Machine Learning for Predictive Maintenance: A Multiple ClassifiersApproach

Susto, G. A., Schirru, A., Pampuri, S., McLoone, S., & Beghi, A. (2015). Machine Learning for PredictiveMaintenance: A Multiple Classifiers Approach. IEEE Transactions on Industrial Informatics, 11(3), 812-820.https://doi.org/10.1109/TII.2014.2349359

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Machine Learning for Predictive Maintenance: A MultipleClassifiers Approach

Susto, G. A., Schirru, A., Pampuri, S., McLoone, S., & Beghi, A. (2015). Machine Learning for PredictiveMaintenance: A Multiple Classifiers Approach. IEEE Transactions on Industrial Informatics, 11(3), 812-820.10.1109/TII.2014.2349359

Published in:IEEE Transactions on Industrial Informatics

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1

Machine Learning for Predictive Maintenance:a Multiple Classifier Approach

Gian Antonio Susto, Andrea Schirru, Simone Pampuri, Sean McLoone Senior Member, IEEE,Alessandro Beghi Member, IEEE

Abstract—In this paper a multiple classifier machinelearning methodology for Predictive Maintenance (PdM) ispresented. PdM is a prominent strategy for dealing withmaintenance issues given the increasing need to minimizedowntime and associated costs. One of the challenges withPdM is generating so called ’health factors’ or quantitativeindicators of the status of a system associated with a givenmaintenance issue, and determining their relationship to op-erating costs and failure risk. The proposed PdM methodol-ogy allows dynamical decision rules to be adopted for main-tenance management and can be used with high-dimensionaland censored data problems. This is achieved by trainingmultiple classification modules with different predictionhorizons to provide different performance trade-offs in termsof frequency of unexpected breaks and unexploited lifetimeand then employing this information in an operating costbased maintenance decision system to minimise expectedcosts. The effectiveness of the methodology is demonstratedusing a simulated example and a benchmark semiconductormanufacturing maintenance problem.

Index Terms—Classification Algorithms, Data Mining, IonImplantation, Machine Learning, Predictive Maintenance,Semiconductor Device Manufacture.

I. INTRODUCTION

The increasing availability of data is changing theway decisions are taken in industry [17] in importantareas such as scheduling [15], maintenance management[24] and quality improvement [6], [23]. Machine learning(ML) approaches have been shown to provide increas-ingly effective solutions in these areas, facilitated by thegrowing capabilities of hardware, cloud-based solutions,

Manuscript received March 17, 2014. Accepted for publication Au-gust 7, 2014.

Copyright 2014 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposesmust be obtained from the IEEE by sending a request to pubs-permissions@ieee.org

G.A. Susto (corresponding author) is with the Department of In-formation Engineering, University of Padova, Italy and with StatwolfLTD, Ireland. E-mail: gianantonio.susto@statwolf.com.

A. Schirru and S. Pampuri are with the National University ofIreland, Maynooth and with Statwolf LTD, Ireland.

S. McLoone is with Queen’s University Belfast, United Kingdom andwith the National University of Ireland, Maynooth.

A. Beghi is with the Department of Information Engineering, Uni-versity of Padova, Italy.

This work has been done within the framework of INTEGRATE (In-tegrated Solutions for Agile Manufacturing in High-mix Semiconduc-tor Fabs), an European Nanoelectronics Initiative Advisory Council’sproject.

and newly introduced state-of-the-art algorithms. At thesame time the efficient management of maintenanceactivities is becoming essential to decreasing the costsassociated with downtime and defective products [14],especially in highly competitive advanced manufactur-ing industries such as semiconductor manufacturing.

Approaches to maintenance management can begrouped into three main categories which, in order ofincreasing complexity and efficiency [22], are as follows:i. Run-to-Failure (R2F) - where maintenance interventionsare performed only after the occurrence of failures. Thisis obviously the simplest approach to dealing with main-tenance (and for this reason it is frequently adopted),but it is also the least effective one, as the cost ofinterventions and associated downtime after failure areusually much more substantial than those associatedwith planned corrective actions taken in advance. ii.Preventive Maintenance (PvM) - where maintenance ac-tions are carried out according to a planned schedulebased on time or process iterations. With this approach,also referred to as scheduled maintenance, failures areusually prevented, but unnecessary corrective actions areoften performed, leading to inefficient use of resourcesand increased operating costs.iii. Predictive Maintenance (PdM)1 - where maintenance isperformed based on an estimate of the health status ofa piece of equipment [7]. PdM systems allow advancedetection of pending failures and enable timely pre-failure interventions, thanks to prediction tools basedon historical data, ad hoc defined health factors, statisticalinference methods, and engineering approaches.

