Management Analysis of Industrial Production Losses by the Design of Experiments, Statistical Process Control, and Capability Indices

doi:10.4236/ojbm.2014.21009

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Open Journal of Business and Management, 2014, 2, 65-72

Published Online Janu ary 2014 (http://www.scirp.org/journal/ojbm)

http://dx.doi.org/10.4236/ojbm.2014.21009

Management Analysis of Industrial Production Los ses by

the Design of Experiments, Statistical Process Control, and

Capability Indices

Djida Bounazef1,2, Smain Chabani1, Abdelhafid Idir1, Mokhtar Bounazef3

1HEC, Commercial Graduate School of Algiers, Algiers, Algeria

2Abderrahmane Mira U niversity of Bejaia, Bejaia, Algeria

3Djillali Liabes University of Sidi Bel Abbes, Sidi Bel Abbes, Algeria

Email: dji da.boun [email protected], [email protected], [email protected], Bounazef@yah oo.com

Received November 21, 2013; revised December 23, 2013; accepted J anuary 10, 20 14

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accor-

ABSTRACT

The machine stops caused by various breakdowns, rupture of raw materials, production changes, scheduled

maintenance and stops related to human resources management generate an important production loss in the

company. Our ca se study is done in a company t hat manufact ures polyethylene pipes with eig ht production lines.

They stop frequently because they undergo external control factors and noise factors. The method of experi-

mental design that relies on statistical surveys is applied to production loss allows us to observe the action of each

factor on the loss of productio n and t heir int era cti ons of these fa ct ors c ombined in pa irs o n this pro cess. Analy sis

of results shows the dominance of controllable or uncontrollable factor on the loss of production. This is illus-

trated by response surfaces and ISO responses lines were derived by mathematical modelling. Solutions are

proposed to improve continuous production, reduce waste and scrap and therefore increase profitability of

company.

KEYWORDS

Design of Experiments; Production Losse s; Response Surfaces; Polynomial Modelling;

Integrated Management System

1. Introduction

The reduction of industrial wa ste is the major preoccupa-

tion of an integrated management system [1,2] which

includes the environmental management system [3], the

system of qualit y management [4,5] and the manage ment

system of health, security and work [6,7]. These sys-

tems are applied within the company following the re-

quirements of ISO 9001:2000 code 4, until 8.5.3, of ISO

14001:2004 and OHSAS 18001:2007 to achieve optimal

production by minimising work stops caused by various

technical and operational reasons. This integrated mana-

geme nt s ystem [8 -10] is ap plied to the production lines at

the be gi n nin g when checkin g the quality of raw materials

until the end when stor ing fini shed pr od ucts to contribute

in reducing production losses and obtaining finished

quality products. For this, the checks are carried out to

the quality of raw materials, during the production proc-

ess, for finished products and after handling and storage.

Howeve r, the implementation of integrated management

system is not sufficient i n itself, in parallel it is necessar y

to reduce production stops caused by mechanical and

electrical problems, by human resour ce s ma na ge me nt , by

the supplies disruption of raw materials and others. To

know the influence of each breakdown reason of ma-

chinery at each production line, a data record has been

established for a period of one year. These causes were

grouped into 3 categories that encompass these machine

stops into the same types. These categories are the acci-

dental stops, the downtimes due to machine maintenance

and human resource management and the third is stops

due to raw material and finished products. The stops are

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D. BOUNAZEF ET AL.

estimated in work ho urs whereas the loss of production is

calculated as a percentage relative to maximum produc-

tion. The three factors of production stops act simulta-

neously on the loss of production. The application of the

met hod of design of experiments shows how each factor

acts on the loss of production by a mathematical model-

ling and therefore what measures should be taken to

avoid this phenomenon.

2. Statistical Reports of the Causes of

Production Stops

Modelling by design of experiments method analyses the

continuous production process of polyethylene pipes by

measuring ca uses of production losses (waste) caused b y

the steering factors and noise factors. The causes of ma-

chines downtimes that increase the percentage of produc-

tion loses (inducing the waste) are defined by three pa-

rameters on the Ishikawa diagram (Figure 1).

The production process is composed of eight inde-

pendent production lines; their stops are caused sepa-

rately by the same reasons and therefore act on produc-

tion losses (lack of production).

