Proceedings of the 5th International Conference on Integrity-Reliability-Failure, Porto/Portugal 24-28 July 2016

Editors J.F. Silva Gomes and S.A. Meguid

Publ. INEGI/FEUP (2016)

-853-

PAPER REF: 6280

MEWMA CONTROL CHART FACTORS WHEN APPLIED TO

EQUIPMENT

Suzana Lampreia1(*)

, Valter Vairinhos2, José Requeijo

3, Rui Parreira

4, Vitor Lobo

4

1CINAV - Mechanical Engineer Department, Alfeite-Almada, Portugal

2CINAV, PORTUGAL.

3UNIDEMI, Faculty of Science and Technology from the Universidade Nova of Lisbon,

Mechanical and

Industrial Engineer Department, Caparica, Portugal 4Naval Academy, CINAV

(*)Email: suzanalampreia@gmail.com

ABSTRACT

MEWMA control chart may be a useful tool (Niaki and Ershadi, 2010) for online process

control (Messaoud et al, 2008). MEWMA can also be used for online equipment control

(Lampreia, 2013) as an instrument in the decision process to intervene the equipment. In this

study, some of those factors will be identified and tested, showing its influence on the charts;

it is shown that the chosen factors can have a significant influence on chart performance.

Keywords: MEWMA control charts, equipment monitoring, condition based maintenance.

INTRODUCTION

Multivariate Exponentially Weighted Moving Average (MEWMA) control charts are an

important tool for industrial process control. In condition based maintenance, several

statistical methods have been applied. In this paper we propose the use of modified MEWMA

(MMEWMA) control charts for online equipment control.

Field data from an electric support plant will be used to illustrate and support the claim of

applicability of multivariate control charts for online equipment monitoring, the effects of

selected factors being graphically illustrated.

EQUIPMENT MONITORING WITH MMEWMA

If we pretend to integrate multi-variables in a study, on phase 1 the T2 chart can be used. In

this article we will test the MMEWMA applicability considering various factors values.

Phase 1 - T2 Control Charts

To use the T2

control chart we must have more than two variables. Before the chart be

applied, enough data should be collected, at least 200 (for more information Pereira &

Requeijo (2012) should be consulted), and then the variables should be analyzed, to see if it

are normal and independent.

If data is independent we have ij j ijX µ ε= + , with ijX the observation i for variable j,

jµ the

process mean for the variable j, ijε are iid normal random variables with mean zero.

(Lampreia et Al, 2013)

Symposium_9: Quality, Maintenance and Lean Approach in Industry

-854-

The mean ( jX ), the variance ijS

and the covariance jhS are the equipment functioning

parameters that are given by:

( )1 2, , ,T

pX X X X= …

11 12 13 1

21 22 23 2

1 2 3

. . . .

. . . .

. . . .

p

p

p p p pp

S S S S

S S S S

S

S S S S

… …

… = …

…

…

(1)

The T2 control charts are based on the statistic in the next equation:

( ) ( ) ( )2 1T

k kkT X X S X X−= − − (2)

The lines that are crucial to the T2 charts interpretation are defined by the Center Line (CL), 0,

and the Upper Control (UCL), ( )2

; /2;( 1)/2

1p m p

m

mαβ − −

− . The ; /2;( 1)/2p m pαβ − − represents the right percentile,

for a probabilityα, with the parameters / 2p ,( 1) / 2m p− − . (Lampreia et Al, 2012)

In this study for autocorrelated data, the ARIMA modell (Autoregressive Integrated Moving

Average) (p, d, q) will be used. In phase 1 to calculate the residues the STATISTICA program

are used. The T2 charts for phase 1 are built with the residues. The phase 2 are built with the

predicted values.