Among statistical inference based methods, thosebased on ML are the most suitable for dealing with mod-eling of high-dimensional problems, such as those aris-ing in semiconductor manufacturing where hundredsor thousands of physical variables (pressures, voltages,currents, flows, etc.) act on the process [10], [26].

In this paper a new PdM methodology based on mul-tiple classifiers is introduced for integral type faults (themost frequent in semiconductor manufacturing), a termwhich describes the failures that happen on a machinedue to the accumulative ’wear and tear’ effects of usage

1Other authors [8] refer to this class of maintenance approaches asCondition-Based Maintenance

. 2

and stress on equipment parts. Even if no direct evidenceof process/machine degradation is available, PdM toolsexploit process and logistic variables collected duringproduction to identify the ’footprint’ of this degradationin the data. The proposed methodology, referred to asMultiple Classifier (MC) PdM, can effectively deal withthe unbalanced datasets that arise in maintenance classi-fication problems, that is datasets where the observationsrelating to normal production greatly outnumber the ob-servations associated with abnormal/faulty production[22]. It also allows planning of maintenance schedulesusing a statistical cost minimization approach.

The remainder of the paper is structured as follows:Section II provides a brief literature review and anintroduction to ML-based approaches to PdM, whileSection III is dedicated to presenting the proposed MCPdM methodology. Tuning guidelines and classificationapproaches are discussed in Section IV. Then in SectionV, to demonstrate the principles and efficacy of MCPdM, results are presented comparing MC PdM withPvM for a benchmark semiconductor manufacturingmaintenance problem, namely, changing of filaments inion implantation tools. Finally, in Section VI, concludingremarks and possible extensions of the work are dis-cussed.

II. LITERATURE REVIEW

Maintenance issues can be completely different innature and the predictive information to be fed to thePdM module has in general to be tailored to the par-ticular problem at hand, thus justifying the presencein the literature of many different approaches to PdM[12]. However, PdM-related solutions based on ML tech-niques seem to be among the most popular (see e.g. [5]and [21] with reference to semiconductor manufacturingapplications).

ML-based PdM can be divided into two main classes:i. supervised - where information on the occurrence offailures is present in the modeling dataset;ii. unsupervised - where logistic and/or process informa-tion is available, but no maintenance related data exists.

The availability of maintenance information mostlydepends on the nature of the existing maintenance man-agement policy: in the case of R2F policies the datarelated to a maintenance cycle (the production activitybetween two successive failure events) is available andtherefore supervised approaches can readily be adopted;on the other hand, when PvM policies are currently inplace the full maintenance cycle may not be observablegiven the fact that maintenance is generally performedwell in advance of any potential failure, and hence onlyunsupervised learning approaches are feasible. Whenpossible, supervised solutions are evidently preferable:given the wide diffusion of R2F maintenance policies inindustry, and hence the availability of suitable datasets,we consider in this work a supervised approach to PdM.

From a ML perspective, supervised approaches re-quire the availability of a dataset S

S = {xi, yi}ni=1 , (1)

where a couple {xi, yi} (called observation) contains theinformation related to the i-th process iteration. Here,vector xi ∈ R1×p contains information related to the pvariables associated with available process or logisticinformation. Depending on the type of output y twoclasses of supervised problem are possible:i. if y assumes continuous values a regression problem isobtained;ii. if y assumes categorical values a classification problemresults.

In PdM problems, regression-based formulations gen-erally arise when predicting the Remaining Useful Lifeof a process/equipment, directly [2] or indirectly (eg.through the computation of the conditional reliability[5]), while classification-based PdM formulations occurwhen seeking to discriminate between healthy and un-healthy conditions of the system being monitored [1].

While classification tools are a natural choice for dis-tinguishing between faulty and non-faulty process itera-tions based on observed process data, they do not mapnaturally to health factors that can be extrapolated formaintenance related decision making, unlike for exam-ple, regression models of Remaining Useful Life. In thefollowing a methodology based on multiple classifiers ispresented to address this limitation.

III. MULTIPLE CLASSIFIER PDMA. Classification for PdM

Let us suppose that data regarding N maintenancecycles are available, for a total of n =

∑Ni=1 ni machine

runs. We define the matrix X ∈ Rn×p containing all thecollectible information

X =[x1 x2 . . . xn

]T (2)

regarding p physical variables or logistic information onthe process or on the tool that are used as inputs tothe PdM module. Information on maintenance events iscontained in the variable Y . If during the run the faultunder consideration takes place, then the observationis marked as faulty (F), and not faulty (NF) otherwise.Accordingly:

Y (i) = yi =

{F if iteration i is faultyNF if iteration i is not faulty . (3)

When dealing with R2F data, each maintenance cycleends with a failure, hence the available data contains Nsamples for class F and n − N samples for class NF .Based on X and Y , a classifier learns a decision rule f(·)that assigns one of the two classes {F,NF} to each pointin the input space Rp.

