Analytica Chimica Acta 569 (2006) 260–266

Statistical intervals to validate an autoanalyzer for monitoringthe exhaustion of alkaline degreasing baths

E. Trullols a, I. Ruisanchez a,∗, E. Aguilera b, R. Lucena b, S. Cardenas b, M. Valcarcel b

a Rovira i Virgili University, Department of Analytical and Organic Chemistry, C/Marcel lı Domingo s/n, 43007 Tarragona, Spainb Department of Analytical Chemistry, Marie Curie Annex Building, Campus de Rabanales, University of Cordoba, E-14071 Cordoba, Spain

Received 8 February 2006; received in revised form 16 March 2006; accepted 21 March 2006Available online 29 March 2006

Abstract

We describe how to use the statistical intervals for validating a qualitative method for determining the alkaline degreasing baths exhaustion. Ahomemade autoanalyzer based on flow-injection-evaporative light-scattering detector (FI-ELSD) coupling measures two instrumental responsesrelated to the contents of surfactant and mineral oil. These two responses are necessary to decide whether the degreasing bath is exhausted. Theinstrumental responses ri are compared to their corresponding decision values i.e. cut-off response (rcut-off) and screening response (rscreening).Tbsa©

K

1

bwrmtdatdma

wdv

0d

hese decision values are calculated by defining the one-side prediction bound around the specification limit (SL) of both analytes. The predictionound of each analyte must be defined differently according to their corresponding specification limit. Performance parameters, such as sensitivity,pecificity, false response rates and the unreliability region, are established. The performance of this qualitative method of analysis is checked bynalyzing a set of 10 real samples. Our results show that the method is accurate as far as mineral oil content is concerned.

2006 Elsevier B.V. All rights reserved.

eywords: Statistical intervals; Flow-injection-evaporative light-scattering detector coupling; Degreasing baths; Validation

. Introduction

The correct performance of an analytical method is importantecause it implies that it satisfies the requirements for which itas designed. This is part of the validation process, which is car-

ied out at the end of the method development stage. This processust be carefully defined if the method’s performance charac-

eristics are to be accurately assessed. According to the ISOefinition [1,2], validating an analytical method means definingnd estimating the performance parameters needed to satisfyhe analytical requirements. In a similar way, the EURACHEMefines validation as the confirmation of the method perfor-ance capabilities consistency with the requirements of the

pplication [3].The validation of qualitative analytical methods has not been

ithin the scope of the main regulatory bodies, although someocuments and guidelines, which are not generally accepted butaluable nonetheless, can be found in the bibliography [4–6].

∗ Corresponding author. Tel.: +34 977558490; fax: +34 977558446.

Some validation proposals have been published addressing tospecific applications. The methodologies used in those casesare different depending on the intrinsic characteristics of themethod of analysis. The main approaches are the PerformanceCharacteristic Curves, Bayes’ theorem, the Contingency Tablesand the statistical intervals. As far as the methodology thatuses Performance Characteristic Curves [7] is concerned,it is suitable for methods providing sensorial (i.e. visual)detection [8]. They allow the estimation of several performanceparameters of the method such as sensitivity and specificityrates, as well as the unreliability region. Bayes’ theorem allowsthe calculation of conditional probabilities referred to just onesample. However, it has been used as an approach to quantifyuncertainty [9]. Contingency Tables also permit the calculationof predictive values of the method of analysis and they havebeen widely used in clinical analysis. Recently, statisticalintervals, and concretely prediction intervals, have been usedto validate a qualitative method providing an instrumentalresponse [10,11].

Following the last presented approach, in this paper we reportthe validation procedure for a qualitative method that assesses

E-mail address: itziar.ruisanchez@urv.net (I. Ruisanchez). if an alkaline degreasing bath is to be replaced. The analytical

003-2670/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.aca.2006.03.070

E. Trullols et al. / Analytica Chimica Acta 569 (2006) 260–266 261

method is not a test kit but a homemade autoanalyzer that uses ahigh-pressure pump, an injection valve, a silica sorbent columnand an evaporative light-scattering detector [12]. It measuressimultaneously two analytes and compares their response withthe response of their corresponding specification limit (SL), i.e.the concentration of the mineral oil and of the surfactant at whichthe bath is exhausted. The decision about the sample is doneconsidering simultaneously the two target analytes. Therefore,statistical intervals are defined around the specification limit ofeach analyte. New decision values such as cut-off and screeninglimits are also defined to take into account the different types oferror.

