543

1 INTRODUCTION

The maritime industry stands at the forefront of global

transportation, with its operational efficiency and

reliability directly influencing international trade and

economic stability [1]. However, as shipping

operations grow increasingly complex, so do the

challenges associated with maintaining the

performance of critical systems under dynamic and

often harsh operating conditions. These conditions

include fluctuating weather patterns, such as high

winds and rough seas, extreme temperatures that can

affect machinery performance, and variability in cargo

loads and fuel quality. Such factors not only introduce

significant stress on shipboard systems but also

demand robust solutions to ensure reliability and

safety. This complexity is further amplified by the

growing demand for sustainable practices, cost

reduction, and compliance with stringent

environmental regulations, compelling operators to

adopt innovative maintenance strategies [2].

In recent years, advancements in data acquisition,

real-time monitoring, and predictive analytics have

laid the groundwork for a paradigm shift in maritime

maintenance. Industry 4.0 principles [3] characterized

by enhanced connectivity, data-driven decision-

making, and automation, have transformed the way

systems are monitored and managed. Modern

integrated automation systems (IAS) enable the

recording of multivariable datasets with high-

frequency precision, offering unparalleled insights into

the operational state of vessels [4]. Despite these

technological strides, traditional monitoring

techniques often fall short in addressing the challenges

posed by highly correlated datasets, where the sheer

Enhanced Predictive Diagnostics for Naval Equipment:

Integrating MYT Decomposition for Advanced Process

Monitoring

D. Boullosa-Falces

, Z. Sanchez-Varela

, E. Urtaran Lavín

, D.S. Sanz

& S. García

University of the Basque Country UPV/EHU, Portugalete, Spain

University of Split, Split, Croatia

University of Cantabria, Santander, Spain

ABSTRACT: The competitiveness in maritime operations demands maintenance strategies that ensure high

reliability and availability at minimal cost. While predictive diagnostics have shown promise in detecting

deviations from optimal operating conditions, current methodologies often fail to effectively isolate and identify

the contributing process variables. This study introduces an enhanced predictive diagnostic approach that

integrates MYT (Mason, Young, Tracy) decomposition with traditional statistical monitoring techniques, such as

Hotelling's T² control charts. By applying this methodology to the auxiliary systems of a 284-meter LNG tanker,

we identified that the key variables driving process anomalies were Superheated Steam in Boiler 1 (Tn/h) and

Superheated Steam in Boiler 2 (Tn/h). These findings underscore the ability of the proposed method to detect

deviations before critical failures occur, providing ship operators with actionable insights to enable precise

maintenance scheduling, reduce operational costs, and prevent unscheduled downtime. The demonstrated

integration of MYT decomposition into predictive maintenance protocols highlights its potential to optimize

monitoring accuracy and decision-making in complex naval systems.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 19

Number 2

June 2025

DOI: 10.12716/1001.19.02.25

544

volume of information can obscure critical anomalies

and delay corrective actions [5].

To bridge this gap, advanced statistical tools and

multivariable analysis methods are becoming

indispensable in predictive maintenance frameworks

[6-8]. Some techniques such as time series are typically

used. Concerning times series, it was applied on a

research vessel at the Norwegian University of Science

and Technology (NTNU). Relevant variables were

selected, unnecessary information or noise was

removed, and essential characteristics of the problem

were extracted in order to reliably identify the vessel's

behaviour [9]. In relation to partial least squares a

statistical framework is developed to process the vast

amounts of navigation data acquired by the on-board

multi-sensor systems and an automatic reporting

system is created to monitor fuel consumption [10].

Among these, Hotelling’s T² control charts have

emerged as a robust technique for detecting deviations

in multivariate processes [11]. In [12] control of the

condition of the oil in the gears of the vessels was

analysed by means of Hotelling's T² statistic or in [13]

where the control of the machining process for

industrial components manufactured on conventional

lathe machines is monitored.

However, their utility is often limited by their

inability to pinpoint the specific variables responsible

for detected anomalies [14]. This limitation is

particularly critical in maritime systems, where

understanding the root cause of deviations is essential

for targeted maintenance and operational

optimization.