The formulation presented above is weak from a PdMperspective in two aspects:1. only the current process iteration is classified, i.e. no

. 3

fault prevention policy can be implemented.2. no operating cost optimization policy is enforced.

As far as total operating cost minimization is con-cerned, two key metrics can be defined, namely2:

1) Frequency of Unexpected Breaks (ρUB) - percentageof failures not prevented;

2) Amount of Unexploited Lifetime (ρUL) - averagenumber of process iterations that could have beenrun before failure if the preventative maintenancesuggested by the maintenance management mod-ule had not been performed.

Different costs, cUB and cUL, can be associated with ρUBand ρUL, respectively, where generally cUB >> cUL, giventhat cUB relates to unplanned interruption of produc-tion. It is not possible to simultaneously minimize bothmetrics, rather an optimal trade-off solution is soughtthrough minimization of the total operating costs, asdefined by the weighted sum

J = ρUBcUB + ρULcUL. (4)

As formulated above, the classification problem is notsuitable for maintenance managements purposes, be-cause it doesn’t facilitate identification of policies thatminimise J in (4).

From a classification perspective, the formulation de-scribed in Eq. 3 also suffers from the fact that the datasetis very unbalanced or skewed, with N samples in class Fand n−N samples in class NF and N � n. Classifica-tion using unbalanced datasets generally results in poorprediction accuracy and generalization performance [9].

These issues are addressed by the MC PdM method-ology presented in the next subsection.

B. MC PdM Concept

A possible approach to preventing unexpected failuresis to consider a different classification problem where,instead of only labeling the last iteration of a mainte-nance cycle as F , we label as F the last m iterations.From a PdM perspective, this approach allows us toprovide more conservative maintenance recommenda-tions by choosing larger values for the failure horizonm. Moreover, by assigning more samples to the F classwe reduce the skewness of the dataset (Nm samples inclass F and n−Nm samples in class NF).

This can be repeated for k different values of the hori-zon m. In the proposed MC PdM approach, k differentclassifiers run on the module, each one facing a differentclassification problem and therefore providing differ-ent maintenance management performance outcomes interms of ρUB and ρUL.

The MC PdM scheme is depicted in Fig. 1. The j-thclassifier is associated with the labels Y (j), where, con-sidering the t-th process iteration of the i-th maintenance

2The R2F approach clearly guarantees a total of ρUB = 1 and ρUL =0, while the performance of PvM and PdM approaches depend onsome tuning parameters as will be illustrated in Section IV

x1

x2

x1

x2

x1

x2

y(1) y(2) y(k)

Classifier 1 Classifier 2 Classifier k

Fig. 1. 2-dimensional example for the k classifiers of the MC PdMmethodology: the labels NF (orange circle) and F (blue plus) changewith failure horizon m resulting in a different classification problemfor each classifier

cycle (of length ni) we have

y(j)t =

{NF if t ≤ ni −m(j)

F otherwise, (5)

where m(j) ∈ N+; the associated PdM performance ofthe j-th classifier is indicated by ρ

(j)UB and ρ

(j)UL .

In the presented approach the k classifiers work inparallel and a maintenance event is triggered by thedecision making logic based on the following operatingcosts minimization philosophy: given the current costscUB(t) and cUL(t) at time t, the MC PdM suggests acorrective action when the j∗-th classifier

j∗ = arg minj=1,...,k

J (j)(t)

= arg minj=1,...,k

ρ(j)UBcUB(t) + ρ

(j)ULcUL(t) (6)

outputs a label F classification.The training procedure for MC PdM is sketched in

Algorithm 1. The performance of each classifier is eval-uated using Repeated Random Sub-Sampling Validation[16], also known as Monte Carlo crossvalidation (MCCV): Qsimulations are performed by randomly splitting the Nmaintenance cycles into a training dataset of NTR = bNqcmaintenance cycles and a validation dataset of NVL =dN(1− q)e maintenance cycles, with 0 < q < 1. It hasbeen shown [20] that MCCV is asymptotically consistentresulting in more pessimistic predictions of the testdata compared with full crossvalidation. Algorithm 1 isapplicable to any choice of classification algorithm. Ingeneral (as in the case of the two algorithms presentedin Section IV-B) to set up the classifiers the tuning of oneor more hyper-parameters is required. This is achievedthrough crossvalidation with the Missclassification Rate(MCR)

MCR[%] = Percentage of missclassified samples

employed as a performance indicator.Fab integration and on-line operation of the MC PdM

module are described in Fig. 2. Estimates of ρUB and

4

Algorithm 1: MC PdM Training

Data: X , Y , k, q1, q2, Q1, Q2,{m(j)

}kj=1

Result: Classifiers{f (j)