In addition to the establishment of the new decision values,performance parameters such as sensitivity and specificity, theunreliability region and false results rates, are also estimatedfrom the statistical intervals defined in response terms.

Degreasing baths are often used as a necessary step beforethe final processing of some metallic components because a per-fectly clean and active surface is required. Previous steps in themanufacturing or processing of these components involve usinggreases and oils, usually mineral, with cooling and lubricantproperties. These are usually removed from the metallic com-ponents using an alkaline degreasing bath by simply dippingthem or sprinkling them with the cleaning solution. Other pos-sibilities involve electrolytic techniques or ultrasounds. A widerange of alkaline degreasing baths exist because the compositionoisi(op

trwrtbo

indicators—basically, the amount of mineral oil collected andthe content of alkaline salts, though the amount of surfactant isan equally useful parameter.

2. Experimental

2.1. Apparatus

The autoanalyzer [12] used as the screening system is shownin Fig. 1. It consisted of a Hewlett-Packard 1050 high-pressurequaternary gradient pump, a Rheodyne (Cotati, CA, USA)7725 injection valve fitted with a 250 �l PTFE sample loop,a laboratory-made silica column constructed by packing 40 mgof silica sorbent into a 3 cm × 4 mm i.d. PTFE tube using smallcotton beads to prevent material losses, and a DDL 31 evapora-tive light-scattering detector (Eurosep, Cergy-Pontoise, France).The detector used air as nebulizing gas at 1.5 bar, the temperatureof the nebulizing chamber was set at 75 ◦C and the photomulti-plier gain was set at 350 V for the mineral oil and at 550 V forthe surfactant. Signals were acquired using an HPChem soft-ware connected to the detector via an HP 35900C (Agilent, PaloAlto, CA) multichannel interface. Peak height was selected asthe analytical signal for the measurement of both grease andsurfactant.

2.2. Reagents and samples

asp(TDPsh(wsS

used

f the bath must suit the problem at hand: e.g. dirt, the clean-ng system, the composition of the metallic component or theubsequent process. They all have a similar formulation, whichs based on the following main components [13]: surfactantsused as humectants), alkaline salts (used for the saponificationf the oil and greases) and chelating agents (used to avoid therecipitation of metallic hydroxides).

As the amount of mineral oil in the degreasing bath increases,he bath becomes less and less efficient until a new one isequired. The exhausted bath must then be submitted to properaste management, which involves both economic and envi-

onmental costs. The exhaustion of the degreasing bath mustherefore be correctly assessed in order to remove any still usableath. Exhaustion is defined by the client or by the end userf the metallic components and measured in terms of different

Fig. 1. The autoanalyzer

The validation standards contained both surfactant (0.39 g/l)nd mineral oil (1 g/l). In addition to these, 20 g/l alkalinealts solution was also added. The surfactant was a commercialroduct called Ridosol®. This, and the alkaline salts solutionRidoline® 1565/1), were kindly supplied by Henkel Surfaceechnologies. Ridosol® is a mixture of four surfactants (TritonF-11 (11%), Genapol PN-70 (3%), Lutensol DN-70 (11%),lurafac LF-431 (5%) in 70% deionised water). Ridoline® is aolution of 48% potassium hydroxide (61.30%), 50% sodiumydroxide (3.20%), 75% phosphoric acid (6%) and boric acid24.50%) in 5% deionised water. Ethanol 96% and n-hexaneere obtained from Sharlau (Barcelona, Spain), sulphuric acid,

odium sulphate and light mineral oil were purchased fromigma–Aldrich (Madrid, Spain).

as the screening method.