The autocorrelation is analyzed by studying the Autocorrelation Function (ACF) and Partial

Auto-Correlation Function (PACF), and to take conclusions the estimated autocorrelation

function (EACF) is compared to the autocorrelation function (ACF) and the estimated partial

autocorrelation function (EPACF) with the partial autocorrelation function (PACF). (Pereira

& Requeijo, 2012)

The data from an equipment follows a ARIMA(p,d,q) model if td X∇ follows ARMA(p,q)

model. The model defined by ARIMA (p,d,q) is:

( ) d

p t q tΦ B X Θ (B)ε∇ = =

( ) 2

1 2(1 )pp pB B B Bφ φ φΦ = − − −…− (3)

( ) 2

1 2(1 )q

q qB B B Bθ θ θΘ = − − −…−

1t

t

XB

X

−= and 1t t

t

X X

X

−−∇ =

(4)

The residues can be estimated by ˆt t te X X= − , where ˆ

tX is the expected value for the period t.

The equipment parameters mean is estimated by 1

( )1

p

jj

E Xξ

µφ

=

= =− ∑

and ( )E X µ= when the

process is modeled by AR(p) or MA(p).

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

-855-

Phase 2 - Modified MEWMA

The MMEWMA control charts, to control the mean are built based on the 2T defined

parameters:

12 ´

i i iZT Z Z

−= ∑ (5)

Where for independent data: 1( )i i iZ RX I R Z −= + − with 0 0Z =

The I is the identity matrix and1 2( , , , )pR diag λ λ λ= … , where

jλ is a weighted constant for j (

1, 2, ,j p= … ) variable. Usually1 2 pλ λ λ λ= = … = = , when this happen, iZ it’s defined by:

( ) 11i i tZ X Zλ λ −= + − (6)

For autocorrelated data it will be use:

1( ) (1 )i i L tZ e T Zλ λ −= − + − 1

1( ( ) (1 ) )i L te T Zλ λ−−Σ − + − (7)

A observation is out of control when 2

iT H> , where H is the control limit.

The values of H for 200In ControlARL = and different values of ( )δ µ are:

2, 4,6,10,15(0,5;1,0;1,5;2,0;3,0)p = and (0,05;0,10;0, 20;0,30;0, 40;0,50;0,60;0,80)λ .

(Pereira & Requeijo, 2012)

The MMEWMA chart shows a complex interaction between its variables, and it is more

sensitivity than the traditional charts, considering small shifts.

METHODOLOGY

� In phase 1, 200 individual observations must be taken, and then data independence

must be study, comparing EACF and the EPACF.

� If data are autocorrelated, the ARIMA model should be applied, and the T2 chart is

executed for the residues, if not the original data are used.

� In the Phase 2 the MEWMAM chart is used to monitor the equipment. The registered

values must be used if the variables is independent, if not the predicted values are

used.

� The limits of the fabricant must be taken in account, TLStandard.

� Rules to act:

� Execute an intervention action if 5 consecutive points are above the AL.

� Proceed to a maintenance intervention when 3 consecutive points above

UCL are observed.

Symposium_9: Quality, Maintenance and Lean Approach in Industry

-856-

Fig.1 - Methodology

RESULTS

Table 1 is a snapshot of the field data from the electric plant, cell batteries. Based in this data,

the autocorrelation was study.

Table 1 – Electric data

Elem (1) Elem (2) Elem (3) Elem (4)

2,057 2,024 1,999 1,983

2,058 2,023 1,997 1,988

2,059 2,02 1,996 1,989

2,06 2,021 1,993 1,99

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

-857-

It was shown that the option for some factors is essential for a credible online monitoring.

Even with the adequate factors the results must be complemented with other non-destructive

tests.

Phase 1

To begin the study of the considered variables the normality and the independent must be

tested. The three variables are independent, so in phase 1 we don´t need to apply the ARIMA

model. In figure 3 we can see the variable 1 independence study. It is important to refer that if

only one variable is autocorrelated, to apply the T2 chart all variables should change for

residues, and in phase 2 the predicted values should be used.

Fig. 2 - Var 1: autocorrelation study

The T2 chart in figure nr 3 represents data stability, so we can pass to the phase 2.