}kj=1

and PdM performances1. Let ρUB = [ · ] and ρUL = [ · ] (empty vectors)for j = 1 to k do

2. Compute Y (j) as in Eq. 5 for i = 1 to Q1 do3. Randomly split the maintenance cyclesbetween training and validation samples,keeping the ratio q14. Compute the MCR of the classifier withdifferent hyper-parameters

5. Chose the hyper-parameters based on theaveraged MCR over the Q1 simulations6. Compute f (j) with the selectedhyper-parametersfor i = 1 to Q2 do

7. Randomly split the maintenance cyclesbetween training and validation, keeping theratio q28. Compute f (j) with the selectedhyper-parameters9. Compute ρUB and ρUL of f (j)

10. Compute ρ∗UB and ρ∗UL as averaged over theQ2 simulations11. ρUB = [ρUB; ρ∗UB] and ρUL = [ρUL; ρ∗UL]

Fig. 2. Overview of how the MC PdM module integrates with theFab

ρUL are provided by the historical and simulation per-formances of the PdM module, while cUB and cUL areprovided by the user, and may be changed at eachevaluation of the PdM module (i.e. unexpected breaksare much more costly during highly intense productionperiods than during normal production periods).

While undesirable from a operating cost perspective,when an unexpected break occurs during operation of aPdM module it means that a full maintenance cycle hasbeen observed, and hence valuable new data is availablewith which to update the MC PdM module and relatedperformance metrics. Therefore, as illustrated in Fig. 2, itis important to retain the facility to update the MC PdMmodule following deployment.

IV. IMPLEMENTATION DETAILS

A. Failure Horizon SelectionPerformance of the MC PdM methodology increases

with the number of classifiers, k, since each classifier pro-vides more information on the health status of the pro-cess. Unfortunately k cannot be considered as a degreeof freedom in the MC PdM design since it is constrainedby the available computational and storage capabilitiesand by the algorithm chosen for the classification. Inthe following we propose two strategies for defining thefailure horizons of the k classifiers.

The k classifiers are distributed in order to haveequally spaced failure horizons in terms of the numberof process iterations; thus the k horizons employed in(5) are assigned as follows

m(j) =

⌊(j − 1)(M1 − 1)

k − 1

⌉+ 1 for j = 1, . . . , k (7)

where bue is the closest integer to u and M1 > 0 specifiesthe maximum failure horizon and is chosen based on thelengths of the maintenance cycles in the training dataset.

An alternative approach for selecting the failure hori-zons is to express them as the percentage of a main-tenance cycle, rather than a fixed number of processiterations. Thus, in this second approach we have

y(j)t =

{NF if t ≤

⌊ni(1−m(j)

)⌉F otherwise

, (8)

withm(j) =

(j − 1)M2

k − 1for j = 1, . . . , k (9)

where M2 ∈ (0, 1].We remark that the choice of criteria used to define

the failure horizons depends on the nature of the faultunder investigation and, as such, there is no a-priori bestsolution.

B. Classification AlgorithmsThe MC PdM methodology presented does not im-

pose any restrictions on the classification algorithm thatcan be adopted for the individual classifiers. Here, weconsider two well known and widely used classificationtechniques, namely: Support Vector Machines (SVMs)and k-Nearest Neighbors (k-NN). This choice is moti-vated by the fact that it provides a comparison betweentwo contrasting types of classifier; a powerful, but com-putationally complex to estimate, model based classifier(SVM); and a low-complexity non-parametric classifier(k-NN). In the following the two selected classifiers arebriefly presented.

1) Support Vector Machines: SVMs are probably themost popular approach to classification, thanks to theirhigh classification accuracy, even for non-linear prob-lems, and to the availability of optimized algorithms fortheir computation [3].

Consider the problem where two classes of data (Fand NF in the problem at hand) have to be classified;

. 5

we initially consider the separable case, where the twoclasses can be linearly separated. Suppose that a trainingdataset S as in Eq. (1) is available and the values {−1, 1}are assigned to the two classes which the data belong to,for example

yi =

{1 if i-th sample ∈ F−1 if i-th sample ∈ NF

We define the hyperplane F0 in the Rp space as

F0 = {x |f(x) = xβ + β0 = 0} , (10)

where β ∈ Rp with norm ‖β‖ = 1. The classification isthen based on the choice of f(x) (and consequently ofF0): for a new sample xnew /∈ S, we classify

ynew =

{1 (Class F ) if f(xnew) > 0−1 (Class NF ) if f(xnew) < 0

(11)

Since, by assumption, the two classes are separable,then it is possible to find a function f(x) s.t.

yif(x) > 0 ∀i;The hyperplane yielding the largest margin Π betweenthe two classes is chosen: this can be rephrased as themaximization problem

maxβ,β0,‖β‖

Π

subject to yif(x) ≥ Π, i = 1, . . . , n.(12)

We refer the interested reader to [4] for details on how(12) is solved.

