLE estimates by finding the value of
that maximizes the likelihood of the set of parameters.
We consider a parametric PH Model with a baseline two parameter Weibull hazard function, which is also known as the
Weibull parametric regression model [41], and is given as
(2)
(4)
B. Parameter Estimation
To construct the parameter estimation model, we assume that
,
,
is
the history of the indicator values up to time . We map this
And then [29],
GHASEMI AND HODKIEWICZ: ESTIMATING MEAN RESIDUAL LIFE FOR A CASE STUDY OF RAIL WAGON BEARINGS
C. Data Requirements for Parameter Estimations
Suitable data for the parameter estimation process of a prognostics model is derived from two sources:
(a) Failure related data are based on the working age at which
the equipment has failed. This information comes from
installation and failure dates.
(b) Performance data are based on the condition indicators
that relate to the performance condition of the equipment
from its installation date up to its failure date obtained in
fixed or near fixed observation intervals.
In this research, the number of pass-bys is considered as the
working age of a bearing. The railway under study is mainly
between one major mine and one port station. Although, there
are other sub railways in the railway network, the data recorded
from wayside monitoring systems shows that more than 80%
of the wagons’ movement is back-and-forth between these two
points in the railway, and do not change their service path frequently. In this study, as it is explained later in the data cleansing
section, we exclude the failure data of bearings with a long period of absence on the main railway. By applying this approach,
the bearings that have been used elsewhere in the network (other
than the main railway) for a long period, or been removed from
one wagon and not replaced immediately on another wagon, are
not taken into account.
By considering the pass-by as the working age of the equipment, and by excluding bearings with a long period of missing
acoustic data, we address two issues in the modeling. First, the
assumption of fixed or near fixed observation intervals is satisfied. Secondly, short idle periods (when a wagon may be parked
up, or in the workshop) during a bearing’s lifetime are not considered in their aging process.
Failure Related Data: To develop the prognostics model, the
following specific failure and historical data are necessary.
• Exact location of the bearing during its lifetime (wagon
number, wheel set ID, left or right bearing on wheel set)
• Installation date
• Removal date
• Failure or suspension
• Bearing type (new, overhauled or second-hand)
• Failure codes
There are 50 000 rail car wheel bearing assemblies in service. Within this population, there are three distinct bearing categories: new, overhauled, and second-hand. Bearings are recalled from service due to 1) hazardous condition monitoring
values, or 2) a routine 2 year service. Part of this recall process
is a hand-qualification and inspection test by the tradesman; following this check, the bearing is sent to an external shop for
overhauling, or returned to service. The former is described here
as “overhauled,” and the latter as “second-hand.”
To collect failure information, bearing failure has to be clearly
defined. We have defined failure as follows. A bearing is failed
if it was removed due to:
• an acoustic alarm (roller, cup, cone),
• a hot bearing detected alarm,
• hand verification, or
• a catastrophic failure.
According to current practice guidelines, only the wagons
creating acoustic alarms are recalled for further investigation.
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But roller, cup, and cone have much higher weight in the decision making process. After a recall, all bearings on the recalled
wagon are examined manually for defects, and replaced as required. We have included all the recalls initiated by acoustic
alarms of roller, cup, and cone as failures. However, in practice,
some of the recalls identified by the acoustic alarms are not actually failures. To better identify these alarms in the future, we
discuss ways to improve data collection to better distinguish between failures and suspensions in the recommendations section.
Failure data were collected on failures on a specific, single
series of bearings over a three month period. This produced an
initial 328 records of failure.
Performance Data: The bearing acoustic monitoring system
(RailBAM) records acoustic data of bearings using arrays of
microphones inside the trackside cabinet assemblies, as well as
wheel sensors on the track. A process of vehicle and wheel-set
tagging allows the system to attribute data to each individual
bearing. The data are analysed by signal processing techniques
to extract acoustic signatures for each individual bearing. This
acoustic signature is then used to calculate the acoustic energy
level for several classes of bearing defects: roller, cup, cone,
looseness and fretting, noisy, clipped or shrieking wheels, and
wheel flats [36]. The energy levels are then used to produce
alarm scores using a preset threshold. An alarm is triggered if
a measured acoustic energy level by RailBAM is higher than
a preset threshold. In this work, the energy levels are used as
condition monitoring indicators (covariates), not the alarms. A
description of the development of the RailBAM system is provided in [36].