Table 1 shows the distribution of hours of production

losses by types and pr o d uction lines. The accidental stops

are designed by X1, the scheduled stops are designed by

X2 and the stops due to raw material and finished prod-

ucts are designed by X3. Table 1 is called mat rix of ex-

peri men ts, it contains column 6 that means losses of

production expressed in percent. They designate the re-

sponses Y. We see that the line E records the hi gh num-

bers of hours of accidental stops with 2731.83 hours and

human resources management stops with 1085.67 hours,

but it is the line H that has the high number of Stops due

to raw material and finished products with 9703.75 hours.

The greatest loss of production is recorded on line E with

66.18% compared to optimal production. T his is the line

that stores the mos t breakdowns and stops. However, it is

the line C that has the smallest losses of production with

20%.

3. Phenomenon Analysis of Machines Stops

by Design of Experiments Method

The loss of industrial production caused mainly by dif-

ferent stops responds to a mathematical law in polyno-

mial form. This polynomial is a sum of monomials that

are composed of coefficient ai (called parameter effect)

multiplied b y the value of the parameter designated b y xi.

In our study, x1 is letter that represents accidental stops,

x2 is letter that represents maintenance and human re-

sources management stops, and x3 repre sents sto p s due t o

raw material and finished products. In the polynomial,

there are monomials that designate the interactio ns be-

tween the parameters that influence the result; these pa-

rameters are appointed by xixj and

(i,j=1,2,3); they

must be multiplied b y the valu e of the effect aij. This sum

of these monomials represents the response “y” i.e. the

loss of production:

011223312 1 213 1 3

222

23 2 311122 2333

ya axax axaxx axx

axxaxaxax

=+++ ++

+ +++

(1)

In the expression 1, the parameters values are coded

values. Generally they are coded because their units and

their scales tha t affect the response “y” are different. For

each parameter, we denote by (−1) the minimum value,

and by (+1) the maximum value; the intermedia te values

are calculated by the following formula:

min max

max min

xuu



−



=−







(2)

where: Umin is minimal value of parameter, Umax: is

maximal value of parameter, Ui is value to be encoded,

and xi is coded value. Table 2 shows these coded values.

The matrices calculation allows us to ob tain the effects

values ai of parameters b y forming 10 diffe rent equa ti ons

from equat ion 1 by replacing the xi parameters by va lues

from Table 1, we could obtain the 10 coef ficients ai,j by

the followin g formula:

( )

a XX XY

−

(3)

Substitutin g the values of ai,j into Equation (1), the

production losses caused by three types of stops is mod-

elled by the following expression:

12 3

1213 23

222

123

37.8259 6.819691.903992.03238

1.30382 8.78769 2.8691

1.422862.72951 0.44013

yxx x

xxxx xx

xxx

=+++

+−−

−++

(4)

4. Results Interpretation

The interpretation is subdivided in two essential parts,

the first consists to analyse causes of production stops of

8 lines of production using design of experiments method,

while the second consists to analyse waste generated by

frequency of production stops using statistical process

control.

5. Analysis of Production Stops Effects by

Experiments Design Method

Equation (4) allows us not only to find the real loss val-

ues of production “y” listed in Table 2, but other values

included b et ween the maximum and minimum losses.

This is a predictive and descriptive model. T his is shown

by the estimators of adjusted descriptive quality

adjust

and predictive quality Q2 of model. Both

adjust

and Q2

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D. BOUNAZEF ET AL.

Figure 1 . Stops due to raw material and finished pro ducts .

Table 1. Hours of production l osses per line.

N˚ Li nes Accidental stops

[H] (X1)

Maintenance and human

resources management stops

[H] (X2)

Stops due to raw material and

fin ished pr oduc ts

[H] (X3)

Produ ction losses

[%] (Y)

1 Li ne A 220.8 798.92 988.08 2 2.49

2 Line B 1692.8 844.08 1048 40

3 Line C 153.67 815.75 795.08 20

4 Li ne D 1891.75 669.42 1291.83 43.27

5 Li ne E 2731.83 1085.67 2074.75 66.18

6 Line F 1393.5 876.92 1515.58 42.52

7 Li ne G 741.88 859.67 779.17 26.74

8 Li ne H 1690.33 795.61 9703.75 41.26

Table 2. Coded values of several st ops of machines.