262 E. Trullols et al. / Analytica Chimica Acta 569 (2006) 260–266

2.3. Sample preparation and analysis by the screeningmethod

The validation standards were prepared by measuring 830 �lof a standard solution of 9.05 g/l surfactant in deionised waterand measuring 830 �l of a standard solution of 30.1 g/l mineraloil in n-hexane. Also, 0.5 g of Ridoline® was added to the 25 mlround flask. The organic phase was left to evaporate overnightand the corresponding amount of water was then added. The25 ml aqueous solution was mixed in a separation funnel with5 g sodium sulphate and 2 ml concentrated sulphuric acid. Itwas then extracted with 15 ml n-hexane and the final volumeof the organic solution was 25 ml. About 250 �l of the extractwas injected into the screening system carried by an n-hexanestream at a flow rate of 0.5 ml/min, passed through the silicacolumn for quantitative surfactant fraction retention while thegrease was directly driven to the detector and quantified. Theflow rate of the n-hexane was raised to 0.8 ml/min (3.5 min)for column clean-up. The surfactant fraction was eluted usingan ethanol stream at a flow rate of 1.0 ml/min (4 min). Apost-time of 5 min with 0.8 ml/min n-hexane was required aswashing step.

The signal recorded was the light scattered by the analyteparticles via previous nebulisation and evaporation of the mobilephase. The response is mass dependent [14], so the peak height ofboth analytes (mV) depends on the concentration of the analyte.T[

3

bsslvpat

tass[rta

((

(

3.1. Cut-off and screening responses

We have introduced the concept of specification limitresponses as the responses at the concentration value of the min-eral oil and at the concentration value of the surfactant, givenby the client, at which we consider that the bath is no longerusable. However, taking the decision at the specification limitlevel is risky because, due to the associated imprecision of themeasurements, the probability of committing an error is 50%.Therefore, it is useful to take the decision at the cut-off response(rcut-off) which is the response value beyond which the sample ispositive with a certain probability of committing a type I error.This probability of committing the type I error is defined bytaking into account the consequences of having false positiveresponses. The rcut-off strongly depends on the variability in theresponse values at the specification limit concentration [11,15].

Although the type I error is taken into account, this maynot be sufficient to make the decision at the rcut-off because theprobability of committing a type II error is rather high. Thedecision is therefore made at the screening response (rscreening)to also take into account the type II error. This probability ofcommitting a type II error is set considering the consequences ofhaving false negative results. It is therefore also a response valuebeyond which the sample is positive with certain probabilities ofcommitting type I and type II errors. Similarly, rscreening dependson the variability of the response values of both analytes at theirc

cius1

odt

s

H

Ttbaaamdl

Ttiro

he purity of the peaks was corroborated by infrared analysis12].

. Validation methodology

According to the requirements of the end user, the degreasingath must be replaced when the mineral oil content is above thepecification limit, and when the alkaline salts content or theurfactant content are below their corresponding specificationimit, both in terms of concentration. Not complying with thesealues will negatively affect the final quality of the metallic com-onents. Then, just by measuring the response of the mineral oilnd of the surfactant, the decision on the bath lifetime can beaken.

In the present case, the final YES/NO result comes fromhe instrumental signal measured. This means that the decisionbout the sample, i.e. bath lifetime, is made by comparing theurfactant response and the mineral oil response obtained for apecific bath with the corresponding one-sided prediction bound15] of the specification limit response (rSL) obtained whenecording several times, in intermediate precision conditions,he response at the concentration specification limit defined forgiven standard. The three main steps in this process are:

1) set the specification limit response for each analyte;2) if error probabilities are considered, estimate new response

values (rcut-off or rscreening) where the right final decisionabout the sample will be taken; and

3) estimate the performance parameters of the analyticalmethod (sensitivity and specificity rates, the unreliabilityregion and the false result rates).

orresponding specification limit concentration level.Both limits (rcut-off and rscreening) are defined from the statisti-

al distribution of the specification limit. Then, the starting pointn the definition of the prediction boundary is the response val-es corresponding to this limit. In the current application, bothpecification limits are set by the client at 0.39 g/l surfactant andg/l mineral oil.