Unlike previous studies that have applied

Hotelling’s T² control charts or multivariate analysis

separately in maritime contexts [12], [14], this work

introduces a novel integration of Hotelling’s T² charts

with Mason-Young-Tracy (MYT) decomposition [15],

to enhance interpretability and diagnostic precision in

predictive maintenance systems. While Hotelling’s T²

charts are effective for identifying deviations in

multivariate data, they often fall short in isolating the

variables responsible for such deviations [14], a gap

directly addressed by the MYT methodology. To the

best of our knowledge, this is the first time that such an

integrated approach has been implemented and

validated using real high-frequency operational data

from an LNG tanker’s auxiliary boiler-turbine system.

The proposed framework not only detects early-stage

anomalies but also identifies their root causes with

clarity, offering a scalable and interpretable solution

that aligns with the growing need for data-driven,

Industry 4.0-aligned maintenance strategies in the

maritime industry [3], [10].

This study introduces an enhanced predictive

diagnostic framework that integrates Hotelling’s T²

control charts with Mason-Young-Tracy (MYT)

decomposition [15]. The MYT approach dissects

multivariable anomalies into their individual

components, enabling the precise identification of

variables contributing to deviations. By applying this

integrated methodology to the auxiliary boiler-turbine

system of a 284-meter LNG tanker, we demonstrate its

ability to detect early-stage anomalies, isolate their root

causes, and provide actionable insights for

maintenance planning.

The proposed framework addresses key challenges

in modern maritime operations, including the need to

manage the complexity of multivariable datasets and

the imperative to optimize maintenance interventions.

This paper not only validates the efficacy of the

methodology through a real-world case study but also

highlights its broader implications for advancing

predictive maintenance protocols in the maritime

sector. In doing so, it underscores the critical role of

data-driven diagnostics in enhancing system

reliability, reducing operational costs, and supporting

the industry’s transition toward more sustainable and

efficient practices.

By bridging the gap between anomaly detection

and root cause analysis, this study represents a

significant contribution to the evolving field of

predictive maintenance in the maritime industry,

offering a blueprint for future research and practical

applications in complex naval systems.

The primary objective of this study is to apply the

MYT (Mason, Young, Tracy) decomposition technique

in conjunction with Hotelling's T² control charts to a

real-world maritime context, specifically on the

auxiliary boiler-turbine system of a 284-meter LNG

tanker. This research aims to evaluate the effectiveness

of the proposed methodology in detecting operational

deviations at an early stage and isolating the specific

variables responsible for these anomalies. By doing so,

the study seeks to demonstrate the practical

applicability of this integrated approach for enhancing

predictive maintenance protocols, reducing

operational costs, and improving the reliability of

complex naval systems.

2 MATERIAL AND METHODS

The auxiliary boiler-turbine system of a 284-meter

LNG tanker serves as the foundation for this study,

designed to explore advanced predictive diagnostic

techniques in real-world maritime operations. This

system plays a critical role in maintaining the vessel's

operational efficiency, ensuring the continuous supply

of thermal and mechanical energy necessary for

propulsion and auxiliary functions. To achieve this,

key performance variables were monitored and

analyzed under carefully controlled conditions to

establish a robust framework for identifying deviations

from normal operations.

This section describes the ship's specifications, the

monitored variables, and the methodology employed

to create the Historical Database Set (HDS) as a

baseline for system behavior. The study's focus extends

beyond simple anomaly detection to understanding

the underlying causes of deviations using MYT

decomposition integrated with Hotelling's T² control

charts. This combined approach provides a powerful

diagnostic tool capable of isolating critical variables

responsible for process anomalies, offering actionable

insights for predictive maintenance.

2.1 System Description

The study was conducted on the auxiliary boiler-

turbine system of a 284-meter LNG tanker. The

characteristics of ship are listed in Table 1.

545

Table 1. Ship’s specifications.

Type of ship

LNG Tanker

Length overall

284 m

Breadth extreme

42.5 m

Draught

11.4 m

Gross tonnage

98478 Tons

Net tonnage

27143 Tons

Six variables were monitored: shaft power (kW),

boiler superheated steam production (Tn/h for two

boilers), outlet temperature of superheated steam (in

both boilers, °C), and daily fuel consumption (m³/day).