N˚ Li nes Coded accidental stops

(X1)

Coded maintenance and human

resources management stops

(X2)

Coded values of stops due to raw

material and finished products

(X3)

Produ ction losses

(Y)

Li ne A

−0.9479241

−0.37777778

−0.95318323

−0.89216111

2 Li ne B 0.19397555 −0.16079279 −0.93975515 −0.13382417

3 Li ne C −1 −0.29691291 −0.99643457 −1

4 Line D 0.34831042 −1 −0.8851128 0.00779558

5 Line E +1 +1 −0.70 966029 +1

6 Li ne F −0.03820554 −0.003003 −0.83497039 −0.02468601

7 Li ne G −0.54369783 −0.08588589 −1 −0.70809874

8 Line H 0.19205945 −0.39368168 +1 −0.07925509

values are numbers usually between ‒∞ and 1. Values

close to 1 for both

adjust

and Q2 indicate very good

model with excellent predictive result. In our case

adjust

0.903R=

and Q2 = 0.863. The first estimator re-

flects the co ntribution of the model in the restitution of

the observed response and the second estimated coeffi-

cient reflects the ability of the model to predict res ponse

without making statistical measurements or experiments.

To illustrate these results, the Figure 2 shows the devia-

tions of measurement points relative to b isec tor.

The details of deviations are shown in Table 3 where

one see s tha t the maximu m deviatio n is estimat ed to 7.9%

in measurement 7. The Student test shows us if the vari-

able xi or the interaction xi,j associated with ai,j affects

response “y” or not. For this, one calculates the coeffi-

cient ti of Student as follo ws:

(5)

With

is variance of effects; it is calculated by fol-

lowing :

(6)

where s2 is estimator of polynomial effects; it is calcu-

lates by this formula:

=−∑

(7)

Here, n is equations number ob tained b y combinations

of values of xi,j from Table 1, it is equal to 33 = 27 (full

factorial design), and p is number of modelling coeffi-

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D. BOUNAZEF ET AL.

20 30 40 50 60

Observed

Predicted

Figure 2 . O bserv ed vs. Predicted plot.

Table 3. Deviations between predic ted and observed values.

N˚ Observed Predicted Difference

1 22.49 21.6865 0.803453

2 40 41.2669 −1.26685

3 20 19.7343 0.265732

4 43.27 43.4725 −0.202545

5 66.18 66.331 −0.151001

6 42.52 39.1532 3.36685

7 26.74 29.5363 −2.79629

8 41.26 41.2793 −0.0193405

cients, it is equal to 10 (see Equation (1)). The compari-

son between tcrit taken from Student table for risk α =

0.05 and freedom degree ν = 17, shows that all “ti” are

higher than tcrit = 0.689, it means that all variables xi,j

influence the response “y”, i.e. the loss of production

(Table 4).

Equation (4) allo ws working simultaneously the three

parameters in the field of work but we cannot interpret it

graphically. However, we vary two parameters while

leaving unchanged the third par ameter (x3).

6. Production Losses According Accidental

Stops When x2 and x3 Are Middle Values

To observe how the losses of production vary according

one parameter, one gi ves to 2 others parameters in Equa-

tion (4) permanent middle values. We can then plot the

variation of production losses according one of 3 pa-

rameters. The statistics collected during the production

indicate that while stabilising the production losses due

to raw materials and finished products as well as main-

tenance to their middle values (x2 = 877.7 hours, x3 =

5241.6 hours), one reaches the maxi mum val ue of 40.5%

of production losses at 900 hours of accidental stops. The

mathematical modelling decreases these losses to 34.3%

at 2730 hours (Figure 3). When x1 exceeds the value of

900 hours, x2 and x3 are statisticall y acting on the model

and are decr easing production losses.

Table 4. Student coefficients.

21.5401757

; s2 = 1.26706916

20.04692849

; si = 0.21662984

t1 174.61 t6 40. 56

t2 31.48 t7 13.24

t3 8.79 t8 6.57

t4 9.38 t9 12.60

t5 6.02 t10 2.03

Figure 3. Graph of production losses acco rding accidental

stops.