In real classification problems, classes are often non-separable, i.e., the two categories overlap: SVMs can stillbe used in this case by allowing some samples to beon the ’wrong’ side of the separation line. With respectto the separable case the optimization problem (12) ischanged by modifying the constraint to:

y (xiβ + β0) ≥ Π− ξ∗i = Π(1− ξi) ∀i, (13)

where the slack variables ξi have to satisfy the conditions:ξi ≥ 0 (the points on the wrong side of their margin arelabeled with ξ∗i > 0, while the points on the correct sidehave ξ∗i = 0) and

∑ni=1 ξi ≤ C ∈ R. The optimization

problem is now (see [4] for a detailed solution):

minβ,β0

12 ‖β‖+ γ

n∑i=1

ξi

subject to{

y (xiβ + β0) ≥ 1− ξi, ∀iξi ≥ 0

,

(14)

where the regularization parameter γ governs the trade-off between the margin width and the sum of values ofthe slack variables.

SVMs are usually employed in combination withKernel Methods to further enhance the classificationperformance by allowing non-linear solutions. Thecomputational cost for training a nonlinear SVM isgenerally between O(n2) and O(n3), depending onthe algorithm employed for its computation. For moredetailed presentations on SVMs we refer interestedreaders to [19] and [25].

Fig. 3. Schematic of a generic Ion Implanter tool. The tool can bedivided into three main parts: the Source ©, the Beamline Area �, theEnd Station �

2) k-Nearest Neighbours: k-NN is probably the simplestapproach to classification as it requires just computationof distances between samples.

In the k-NN procedure each point of the input space islabelled according to the labels of its k closest neighbour-ing samples (where distances are computed according toa given metric, often the Euclidean norm).

The only parameter that requires tuning in k-NN is k,the value of the number of samples in the consideredneighbourhood: the choice of k is usually data-driven(often decided though cross-validation). Larger valuesof k reduce the effect of noise on the classification, butmake decision boundaries between classes less distinct[28].

Optimized algorithms for computing k-NN have acomputational cost of O(log n).

V. EXPERIMENTAL RESULTS

A. Use CaseWe test the proposed MC PdM methodology for re-

placing tungsten filaments used in Ion Implantation [13],one of the most important processes in semiconductormanufacturing fabrication. Ion Implantation is used tomodify the electrical properties of wafers by injectingdoping atoms. It is often considered a ’bottleneck’ inproduction lines due to the high cost of the tool, makingit a critical operation for throughput [11].

The components of a typical Implanter tool are illus-trated in Fig. 3. The filament is part of the Ion Sourcesection of the tool. During the process, the filament isheated and electrons are ’boiled’ off the heated filament.The electrons are then accelerated in the beamline areaand impinge on the target wafers in the End Station.The tungsten filament must be frequently replaced. Ev-ery time a filament is changed, the tool is down forapproximately 3 hours making this the most importantmaintenance issue for process engineers working on thetool.

Several factors may influence the working duration ofa filament. For example, it is known that high valuesof pressure, voltage and filament current can drasticallyreduce the lifetime of the filament. The operations ofcleaning, installation and degasification can also have afundamental impact on filament ’health’ and duration.

. 6

Physical/Electrical Variable QuantityCurrent 9

Current Transfer Ratio 1Deceleration 1

Flow 1Number of Scans 1

Plasma Gun Emission 1Position 2Pressure 3

Quantity of Electric Charge 2Scan Speed 1Tilt Angle 2

Voltage 7

TABLE IRECORDED TOOL VARIABLES

Type Based on: Acronym

PvM Mean µ PvM-µMedian η PvM-η

PdM Linear SVM PdM-linGaussian Kernel SVM PdM-rbf

MC PdM k-NN MC PdM-knnSVM MC PdM-svm

TABLE IITESTED MAINTENANCE MANAGEMENT TECHNIQUES

B. Data Description

The available data consists of N = 33 maintenancecycles, with the filament maintained using a R2F policy(i.e. each maintenance cycle consists of the data for theimplanter tool from the installation of a new filament tothe point that the filament breaks and the tool is stoppedfor maintenance), for a total of n = 3671 batches.

A total of 31 variables, as listed in Table I, wererecorded from the ion-implantation tool during the nruns. These variables have a time series evolution duringeach run, with some presenting with a non-uniformsampling rate from observation to observation. In or-der to construct a design matrix to feed the classifiers,features must be extracted. A classical approach [18] toextracting such features is to rely on statistical moments.In this work we extracted 6 features for each of the31 time series, namely: maximum, minimum, average,variance, skewness and kurtosis. After constant variablesare discarded a total of p = 125 input variables areretained in the dataset.