Data were collected using the ship’s integrated

automation system over two voyages, each lasting 12

days, under normal operational conditions: vessel

speed between 10 - 13.5, average engine room

temperature of 27-32°C and average ambient

temperature of 16 - 32°C. The voyages covered routes

from Malta to Trinidad. The process is show in figure 1.

Figure 1. Process system.

2.2 Data Purging and Historical Database Creation

To build the historical database (HDS), the n=77 of the

preliminary data base, estimated for the multivariate

process were monitored using Hotelling's T² chart [16]

following the expression (1).

( ) ( )

T X ´ S X

−

= − −

(1)

where:

( )

; ;;=

i i i iP

X X X X

preliminary data,

, is the

vector of sample means y

−

, the inverse of the

covariance matrix.

Depending on the circunstances, the T² statistic can

be described by three different probability functions:

the Beta, the F and the chi-square distributions. When

µ,σ are estimated, the Beta distribution is used in the

purging process of a Phase I operation, whereas the F

distribution is used in the development of the control

process in a Phase II operation. When µ,σ are known,

the chi-square has applications in both Phase I and

Phase II operations [17].

During the purging process, the atypical

observations of the process, obtained in the generation

the preliminary database, were detected and

eliminated, in order to avoid possible errors in results.

In this case, with a mean and standard deviation µ,σ

estimated, for the calculation of the UCL (Upper

Control Limit), the β distribution of α=0.05, was used

in the process of purging outliers from those

observations that were outliers in the process. The level

of α is typical value for this type of process.

The UCL was determined by the following

expression:

( )

α; ; n p 1 /2

UCL β



−−







−









(2)

where:

n: Is the size of the data set, p: Number of variables,

β{α;p/2;(n-p-1)/2}, is the αth, quantile of the beta

distribution, β{p/2;(n-p-1)/2}

If the value of T², which was monitored for an

observation, exceeded the UCL, the observation was

removed from the preliminary database.

With the remaining observations, we calculated a

new vector of means and covariance matrix and again,

outliers, produced by errors in the measurements, were

detected and eliminated, this process was repeated,

until a homogeneous set of observations was obtained.

The final data set was the (HDS), from the normal

operation mode of the process, consisting of 54

samples.

The premilinary data base, consisting of 77 samples

is showed in Table 2. In Table 3, the detected outliers

are represented in each step until the HDS was

obtained.

Table 2. Part of Preliminary data base.

1-shaft power (kW)

2- superheated steam in Boiler 1 (Tn/h)

3- superheated steam in Boiler 2 (Tn/h)

4- outlet temperature of superheated steam in bolier 1 (°C)

5- outlet temperature of superheated steam in bolier 2 (°C)

6- daily fuel consumption (m³/day)

8009

25.9

25.6

514

510

162

8232

26.1

27.2

514

510

162

8085

28.5

28.4

514

510

162

8126

27.7

27.8

515

512

168

7841

27.5

515

512

168

7685

27.5

27.4

515

512

168

8622

28.8

515

512

168

8340

27.1

27.4

515

512

168

8469

26.4

26.6

515

512

168

8520

26.5

26.7

514

496

164

8286

27.3

27.6

514

496

164

8380

26.4

26.6

514

496

164

8287

26.4

26.7

514

499

168

8461

26.9

27.2

514

499

168

8358

26.8

514

499

168

8490

27.2

514

499

168

Table 3. Steps to get the HDS.

No. of observations

UCL

No. outliers detected

12.043

11.995

11.959

11.918

11.895

11.871

11.858

11.845

11.832

11.803

546

2.3 Process Control and MYT decomposition application

In this step, it was tested to see if a new entry of data

generated a signal, with respect to the historical data

set (HDS). Considering a continuous steady-state

process where the observation vector are independent

and the parameters of the underlying normal

distribution are unknown and must be estimated. We

assume the process is being monitored by observing a

single vector of 23 new valid samples acquired after

having analyzed them according to the criteria of the

normal condition of the operation.

The T² values, for the new data input, were

calculated, following the expression (3).