7. Production Losses According

Maintenance and Human Resources

Management Stops When x1 and x3 Are

Middle Values

Maintaining accidental stops x1 and stops due to ra w ma-

terial and finished products x3 constant respectively at

1476.40 hours and 5241.6 hours, o ne varies only x2 from

its minimum value to its maximum value, we obtain a

minimal loss of production of 39.8% for x2 = 860 hours

(Figure 4).

This means that the parameter x2 has a positive influ-

ence in reducing production losses in the model (4), but

from x2 = 860 hours, fact ors x1 and x3 are more influential

than x2. This explains why the curve increases until pro-

duction losses of 50.2% for x2 = 1090 hours.

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D. BOUNAZEF ET AL.

Figure 4. Graph of production losses according mainte-

nance and human resources manag ement st ops.

8. Production Losses According Stops Due to

Raw Material and Finished Products

When x1 and x2 Are Middle Values

When we leave constant x1 = 1476.40 hours and x2 =

877.70 hour s (middle values), we note that the minimum

losses of production is q uickly rea ched at 30.8% for x3 =

3260 hours when the curve decreases. This shows that

from this minimum, the factors x1 and x2 are increasing

the response “y” (production losses) when x3 varies from

its minimum value to maximum value (Figure 5).

9. Results Interpretation When x1 and x2

Are Varied Together

For this, one gives to third parameter x3 an invariable

value and one changes the 2 other from their minimum

value to their maximum value. One can plot response

surfaces in three dimensions and c urves iso -responses in

two dimensions to illustrate the action of two parameters

simultaneously on the production losses.

10. When x3 Is Equal at the Low Value

(x3 = 779.17 Hours)

In this case, the response surface is concave rectangular

form; it shows parallel areas of production losses ma i n ly

when accidental stops (x1) and stops caused by ma i nt e-

nance and management of human resource s (x2) are high

(Figure 6).

When accidental stops are less than 1500 hours, these

areas are parallel to the axis of x2. It shows that acciden-

tal stops act very low in the model response. All this is

visible on curves ISO response, where one notes that the

losses of production remains relatively constant between

20.8% and 24.2% for stops due to maintenance and

management of human resources between 675 hours and

937.5 hours. From 1330 hours of accidental stops that the

increase of x2 increases clearly the production losses.

11. When x3 Is Equal at the Middle Value

(x3 = 5241.60 Hours)

When x3 takes the mid dle val ue of 5241.6 hours, the ma -

Figure 5. Graph of production losses according stops due

raw material and finished pr oduc ts.

Figure 6. Response surface and ISO response curves when

x3 is low.

thematical model (4) presents respo nse s surface as a sad-

dle of horse (Figure 7). Its complexity shows how the

simultaneous influence of x1 and x2 acts on production

los ses of finished products. The projection of the re-

sponse surface on the lower plane gives ISO responses

curves that’s the central part is in the form of four ten-

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D. BOUNAZEF ET AL.

Figure 7. Response surface and ISO response curves when

x3 is middle.

tacles. In t his section, the resp onse “y” remains relativel y

constant; it varies from 40.5% to 41.3% over a large part

of the work domain. T his shows tha t we can get the con-

stant value of production losses defined by the 41.3% by

several combinations between accidental stops (x1) and

maintenance and manage ment of human resources stops.

Table 5 gives some values of production losses outside

the central zone with tentacles.

It is clear, that the columns and rows (Table 5) display

for constant values of the parameter x1, that production

losses decrease in first with increasing parameter x2, sta-

bilise at central area of the graph 8, and subsequently

increase. However, when x2 re mains c onsta nt, production

losses decrease for the 2 first rows with increasin g x1, but

increase in first and subsequently decrease for the 2 last

r ows of Table 5 with increasing x1.

12. When x3 Is Equal at the High Value

(x3 = 9703.75 Hours)

When the parameter x3 take s i ts ma ximu m a nd invariable

Table 5. Pr oduction loss e s in cent r a l zone when x3 is middle.

x2 500

hours 1000

hours 1500

hours 2000

hours 2500

hours

700

hours 47.4% 46.5% 44.7% 42% 38.4%

750

hours 44.1% 43.5% 42% 39.7% 36.4%

1000

hours 42.7% 43.8% 43.9% 43.1% 41.4%

1050

hours 45.5% 46.9% 47.3% 46.8% 45.4%

value of 9703.75 hours in the mathematical model 4, the

responses surface is the concave form upwards (Figure 8).