Fig. 3 - Phase 1: T2 with 3 variables

Phase 2

On phase 2 the limits for the factors considered, ARL=500 and ARL=100 for δ=0.5; 1.0; 1.5,

are UCL=2.7 and AL=2.1.

In figure 4 none observation is registered, because none anomaly simulation was introduced.

Symposium_9: Quality, Maintenance and Lean Approach in Industry

-858-

Fig. 4 - Phase 2: None Progression

On figure 5 we have observation registration, but none indicates the need of intervention, the

observations nr 18 and 19 are above the AL.

Fig. 5 - Phase 2: 1

st Progression

On figure 6 there is a need of investigation of eventual anomaly on observation nr 48.

Fig. 6 - Phase 2: 2

nd Progression

Proceedings of the 5th International Conference on Integrity-Reliability-Failure

-859-

For the third progression we will present two variations on the chosen factor that traduces the

change in the limits values. In figure nr 7 the factors are the same as in the other progressions.

For this factor we need an investigation action on observation nr 13 and 20, and a

maintenance action on observation nr 11. So mathematically, we need maintenance before an

investigation. When the sensors values fluctuate rapidly, we must observe the data tendency,

and always complement the diagnosis with other non-destructive tests.

Fig. 7 - Phase 2: 3

rd Progression

In table 2 we can see the limits presented based on two different factors.

Table 2 - Limits for different factors

δ

UCL1 UCL2 AL1 AL2

1,5 1 1,5 1

λ 0,25 0,13 0,34 0,18

K 3 2,9 2,5 2,3

In figure 8, we can see that different factors traduce different limits. In this case the limits are:

Fig. 8 - Phase 2: 3rd

Progression for two other factors values

Symposium_9: Quality, Maintenance and Lean Approach in Industry

-860-

With different factors, in this case we have higher limits, so the need of intervention is

delayed, in this case we need investigation and maintenance action on the observation nr 20

for limits 1, and coincidentally for limits 2 the same.

CONCLUSIONS

The equipments conditioning monitoring can be made with statistical methods. The statistical

process control with adaptation to equipment can be used in a monitoring system.

If only one or two variables are autocorrelated, all variables under study should be

transformed in residues using the STATISTICA program in way to apply the T2 chart.

The MMEWMA control charts can be suitable for use in control monitoring.

Different factors on MMEWMA control charts can traduce different sensibility. We must

choose those that suit the monitoring object.

The use of these statistical methods can help planning an investigation and maintenance

intervention. And these can conduce to a lean maintenance system where the equipment had

maintenance when it is needed, and its state is always known.

ACKNOWLEDGMENTS

Portuguese Naval School and CINAV are kindly acknowledged for the use of the machinery

workshop and also for the fruitful collaboration of the Faculty of Science and Technology

from the Universidade Nova of Lisbon.

REFERENCES

[1]-Niaki S, Ershadi M. Economic and economic-statistical designs of MEWMA control

charts-a hybrid Taguchi loss, Markov chain, and genetic algorithm approach. In International

Journal Adv. Manuf. Technology, 2010, 48, p. 283-296.

[1]-Messaoud A, Weihs C, Hering F. Detection of chatter vibration in a drilling process using

multivariate control charts. In Elsevier – Science Direct: Computational Statistics & Data

Analysis, 2008, 52, p. 3208-3219.

[1]-Lampreia S, Requeijo J, Dias J, Vairinhos V. Equipment condition monitoring with an

application of MEWMA control charts and others charts. In ICOVP2013, September 2013.

[1]-Pereira Z L and Requeijo G , Qualidade: Planeamento e Controlo Estatístico de Processos

(Quality: Statistical Process Control and Planning), FCT/UNL Foundation Editor, 2012,

Lisboa.

[1]-Lampreia S, Requeijo J, Dias J, Vairinhos V. T 2

Charts Applied to Mechanical

Equipment Condition Control, International Conference on Intelligent Engineering Systems

2012-INES2012. Caparica, June 2012.