( ) ( )

T X ´ S X

−

= − −

(3)

where

is the vector of sample means and

−

the

inverse of the covariance matrix, obtained from the

HDS and

, the new data entry.

( )

; ; ';=

i i i ip

X X X X

. Here, the T² statistic [18]

follows the F distribution. For the calculation of the

UCL (Upper Control Limit), the F distribution of

α=0.05, for Type II errors, was used [18]. The level of α

can be variable, making more or less strict the method.

The chosen alpha level is normally used in industrial

processes. The UCL is computed as:

( )( )

( )

 

α;p; n p

p n 1 n 1

UCL F

n n p

−



+−





−





(4)

Where p, is the number of variables, n, is the size of the

HDS and F{



;p;(n-p)} , is the αth, quantile of F{p;(n-p)}.

The values of T² which exceeded the UCL, were

declared as signals and this concluded that the

observation was out of rank with respect to the mode

of normal operation of the process.

Once the T² statistical detected samples which were

out of rank in the process from normal operating

conditions, the MYT decomposition was used [19, 20]to

identify the variables with more weight, responsible

for state out of rank for each sample.

The general decomposition for “p” variables of the

Hotelling´s T² statistic, follow the equation:

2 2 2 2 2 2 2 2

1 2.1 3.1,2 4.1,2,3 .1, , 1 1 1.1, ,

−

 − + −−−

= + + + ++ =



P P j j

T T T T T T T

(5)

The final

value,

, is Hotelling´s statistic for

the first variable. It reduces to the square of the

univariate t statistic for the initial variable:

( )

X −

(6)

where,

and S1 is the mean and standard deviation

of variable X1.

The statistic

.1, , 1−PP

is the p

component of the

vector Xi adjusted by the estimates of the mean and

standard deviation of the conditional distribution of XP

given X1, X2, …, Xp-1. It is given by

( )

P.1, , P 1

.1, , 1

p.1, ,p 1

−

−

(7)

where:

( )

P.1, , P 1 P p

X X b ´( X )

−

−

= +  −

is the sample mean of n observations on the p

variable,

−

XX xX

is a (p-1) – dimensional vector estimating

the regression coefficients of the p

variable regressed

on the first p-1 variables,

2 2 ´ 1

.1, , 1

−

−

=−

p p X xX

XX xX

S S S S

and

´2







XX xX

xX X

3 RESULTS

T² values were calculated according to Eq. (3), for

each one of the 23 new observations, and they were

monitored in a control chart, according to Fig. 2 with a

upper control limit previously calculated, according to

the expression Eq. (4), valued in UCL = 15.4833, with

α=0.05., to detect changes significant in the normal

operation condition.

The control chart shows that in the observation 5,

there is a value, over the UCL, which indicates, that in

that interval of time, the process had a deviation from

its normal operation mode.

This situation does not mean that the process was

failing, but that at that moment it deviated from its

normal operating conditions. But if such a negative

trend is repeated over time, it would be an indication

of the need to take corrective maintenance action to

restore process operability.

Figure 2. Control Chart.

In the next stage, it was identified which were the

variables that had produced the state out of rank of

each observation.

Through MYT decomposition technique, each T²

value was decomposed for each one of the signals to

detect, which was the variable which had contributed

most strongly to the state out of rank of process, the

unconditional terms was calculated following Eq. (6),

and the conditional terms were calculated following

Eq. (7), the decomposition is listed in Table 4. It shows

that the variables (2 and 3) Superheated steam in Boiler

1 (Tn/h) and Superheated steam in Boiler 2 (Tn/h),

caused the state out of rank of process.

547

Table 4. MYT Decomposition.

No. Observation

No. Variable

Variable

Superheated steam in Boiler 1

(Tn/h)

Superheated steam in Boiler 2

(Tn/h)

The variables related to superheated steam

production in both boilers serve as key indicators of the

system's thermal and energy performance. These

variables are fundamentally connected to the

equilibrium between energy demand and the system’s

capacity to fulfill that demand under normal

operational conditions.

Simultaneous deviations in both variables often

point to a potential interdependence or imbalance in

the coordinated operation of the boilers, which can

compromise the system's ability to maintain stable

performance. Superheated steam production plays a

critical role in energy transfer to the turbine system,

and any deviation from established production limits

can lead to efficiency losses and destabilization of the

overall system.