Its projection gives curves ISO responses directed from

top to bottom and curved in the centre of the graph. This

shows that for a given value of accidental stops (x1),

losses of production vary slowly with the c ha n ge of stops

due to maintenance and human resource management. It

is easy to see that for maximum value of x3 = 9703.75

hours, the increase of accidental stops (x1) reduced the

losses of production; this is due to the effect of negative

sign of the interaction of parameters x1 and x3 in the

polynomial (4) and equal to a13 = −8.78769 which re-

duces considerably the value of the response “y”. One

remarks that in passing from value x1 = 500 hours to

x1=2500 hours for the same value of x2 = 900 hours,

losses of production fells from 55.8% to 22.2 %.

13. Management of Production Waste by

Statistical Process Control

The losses rate of production per lines caused by the

various stops does not explain alone the waste of fini s hed

products during production process. It is r at her frequency

of repeated stops that causes restarts manufacturing

process. T his will requires each time the equipments set-

tings to obtain the finished standardised products. Know-

ing annual waste rate of polyethylene products for water

of 3.15% and for ga s of 2.54%, the average waste rate of

8 lines is:

Waste rate2.845%

= =

∑

(8)

where:

∑

is sum of distribution values equal to

5.69%; n is samples number equal to 2; this is giving us

process quality “m” or “Yield” of 97.155% (Figure 9).

This value is considered as the average value of the

process target to achieve (average value of distribution).

As the value of the standard deviation is sigma equal to

0.9425071, the repetition frequency of production stops is:

10.42328

2π

= =

(9)

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D. BOUNAZEF ET AL.

Figure 8. Response surface and ISO response curves when

x3 is high.

Thi s val ue i s represented by the top of the Gauss c ur v e

of production process. It corresponds to 0.91569σ on the

X axis and represents the lag due to the production proc-

ess and waste estimated at 28500 DPMO (defects per

millions of opportunities) (U n hatched area of Figure 9).

The beginning of waste area corresponding to end of

process performance z, it is found in the following man-

ner:

coefz

= ⋅

(10)

where z is sigma process quality; it is calculated with

coefficient who take n from the normal distrib ution taking

acco unt the risk of 0.05 and “UCL, LCL” values through

manufactured tables (coef = 3.403311); the process per-

formance z is equal at 3.403311σ. The σ value is the

standard de viation, it calculated by this formula:

()

−

∑

(11)

Figure 9 . Gauss curve of pro duction lo s ses .

The process performance z is then 3 .20 76447. The lo w

control limit (LCL) and the upper c ontrol limit (UCL) ar e

calculated by this following formula; here, the target is

the process quality m = 100% ‒ 2.845% = 97.155%:

LCL,UCLtarget 3

= ±

(12)

Their respective values are then 94.327419 and

100.377521. The process quality area of the real produc-

tion process is thus defined by LCL, UCL and the Gauss

curve of normal distribution (hatched zone in Figure 9).

It is equal to 97.155%. The combination of two methods

of analysis, the experimental design and statistical proc-

ess control in management showed us that performance

of studied process is relatively small compared to a

process without stops or waste. The management of

waste during the production process is directly linked to

the frequency of stops and starts of manufacturing lines.

To achieve Six Sigma pr ocess with performance of

99.999%, one must impr ove the process capability index

Cp in order to be higher than 2. However, the capability

index of six production lines is z/3 = 1.1344; the produc-

tion process of PE is then just capable. To achieve high

performance, one must act in several fields that cause the

increase of waste. Managing production waste is to un-

der stand the real causes that pus h businessmen to s ubmit

pro gra m change s on the production lines, and see if there

are opportunities for t heir red uctions. It must also under-

stand the real causes o f mechanical and electrical failures

and assess the reliability of the maintenance planning.

Finally know the real causes of non conformities of

products and analyse the production process and inter-

vention function responsible for the technical quality.

Thereafter take the necessary technical and financial

measures and control by means of managerial actions to

reduce this waste.