C. Comparison of SVM and kNN Based Approaches

The MC PdM approach has been tested on the prob-lem described above using the classification algorithmsdescribed in Section IV-B. We use MC PdM-knn andMC PdM-svm to denote MC PdM implemented withk-NN and SVM, respectively. In the case of SVM, wehave employed Radial Basis Function (RBF) kernels toimplement the non-linear classification boundaries inthe linear framework presented in Section IV-B (at theexpense of a more complicated tuning procedure, see[4]). A linear SVM implementation, denoted PdM-lin, isalso considered.

The maintenance strategies investigated aresummarized in Table II. A number of approachesare compared to MC PdM as follows:

1) A simulated PvM policy: PvM policies are usuallybased on the mean µ or median η of the maintenancecycle lengths and on the definition of an optimal actionthreshold τ∗µ or τ∗η . Once τ∗µ is computed, then the PvMmaintenance is triggered if

fµ = iterations since last maintenance > µ− τ∗µ , (15)

and similarly for the median. The PvM policy based onthe mean (PvM-µ) is outlined in Algorithm 2 (the versionbased on the median, PvM-η, is a natural extension).

Algorithm 2: PvM moduleData: Y , cUB, cULResult: Maintenance Rule (defined by τµ∗), ρµUB, ρµUL

and Jµ(Tµ)1. Compute µ, the mean number of processiterations in a maintenance cycle2. Define a set of threshold values Tµ ∈ Rd3. Let ρµUB = [ · ] and ρµUL = [ · ] (empty vectors)for j = 1 to N do

4. Compute ρµUB and ρµUL for all entries in Tµ

5. ρµUB = [ρµUB; ρµUB] and ρµUL = [ρµUL; ρµUL]

6. ρµUB = Mean(ρµUB) and ρµUL = Mean(ρµUL)7. Compute Jµ(τµ) for all entries in Tµ: Jµ(Tµ)8. Let τµ∗ = minτµ∈Tµ Jµ(τµ)

2) An SVM Classification distance-based PdM system:This is based on the PdM approach developed in [24]and involves exploiting the distance from a computedSVM decision boundary to define a metric for the dis-tance an observed sample is from a faulty situation.The assumption is that the more stress on a machine,the closer statistically we get to a faulty situation andhence the distance from the separation boundary of thetwo SVM classes decreases. The resulting PdM modulerecommends that a corrective action be performed when

f(x) < τ ∈ R+, (16)

and different choices of τ affect the performance of thePdM in terms of ρUB and ρUL. We consider here bothlinear SVM (PdM-lin) and RBF kernel SVM (PdM-rbf)classifiers.

D. Settings and ResultsThe parameters employed in the simulations of the

MC PdM methodology are• k = 10;• M1 = 85.

These values have been selected manually for illustra-tive purposes. Setting M1 = 85 ensures that the PdMmodules produce no unexpected breaks, while selectingk = 10 gives sufficient diversity in performance in terms

. 7

5 15 25 35 45 55 65 75 85

20

30

40

50

60

70

80

90

m

UnexploitedLifetime

PvM−µ

PvM−η

PdM−lin

PdM−rbf

MC PdM−knn

MC PdM−svm

Fig. 4. Average ρUL over Q2 Monte Carlo simulations with the variousmaintenance management approaches

of ρUL and ρUB to be effective. The criterion describedin Eq. (5) and Eq. (7) was used to select the failurehorizon for each classifier as this was found to provide abetter distribution of results in terms of ρUL and ρUB thanthe one described in Eq. (8) and Eq. (9). In the interestof compactness, the results of this investigation are notincluded here.

As described in Algorithm 1, prior to applicationthe hyper-parameters of the MC PdM classifiers mustbe tuned using cross-validation techniques. This alsoapplies to the SVM classification distance based PdMapproach. In the case of linear SVMs, only one parameterhas to be optimised, namely, the variable γ in Equation(14), while for RBF SVMs two parameters need to betuned (γ and the variance of the Gaussian kernels). Inthe case of k-NN the parameter k (the size of the neigh-bourhood) has to be set. The parameters we employedin the cross-validation procedure are:• q1 = q2 = 0.7;• Q1 = Q2 = 1000.

Cross-validation outcomes are not detailed here due tospace constraints, but we report the fact that the optimalvalue for the parameter k in MC PdM-knn is consistentlyequal to 1 in the simulations. This may be due to the highdimensionality of the problem.

In Fig. 4 and 5 the average performance of the variousmaintenance approaches is reported in terms of ρUL andρUB for different values of m over Q2 Monte Carlo simu-lations. The thresholds of the PvM and PdM approachesare scaled to facilitate comparison with the MC PdMapproaches. The linear scaling has been applied after ρULand ρUB has been computed with the various approachesso that their performances are in a similar range whenplotted in Fig. 4 and Fig. 5.