The proposed method proved effective in detecting

observations that deviated from the normal process

conditions. For the ship’s engineers, identifying that

the process was out of rank provided an early warning,

enabling them to remain vigilant and prepared to

address significant changes in the system.

Additionally, the application of MYT

decomposition facilitated the identification of the

specific variables causing the deviation—namely,

superheated steam production in Boiler 1 (Tn/h) and

Boiler 2 (Tn/h). This insight was instrumental for the

ship’s engineers, as it allowed them to focus on

correcting the deviations and restoring the process to

its normal operating conditions.

Traditional monitoring methods operate on a

fundamentally different principle: they rely on

univariate thresholds and detect anomalies only after a

specific variable exceeds its acceptable range. In such

reactive systems, no early warning is available, and the

failure must occur—or be imminent—before any

corrective action can be triggered. Conversely, the

methodology proposed here identifies multivariate

deviations before any individual variable breaches its

limits, enabling earlier detection and diagnosis. This

predictive capability underscores the utility and

effectiveness of the MYT-enhanced Hotelling’s T²

approach, offering significant advantages over

conventional techniques in managing complex

systems.

4 CONCLUSIONS

This study has demonstrated the effectiveness of

integrating MYT decomposition with Hotelling T²

control charts for advanced monitoring of naval

systems. This methodology not only enabled the early

detection of deviations in the operational performance

of the boiler-turbine system of a 284-meter LNG tanker

but also precisely identified the variables responsible

for these anomalies, providing a robust framework for

predictive maintenance. The combination of advanced

statistical tools and multivariable decomposition

techniques offers significant advantages for managing

complex systems, including early anomaly detection,

which allows deviations to be identified before they

manifest as critical failures, providing sufficient time to

implement corrective actions. Moreover, the MYT

decomposition highlighted the variables with the

greatest impact on the out-of-range state, facilitating a

more focused and efficient diagnosis and enabling

resource optimization by prioritizing maintenance

interventions based on the responsible variables,

thereby reducing the need for generalized inspections

and minimizing operational costs.

The ability to identify specific deviations in key

variables, such as superheated steam production in

both boilers, demonstrates the practical value of this

approach in the maritime industry, underscoring the

importance of integrating advanced monitoring tools

into maintenance protocols, especially in systems

where operating conditions are dynamic and failures

can have significant consequences. Additionally, the

proposed approach supports the transition toward

more proactive, data-driven maintenance strategies,

aligning with Industry 4.0 objectives and promoting

greater reliability and operational efficiency in ships.

Advancing the current state of knowledge, this

work operationalizes an integrated diagnostic

approach that not only detects anomalies but also

explains them in a multivariate context. The

application of MYT decomposition within the

maritime domain—particularly in combination with

Hotelling’s T² control charts and using real onboard

datasets—has not been previously demonstrated in

such a comprehensive manner. By bridging the

interpretability gap in multivariable monitoring, this

contribution offers a methodological innovation with

immediate applicability for condition-based

maintenance strategies, reinforcing the novelty and

practical value of the proposed framework in

enhancing reliability and operational intelligence in the

maritime sector.

This work validates the utility of MYT

decomposition as a complementary tool to traditional

techniques in multivariable monitoring of maritime

systems. The findings highlight its potential to

optimize decision-making, reduce operational costs,

and enhance the reliability of vessels in a highly

competitive environment. In conclusion, the proposed

methodology represents a significant advancement in

monitoring and predictive maintenance strategies for

naval systems. Its ability to manage the complexity of

multivariable data and provide accurate diagnostics

positions it as a key tool for improving operational

efficiency in the modern maritime industry.

REFERENCES

[1] I. Ali, "The world's maritime industry in the 21st century:

Challenges, expectations, and directions," South East

Asian Marine Sciences Journal, vol. 2, (2), pp. 64–75, 2025.

[2] A. Sardar, "No title," Improving Safety and Efficiency in

the Maritime Industry: A Multi-Disciplinary Approach,

2024. .