In the current practice, a heuristic method is used to calculate an alarm score by giving a severity weight (1 to 7) to different possible alarms, and summing the weights over the last
40 passes of the bearing. Bearings with high score are prioritized in a recall list, and removed from wagon.
A wayside Hot Bearing Detection (HBD) system also sends
alarms to the operator of the train if a bearings temperature is
higher than a pre-set threshold. The operator then stops the train
immediately, and investigates the situation. We have only used
these alarms to identify the historical failures, and they are not
used as performance data in the proposed model. A suggestion
for inclusion of this information in the PH Model is discussed
later in the discussion section.
A PH-Model models the degradation due to two sources: the
aging process, provided by failure data, and represented by a
; and a diagnostic process represented
baseline failure rate
that
by a vector of -independent variables or covariates
reflects the conditions of utilization of the system [20].
The output of the first phase is used to estimate the parameters of the model, and to test its efficiency. Once the model is
constructed, current performance data of the asset are fed to the
model to calculate the MRL of the asset, and make the maintenance intervention or replacement decision.
D. Modeling the Residual Life
The two most used measures of equipment health are the
hazard function, and the MRL. These two measures are calculated from the reliability function.
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IEEE TRANSACTIONS ON RELIABILITY, VOL. 61, NO. 3, SEPTEMBER 2012
In reliability analysis, two reliability functions are of interest.
The first is the unconditional reliability function given by the
probability
, which is the probability that the failure
time , of a piece of equipment that has not yet been put into
operation, is bigger than a certain time . The second is the conditional reliability function calculated by
,
which is the probability that the time to failure is bigger than
, knowing that the equipment has already survived until time
, where
. In this later case, the MRL is
[42], which is equal to
where has distribution function . The hazard function
is obtained from
. In
this equation,
is a small time interval less than the time to
next inspection.
In some reliability analysis, it is assumed that every piece of
equipment is used in the same environment, and under the same
conditions. This assumption allows the calculation of the MRL,
and the hazard function prior to the actual use of the equipment. In real-life, the environments in which the equipment is
performing, and the conditions of utilization affect the process
of degradation. Consequently, the conditional reliability, the
residual life, and the failure rate of the equipment are affected.
Taking this fact into consideration improves the diagnosis of
the equipment’s degradation state, and the prognosis for future
performance.
Many researchers have proposed different reliability models
incorporating the information gathered periodically regarding
the equipment’s condition. These models are used to calculate
an adjusted hazard function, and the corresponding MRL. In
this study, the PH Model with imperfect information is used. In
the initial PH Model with perfect information, the conditional
reliability is given by [43]
(5)
The conditional reliability indicates the probability of survival until time
,
, knowing that the failure
has not happened until time
, and the states of the equipment
have been
, at
. is the random
variable indicating the time to failure.
Equation (5) is not valid for
because
may change at
any subsequent interval. The conditional reliability for the case
of perfect information for all is [39]
(6)
Fig. 2. Approximate removed records during data cleansing.
In the case of imperfect information, the conditional reliability can be calculated by [40]
(7)
, calculated at the th obAnd consequently, the MRL,
servation moment, while the state conditional probability is ,
is calculated by
(8)
The steps for calculating the MRL at each observation moment , where the indicator obtained is , are as follows. At any
observation moment , when an indicator value is obtained,
follow this procedure.
(a) Calculate the conditional probability distribution , at
period using (1).
(b) Calculate the conditional reliability of the equipment,
, at the -th observation moment by using (7).
(c) Calculate the MRL of the equipment,
, by applying (8).
IV. RESULTS
A. Performance Data Acquisition, and Cleansing Outcomes
The original data set contained 328 failure records. However,
in the cleansing process, a large number of records had to be
removed due to numerous reasons:
• unknown age of the failed bearing,
• unknown type of the bearing at installation moment,
• absence of historical acoustic data for a long time period
(lost data or indication of wheels being used in sub sections
of railway network), and
• inconsistency of dates in the databases.