14. Capability Indices and Process

Performance

The capability indices of process “Cp”, of machine “Cm”

and process performance “Pp” are important data that de-

monstrate the real capacity continuous production pro-

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D. BOUNAZEF ET AL.

cess of the manufacturing company of tubes. The capa-

bility index that takes account process, machine, and the

performance is calculated as follows:

( )

UCL LCL

Index, ,6

pmp

CCP

−

(13)

The val ue of t hi s i nd e x i s t he n 0 , 9 999 9 3 , i. e . close to 1.

The capability index of the process Cp is found in the

following manner:

3.2076447 1.0692149

C= ==

(14)

The Cp index exceeds the value of 1, but the quality of

process 6σ requires a capability of process more than 2.

The production process of the tubes is barely capable but

is not very efficient. The capability index of Machine Cm

allows measuring the material resources available the

continuous production process of the tubes is able to

achieve the target of 99.999966% of performance; the

value of this ind e x is :

( )

UCLLCL;

target

;

0.6292

−

=−

∑

(15)

The Cm index does not exceed 1.11 which allows the

reduction of waste of 0.00034%. The tools and machin-

eries of production plant are not capable to achieve per-

formance of 6σ quality. The plant must innovate and re-

duce the variability due to different causes of machine

stops.

15. Conclusion

Causes a nalysis of wa ste by 2 methods statistica l process

control and design of experiments are a very effective

means that can take me asures to manage the losses.

These methods permit to develop recommendations.

They can satisfy demands to achieve the production re-

quirements mastering the c ontrollab le factors, reducing

the impact of uncontrollable factors, minimising the fi-

nancial losses and improving the quality of production.

The reduction of waste is the result of the reduction of

machine stops; this reduction supports the achievement

of measurable and non-measurable gains such as reduc-

tion of the manufacturing cost and coast of control fac-

tors, reduction delay time, improvement employee com-

petence, improvement working environment due to the

reduction of machine stops hours. All this will automati-

cally change the pr ofitability of the process and the gains

of the company. The performance of production is treat-

ed in sigma process quality (performance quality) by

Equation (10).

REFERENCES

[1] P. Bousselet, “The process Computerisation QSE in Ag-

ribusiness: The 30 Questions to Consider Quality, Safety

and Environment,” PBC Soft, Paris, 2010.

[2] B. F r o ma n, J. M. Gey and F. Bonnifet, “Quality, Safety

and Environment: Construct an Integrated Management

Sys te m, ” AFNOR, La Plaine Saint-Denis, 2007.

[3] M. Bernardo, M. Casadesus and S. Karapetr ovic, “How

Integrated Are Environmental, Quality and Other Stan-

dardised Management Systems? An Empirical Study,”

Journal of Cleaner Production, Vol. 17, No. 8, 2009, pp.

742-750. http://dx.doi.org/10.1016/j.jclepro.2008.11.003

[4] K. R. Bhote, “The Po wer of Ultimate Six Sigma, Quality

Excellence t o To tal B usi ness E xc el len ce,” Amacom, New

York, 2003.

[5] D. Duret and M. Pillet, “Quality in Production: From ISO

9000 to Six Sigma,” 4th Edition, Eyrolles Edition, Paris,

2005.

[6] H. Aadi and B. John, “Hygiene and Safety at Work,”

Office of Professional Training and Work Promotion,

Rabat, 2011.

[7] Fernand ez-Toro and A. H. Schauer, “Management of

Information Security: Implementing ISO 27001, Imple-

mentation of ISMS and Certification Audit,” Eyrolles,

Paris, 2008.

[8] R. Holdsworth, “Practical Applications Approach to De-

sign, Development and Implementation of an Integrated

Management System,” Journal of Hazardous Materials,

Vol. 104, No. 1-3, 2003, pp. 193-205.

http://dx.doi.org/10.1016/j.jhazmat.2003.08.001

[9] T. H. Jorgensen, A. Remmen and M. D. Mellado, “Inte-

grated Management Syste ms —Three Levels of Integra-

tion,” Journal of Cleaner Production, Vol. 14, 2006, pp.

713-722.

[10] R. Salomone, “Integrated Management S ys t em s : Experi-

ences in Italian Organisations,” Journal of Clearner Pro-

duction, Vol. 16, 2008, pp. 1786-1805.

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