[3] T. Zonta, C. A. Da Costa, R. da Rosa Righi, M. J. de Lima,

E. S. Da Trindade and G. P. Li, "Predictive maintenance in

548

the Industry 4.0: A systematic literature review," Comput.

Ind. Eng., vol. 150, pp. 106889, 2020. .

[4] M. Sadat Lavasani, N. Raeisi Ardali, R. Sotudeh-

Gharebagh, R. Zarghami, J. Abonyi and N. Mostoufi, "Big

data analytics opportunities for applications in process

engineering," Reviews in Chemical Engineering, vol. 39,

(3), pp. 479–511, 2023. .

[5] I. González and I. Sánchez, "Variable selection for

multivariate statistical process control," Journal of

Quality Technology, vol. 42, (3), pp. 242–259, 2010. .

[6] S. Kapp, J. Choi and T. Hong, "Predicting industrial

building energy consumption with statistical and

machine-learning models informed by physical system

parameters," Renewable and Sustainable Energy

Reviews, vol. 172, pp. 113045, 2023. .

[7] S. Lipovetsky, "Multivariate statistical methods: A brief

review on their modifications and applications," Model

Assisted Statistics and Applications, vol. 17, (2), pp. 145–

147, 2022. .

[8] S. Lipovetsky and V. Manewitsch, "Analytical Closed-

Form Solution for General Factor with Many Variables,"

Journal of Modern Applied Statistical Methods, vol. 18,

(1), pp. 2, 2020. .

[9] A. Abbasi Hoseini and S. Steen, "Multivariate time series

data mining in ship monitoring database," Journal of

Offshore Mechanics and Arctic Engineering, vol. 139, (6),

pp. 061304, 2017. .

[10] C. Capezza, S. Coleman, A. Lepore, B. Palumbo and L.

Vitiello, "Ship fuel consumption monitoring and fault

detection via partial least squares and control charts of

navigation data," Transportation Research Part D:

Transport and Environment, vol. 67, pp. 375–387, 2019. .

[11] R. L. Mason and J. C. Young, "Why multivariate

statistical process control?" Qual. Prog., vol. 31, (12), pp.

88, 1998. .

[12] M. Henneberg, B. Jørgensen and R. L. Eriksen, "Oil

condition monitoring of gears onboard ships using a

regression approach for multivariate T2 control charts," J.

Process Control, vol. 46, pp. 1–10, 2016. .

[13] K. Joshi and B. Patil, "Multivariate statistical process

monitoring and control of machining process using

principal component-based Hotelling T2 charts: A

machine vision approach," International Journal of

Productivity and Quality Management, vol. 35, (1), pp.

40–56, 2022. .

[14] S. Lee, "Identification of the out-of-control variable based

on Hotelling's T 2 statistic," The Korean Journal of

Applied Statistics, vol. 31, (6), pp. 811–823, 2018. .

[15] R. L. Mason and J. C. Young, Multivariate Statistical

Process Control with Industrial Applications. SIAM,

2002.

[16] R. D. Pangesti, A. A. Suhaimi, E. Sunandi and I. R. A.

Islami, "Control Chart of T² Hotelling on Quality Control

Activities of Crude Palm Oil (CPO) at PT Cipta Graha

Garwita, Seluma Regency, Bengkulu Province," Journal

of Statistics and Data Science, vol. 3, (1), pp. 21–26, 2024. .

[17] R. L. Mason, Y. Chou, J. H. Sullivan, Z. G. Stoumbos and

J. C. Young, "Systematic patterns in T 2 charts," Journal of

Quality Technology, vol. 35, (1), pp. 47–58, 2003. .

[18] R. L. Mason, N. D. Tracy and J. C. Young, "A practical

approach for interpreting multivariate T 2 control chart

signals," Journal of Quality Technology, vol. 29, (4), pp.

396–406, 1997. .

[19] A. C. Rencher, "The Contribution of Individual Variables

to Hotelling's T 2, Wilks' Λ, and R 2," Biometrics, pp. 479–

489, 1993. .

[20] R. L. Mason, N. D. Tracy and J. C. Young,

"Decomposition of T 2 for multivariate control chart

interpretation," Journal of Quality Technology, vol. 27,

(2), pp. 99–108, 1995.