It can be appreciated how PdM and MC PdM outper-form PvM approaches for both metrics. In the case of ρULthe MC PdM classifiers achieve similar performance tothe PdM approaches, with PdM-rbf marginally superiorfor low values of m and MC PDM-svm marginallysuperior for higher values. The improves performancewith higher m can be ascribed to the fact that these

5 15 25 35 45 55 65 75 850

0.1

0.2

0.3

0.4

0.5

m

UnexpectedBreaks

PvM−µ

PvM−η

PdM−lin

PdM−rbf

MC PdM−knn

MC PdM−svm

Fig. 5. Average ρUB over Q2 Monte Carlo simulations with the variousmaintenance management approaches

2 3 4 5 6 7 8 9 10

x 10−3

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Costs Ratio

J[A

rbitrary

Unit]

PvM−µ

PvM−η

PdM−lin

PdM−rbf

MC PdM−knn

MC PdM−svm

Fig. 6. Optimal value of J for the various maintenance strategies asa function of the ratio of the costs cUL/cUB (averaged results over Q2

Monte Carlo simulations)

classifiers are estimated using more balanced (i.e. lessskewed) datasets. In the case of ρUB, MC PdM-svmconsistently achieves the best results. Overall when con-sidering both ρUL and ρUB MC PdM-svm guaranteesbetter performance than MC PdM-knn, but this is atthe expense of a much more time consuming tuningprocedure.

In Table III the average classification accuracy (100% -MCR), precision and recall are reported for the various

kNN SVMm Accuracy Precision Recall Accuracy Precision Recall1 98.51 69.27 61.69 98.52 69.34 62.96

10 98.47 64.09 67.85 98.47 63.14 70.8420 98.39 58.00 75.42 98.37 56.61 77.7729 98.29 53.22 81.72 98.33 54.46 85.7938 98.15 48.27 87.03 98.16 48.85 88.9548 97.95 43.31 91.09 97.95 43.36 92.9457 97.74 39.44 95.30 97.74 39.61 98.1566 97.52 35.96 97.76 97.57 36.96 99.6376 97.26 32.74 99.36 97.26 32.86 100.0085 97.03 30.23 99.94 97.08 30.08 100.00

TABLE IIIAVERAGE ACCURACY, PRECISION AND RECALL FOR THE MC PDM

MODULES (PERCENTAGE RESULTS) OVER Q2 MONTE CARLOSIMULATIONS

. 8

classifiers that make up MC PdM-knn and MC PdM-svm. In computing these values a process iteration witha broken filament is considered as the positive condition,while an uninterrupted process iteration is consideredas the negative condition. It can be observed that as thefault horizon m increases, precision decreases (more falsepositives, i.e. unexploited lifetime) while recall increases(less false negatives, i.e. unexpected breaks).

In Fig. 6 the performance of the six maintenance ap-proaches is plotted as a function of the ratio of the costs,cUL/cUB. Here, J is the minimum total cost achieved witheach approach and is computed based on the averageMonte Carlo results reported in Fig. 4 and 5. The valuesof the costs ratio cUL/cUB were chosen with the aid ofprocess experts in order to have plausible results for theproblem at hand.

These results highlight that MC PdM-svm consistentlyguarantees better performance than any of the otherapproaches considered. This is the most important out-come of the present work, since it demonstrates thatthe proposed maintenance methodology achieves thelowest operating costs while at the same time beingrobust to different choices of ρUL and ρUB. MC PdM-knnconsistently delivers lower operating costs than classicalPvM techniques and exhibits comparable performance toPvM-svm, especially for low values of the ratio cUL/cUB.

VI. CONCLUSIONS

A novel multiple classifier PdM system for integraltype faults has been presented. The multiple ML clas-sifiers work in parallel to exploit the knowledge of thetool/logistic variables at each process iteration in orderto enhance decision making. The proposed tool guar-antees improved maintenance management decisions interms of minimising operating cost and can be appliedto any maintenance problems characterised by integraltype faults provided R2F historical data is available orcan be collected.

The MC PdM module is robust to variations in theoperating costs associated with unexpected breaks andunexploited equipment part lifetime that can occur overtime. It also allows the user to dynamically change main-tenance policy based on current costs and needs of man-ufacturing production. Process engineers are providedwith a tool that enables them to adjust the performanceand the action policy so that the total operating cost isminimized. Moreover, the presence of several classifiersallows the proposed tool to be employed as a healthfactor indicator in a more natural and straightforwardfashion that with other PdM approaches. Specifically, thek classifiers provide an estimate of the current status ofthe maintenance issue, enhancing process understand-ing and allowing cost aware maintenance managementdecisions at any time.