GHASEMI AND HODKIEWICZ: ESTIMATING MEAN RESIDUAL LIFE FOR A CASE STUDY OF RAIL WAGON BEARINGS
725
Fig. 3.
TABLE I
AVERAGE LIFE OF DIFFERENT BEARING TYPE
TABLE II
MODEL FITNESS WITHOUT CM INDICATORS
WITH 2 PARAMETER WEIBULL MODEL
Fig. 2 shows the approximate number of records removed due
to these reasons.
The outcome of the data acquisition and cleansing stage is
a set of 63 records of failure: 57 for modeling, and the six remaining records (almost 10%) for testing the model result. The
six records are selected by choosing equipment numbers ending
with 1 to maintain a random selection. These were removed
from the data set used to develop the model parameters.
The distribution of bearing types for the 57 records is shown
in Table I.
The estimation of mean life for the bearing data set is shown
in Table II. This table shows that the mean life of the bearings
is 343 pass-bys.
TABLE III
MODEL FITNESS WITH ACOUSTIC BEARING INDICATORS AND BEARING TYPE
B. Parameter Estimation Results
Table III shows the result of the parameter estimation method
applied to the collected data. The current heuristic practice used
by the practitioners uses only the final alarm of the system to
make a decision. The alarm is initiated if one of the energy levels
is higher than a pre-set threshold level. In this study, we use the
energy level obtained from the acoustic condition monitoring
system. These energy levels are condition monitoring indicators (covariates) used for the PH-Model. Based on statistical
tests, cup, cone, roller, and noisy energy levels are not significant in the PH Model. However, looseness, and bearing type
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IEEE TRANSACTIONS ON RELIABILITY, VOL. 61, NO. 3, SEPTEMBER 2012
TABLE IV
15 DAY ALARM RECALL POLICY ANALYSIS
FOR SELECTED CONFIDENCE INTERVALS
that have been advised to be replaced could survive on average
11 days more than predicted.
V. DISCUSSION
In this part, we explore the significance of the results in detail
in each of the following five sub sections.
A. Outcomes of the Parameter Estimation
are of great meaningful significance in the model. Bearing type
is almost ten times more significant than looseness.
C. Testing a 15 Pass-By Replacement Policy
Although the current heuristic replacement policy considers
alarms levels obtained from RailBAM system for cone, cup, and
roller in decision making, and practically ignores the bearing
type, and looseness alarms (and consequently energy level),
while latter pieces of information carry much more meaningful
data related to the bearing failure.
A replacement policy is criterion-based. For example, we decide whether to replace a bearing, or leave it until the collection
of the next indicators. In this research, we have introduced and
tested following replacement policy: “Replace the bearing if
the
lower confidence interval of the MRL is less than 15
pass-bys.” We found the best value of x that suits this replacement objective.
This criterion has been tested for confidence intervals of
68.3%, 86.4%, and 89.3%. The results are summarized in
Table IV. A 68.3% CI demonstrates 50% True Negative (TN),
and 50% False Negative (FN) results. The FN results are 31
pass-bys longer than real failure pass-by of the bearings. This
result means that, in 50% of the cases, the policy has estimated a
longer residual life for the bearings. On average, the estimation
has been 31 pass-bys longer than the real residual pass-bys.
At 89.3% CI, the results are satisfactory. Out of 12 simulated
decisions, 50% have been correctly advised to replace before
15 pass-bys (True Positive). 17% of the cases did not need to
be replaced, and are correctly advised not to be replaced before
next 15 pass-bys (True Negative). The remaining 33% are the
cases in which the policy advises to replace the bearing before
the next 15 pass-bys, while in reality the bearing could survive
more than 15 pass-bys. However, in the latter case, the average
difference of the estimated remaining pass-bys and the actual
failure time is 11 pass-bys. This means that the 33% of the cases
Table III shows the result of the parameter estimation method
applied on collected data. Based on statistical tests, cup, cone,
roller, and noisy energy bonds are not significant in the model.
However, looseness, and bearing type have meaningful significance in the model. Insignificant behavior of these bearing
acoustic indicators is contrary to expectations, and may be due
to one or a combination of the following reasons.
• Cone, roller, and cup were the indicators with the most
missing data, having values of zero in the field. These
missing data were replaced with the moving average.