The proposed methodology has been demonstrated fora semiconductor manufacturing Ion-Implanter relatedmaintenance task and shown to guarantee better perfor-mance than classical PvM approaches and a single SVM

classifier distance based PdM alternative. It has also beenshown in this case study that SVMs offer superior per-formance to k-NN classifiers when implementing MC-PdM, and that in general MC-PdM-knn also consistentlyoutperforms PvM approaches.

The high dimensionality of datasets typical of PdMproblems encountered in semiconductor manufacturingand other manufacturing industries, suggests that par-simonious (or sparse) classification approaches such asRelevance Vector Machines [27] could provide competi-tive results. This will be the subject of a future extensionof the present work.

We have seen how the choice of the fault horizon mstrongly affects the performance of the correspondingclassifier in MC PdM. It may be the case that some areasof the [ρUB, ρUL] space are more ’interesting’, given theassociated costs, than others in the context of minimis-ing total operating costs. One approach to cope withthis issue is to employ a two steps procedure, whereclassifiers assigned to an uninteresting area of [ρUB, ρUL]are reallocated in the second training iteration to morerelevant areas of the cost space.

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Gian Antonio Susto (S’11) received the M.S.degree (cum laude) in control systems engineer-ing and the Ph.D. in Information Engineeringfrom the University of Padova, Padova, Italy, in2009 and 2013. He is currently a post-doctoralassociate at University of Padova and ChiefOperating Officer at Statwolf Ltd.

He has been a visiting student at the Uni-versity of California, San Diego (2008-09), andat National University of Ireland, Maynooth(2012) and an Intern Researcher at Infineon

Technologies Austria AG, Villach, Austria (2011). During his studieshe has been awarded with IEEE-CASE Best Student Conference PaperAward (2011), IEEE/SEMI-ASMC Best Student Paper Award (2012)and IEEE-MSC Best Student Paper Award (2012). His research inter-ests include manufacturing data analytics, machine learning, gesturerecognition and partial differential equations control.

Andrea Schirru received the M.S. degree (cumlaude) in computer science and the Ph.D. inInformation Engineering from the University ofPavia, Pavia, Italy, in 2008 and 2011. He is cur-rently a post-doctoral associate at National Uni-versity of Ireland, Maynooth and Chief Technol-ogy Officer at Statwolf Ltd.

He has been an Intern Researcher at Infi-neon Technologies Austria AG, Villach, Austria(2010-2011), and during his studies he has beenawarded with the ICINCO Best Student Paper

Award (2011) and the Best Student Presentation at the Intel EuropeanResearch and Innovation Conference (2010).

Simone Pampuri received the M.S. degree incomputer science and the Ph.D. in Informa-tion Engineering from the University of Pavia,Pavia, Italy, in 2009 and 2012. He is currentlya post-doctoral associate at National Universityof Ireland, Maynooth and Chief Executive Offi-cer at Statwolf Ltd.

He has been an Intern Researcher at Infi-neon Technologies Austria AG, Villach, Austria(2011). His research interests include manu-facturing data analytics, machine learning and

sentiment analysis.

Sean McLoone (S’94, M’96, SM’02) received aMaster of Engineering degree with Distinctionand a Ph.D. degree in Control Engineeringfrom Queens University Belfast (QUB), Belfast,Ireland, in 1992 and 1996, respectively. He iscurrently Professor and Director of the EnergyPower and Intelligent Control (EPIC) ResearchCluster at QUB.

His research interests lie in the general areato data based modelling and analysis of dy-namical systems. This encompasses techniques

ranging from classical system identification, fault diagnosis, and sta-tistical process control to modern computational intelligence basedadaptive learning algorithms and optimization techniques. He is a PastChairman of the UK and Republic of Ireland (UKRI) Section of theIEEE.

Alessandro Beghi (M’06) received the laureadegree cum laude in Electrical Engineering in1989 and the Ph.D. degree in Control SystemsEngineering in 1993, both from the Universityof Padova, Italy. In 1994 he joined the Depart-ment of Information Engineering, University ofPadova, Italy, where he is currently an Asso-ciate Professor of Control Systems Theory.

He held visiting positions at universities andinternational research centers both in Europeand in the USA. He is a member of the IEEE

Control System Society, serving also as Associate Editor for the Con-ference Editorial Board and co-chair of the Technical Committee onPower Generation. He has worked on a wide range of control applica-tions, from control of fusion devices, guidance algorithms for virtualvehicles, to control of HVAC&R systems, Adaptive Optics systems, andSemiconductor Manufacturing processes. He is the author of more than130 publications in journals, books, and conference proceedings. Heis co-inventor of 5 International Patents on applications of advancedcontrol techniques.