• The looseness energy level correlates with some of the
other indicators, and is reflecting their effect.
• There is much more significant information in the looseness indicator than imagined, which is not being used
currently.
• There is an insufficient number of failure data (samples).
• There is error in data (as discussed in the following
section).
The significance of bearing type in the model is an important
finding, and indicates that the maintenance staff should consider
the consequences of selecting a second-hand bearing over a new
or overhauled bearing. The rest of the indicators (cone, roller,
cup, noisy) do not have significant effect on the hazard (failure)
rate. This result can be explained through the indicator-state
(health condition) matrix Q, used in the modeling stage.
The structure of the matrix Q is shown in Table V(a). Element
, for example, is the probability of seeing indicator
level 2 when the bearing is in health condition 2 (example: 0.10
in Table V(b)). Table V(b) and (c) show two possible examples
of this matrix. As can be seen in (b), any possible health condition can have diverse probabilities for different levels of the
indicator. However, in case (c), the probabilities in each line are
more or less equal. If the estimated values of matrix Q show statistically equal values in each line, then the indicator is assumed
to be insignificant in the model.
B. Sample Population Characteristics
Table I summarizes the mean working age (pass-by) of bearings grouped by different bearing types. The last column is an
approximation of each bearing type percentage used in the fleet.
This approximation was calculated using notification entries in
the maintenance management system, where the type of bearing
installed each time is recorded.
The samples for all three bearing types have large standard
deviations. The large standard deviation of two first types (new
and overhauled) can be explained by the small sample sizes
available (nine and five). However, second-hand bearings with
43 samples also show a large standard deviation value. The authors postulate that this result is mostly due to the diversity of
second-hand bearings. In this case study, there is no record of
GHASEMI AND HODKIEWICZ: ESTIMATING MEAN RESIDUAL LIFE FOR A CASE STUDY OF RAIL WAGON BEARINGS
TABLE V
INDICATOR OR STATE MATRIX STRUCTURE, AND EXAMPLES
the times a bearing has been used, removed, and reinstalled as
a second-hand bearing. Also, it may have been on other wheels
as little as few weeks to several months. It also can be a second
hand bearing of an originally new or overhauled bearing. Improvements in data collection, discussed in the recommendation
section, should assist in accounting for this fact in future models.
C. Significance of the MRL Model Results
MRL is one of the major tools used by maintenance practitioners in environments where cost is not the major issue. In
these systems, usually the availability, reliability, or the risk are
of interest. In this research, we have been able to calculate the
MRL of the bearing based on available condition monitoring
data. By comparing the MRL to the next planned inspection of
the equipment, while taking into account the CI, one will be able
to decide whether to recall the equipment for further investigation before the next planed inspection, or leave it to work until
the next updated MRL calculation result.
Table VI summarizes the result of the MRL calculation for
the six test failure records. However, the standard deviations
are relatively large, which results in the cumulative distribution
function (CDF) curve having a large spread. This result is also
due to one or a combination of issues:
1 a lack of sufficient records of failure;
2 an imprecise definition of second-hand bearings, and a lack
of information on their history; or
3 a combination of different types of failures into just one
failure type.
Fig. 4 shows more detailed steps of the data acquisition and
modeling phase, and also demonstrates the processes performed
by the research group during this project.
A key part of this project involves developing and understanding the time required to complete different stages. The
most time consuming stage, 40–50% of the total project time,
was preparing data. This preparation includes data sorting,
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TABLE VI
CALCULATION OF MRL FOR TEST DATA
cleansing, matching, and validation. This work is a key consideration in the development of data-based models.
To improve the efficiency of model development and testing,
the following steps would help with future models.
• Data should ideally be recorded in the maintenance management system for individual bearings. Bearings carry a
unique serial number that should be possible to track in the
system. However, there can be practical challenges. Ideally, the CM system records, which are collected for both
sides of each wheel-set should be matched with the maintenance records of bearings.
• Improvement in the tag reading hardware and software
will facilitate the data acquisition and cleansing part of the
project.
• Improve the consistency of data in the databases. There
were many instances of inconsistent data due to data entry
error, tag code change, and different coding systems in
different databases. Improve these point to increase the
amount of reliable data available, and reduce the time to
cleans the data.
D. Recommendations and Future Work
Recommendations and future work can be discussed in short,
and long terms. We suggest improving and applying this model
by considering the following tasks.
• Extend the data set. Currently the model is constructed
based on 57 failures, and their related performance records.
A first step to improve the output of the model is to extend
the data to a larger set of failure data. At the same time,
better cleansing techniques and assumptions should be applied to the data. This approach will assure the integrity
and correctness of the data fed to the model.
• Extend the use of the acoustic energy levels available for
modeling. In this work, we used 10 (five for each bearing
side) acoustic energy levels to feed the model. Ideally, one
may consider using some or all 124 fields of acoustic signature produced by the acoustic monitoring system to construct the model.
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IEEE TRANSACTIONS ON RELIABILITY, VOL. 61, NO. 3, SEPTEMBER 2012
Fig. 4.
• Extend the use of other degradation indicators such as the
HBD, and the Wheel Impact Detector (WID) systems from
the data acquisition, data cleansing, and modeling phases
in this project.
One of the ongoing challenges for equipment prognostics is
the availability of clean, appropriate data. As mentioned earlier,
40–50% of the time spent on this project was on cleaning data,
on the order of months. Although 328 records were originally
identified, only 63 records were complete and appropriate for
the final analysis. The cleansing process required access to multiple systems, and was labor intensive. For this work to be done
cost-effectively, more thought will need to be given to what
data are collected, how they are stored, and how they are coded
across multiple systems. The ability to align data between systems, for example the computerized maintenance management
system, and the condition monitoring system(s), continues to be
a challenge, and stands as a barrier to routine use and updating
of prognostic models.
VI. CONCLUSIONS
We have presented a model for estimating the mean residual
life of wagon bearings to support maintenance interventions.
Data for the model have been collected from a rail industry case
study. Data collected include acoustic signatures of the bearing
GHASEMI AND HODKIEWICZ: ESTIMATING MEAN RESIDUAL LIFE FOR A CASE STUDY OF RAIL WAGON BEARINGS
at each pass-by. Acoustic data in this study are inherently imperfect due to the noisy environment, and the nature of the data
monitoring technique. A prognostics model based on selected
bearing acoustic data levels, bearing type, and its age was developed. This work provides an ability to detect failure in a 15
pass-bys window with acceptable levels of -confidence.
Significant indicators that can be effectively used in the calculation of MRL were distinguished, and the MRL model was constructed based on these indicators. This case study has shown
that a) bearing type is of high significant impact in the MRL, and
b) some indicators like looseness that have not been considered
previously can carry very indicative information regarding the
bearing MRL. We have also explored the frustrations and time
consumption of the data acquisition and cleansing process, and
have suggested ways to address these problems. The positive
impact of improving the data acquisition and cleansing process
on getting reliable MRL result was discussed.
Future work includes testing the significance of other condition monitoring indicators (like Hot Wheel Detector and Wheel
Impact Detector), and also a higher level of information from
the existing acoustic system data.
ACKNOWLEDGMENT
The authors would like to thank the staff at Rio Tinto Technology & Innovation and Rio Tinto Railways Division who supplied data, information, time, and expertise to this project.
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Alireza Ghasemi is an Assistant Professor at the Department of Industrial Engineering of Dalhousie University, Halifax, Canada. He holds a Ph.D. in Industrial
Engineering from École Polytechnique de Montréal in Canada. He also holds
a M.Sc. degree from École Polytechnique de Montréal, a M.Sc. Degree from
Sharif University of Technology in Iran, and a B.Sc degree from Isfahan University of Technology in Iran, all in Industrial Engineering. His research field is
Condition Based Maintenance with Imperfect Observations. He is a member of
the Institute of Industrial Engineers, and a member of the Canadian Operational
Research Society.
Melinda R. Hodkiewicz is a Professor in the School of Mechanical and Chemical Engineering at the University of Western Australia (UWA) in Perth. She
holds a Ph.D. in Mechanical Engineering from UWA, and a BA (Honors) in
Metallurgy and Materials Science from Oxford University. She is responsible
for teaching and research programs in asset management at UWA, and sits on
the ISO committee PC251 for asset management.