As the content of the mineral oil increases and the contentf the surfactant decreases, their prediction boundary must beefined differently (Fig. 2). This definition is done according tohe following hypotheses:

urfactant : H0 : ri ≥ rSL (SL = 0.39 g/l),

1 : ri < rSL (1)

A type I error means accepting H1 when actually H0 is true.his means affirming that the content of the surfactant is less

han 0.39 g/l (the bath is exhausted) when it is not. The proba-ility of making this type of error should, for several reasons, bes low as possible. An exhausted degreasing bath is subjected towaste management process, which involves both economical

nd environmental costs. For those involved in waste manage-ent, therefore, it is more attractive to replace a truly exhausted

egreasing bath that has perhaps been used longer than its shelf-ife than to replace a falsely exhausted degreasing bath.

A type II error means accepting H0 when actually H1 is true.his means incorrectly affirming that the content of the surfac-

ant is more than 0.39 g/l, i.e. the bath is not exhausted whenn fact it is. Since the consequences of this wrong decision areelatively unimportant, it is not necessary to set the probabilityf this type of error very low.

E. Trullols et al. / Analytica Chimica Acta 569 (2006) 260–266 263

Fig. 2. Specification limit, cut-off and screening response for (a) the surfactantand (b) the mineral oil.

The prediction boundary is therefore defined as in the fol-lowing equation:

rcut−off = rSL − t(α,ν)sSL (1a)

To establish the cut-off response value we need to set theprobability of committing a type-I error (false positive) as low aspossible. Also, though in the present case, it is not so important,defining the β-type probability error would avoid a consider-able number of false negative results. Therefore, if we take intoaccount the probabilities of committing both types of error, weobtain the so-called screening response value, which depends onα, β and the bias ∆, which is defined as the difference betweenthe screening response and the response at the specification limit(∆ = (rscreening − rSL)). From Fig. 2 we can see that α, β and ∆

are closely related. The previous definitions of α and ∆ involvea particular β. Similarly, therefore, from pre-defined α and β,the bias is automatically set.

This new decision value is expressed as shown in Eq. (1b),which takes into account the specification limit response of thesurfactant:

rscreening = rSL − ∆(α, β, ν)sSL (1b)

mineraloil : H0 : ri ≤ rSL (SL = 1 g/l), H1 : ri > rSL (2)

imp

mep

Fig. 3. Experimental design.

Table 1ANOVA for a two-factor fully-nested design

Source Mean squares Degrees of freedom

Run MSrun = n∑

i(xi − x)2

p − 1p − 1

Residual MSE =∑

i

∑j(xij − xi)2

p(n − 1)p(n − 1)

Total (pn) − 1

The prediction interval is defined as in the following equation:

rcut−off = rSL + t(α,ν)sSL (2a)

The same occurs if we consider the probability of committinga type II error (see Eq. (2b)) and take into account the specifica-tion limit response of the mineral oil:

rscreening = rSL + ∆(α, β, ν)sSL (2b)

3.2. Experimental procedure

The variability of the measured responses needs to be reliablyevaluated. The experimental design is crucial to achieving thisaim.

A key value in the estimation of the screening response isthe standard deviation of the specific limit response sSL. Thisvalue must be conveniently calculated using the following exper-imental design. To calculate the major sources of variability, theexperimental design is therefore a four-factor fully nested designin which, for 22 days, two operators twice analysed two new anddifferent validation standards (Fig. 3).

The variance estimated in intermediate precision conditionscontains the variability from the operator, day and sample. Itis the estimated variance of an individual measurement madeby an arbitrary operator on an arbitrary day. The intermediateprecision can easily be estimated [16] by applying ANOVA tottswant

t

s

A type I error means affirming that the content of mineral oils higher than 1 g/l (the bath is exhausted) when it is not. For the

ineral oil, the probability of a type-I error should be as low asossible.

A type II error means incorrectly stating that the content ofineral oil is equal to or lower than 1 g/l, i.e. the bath is not

xhausted when in fact it is. Again, it is not necessary to set thisrobability of error as low as possible.

he results of this experimental design. However, the ANOVAable for the four-factor fully nested design is quite rare and aimpler design can be used if we consider the factors we varyithin a run, which in the present case are the operator, the day

nd the sample. The design therefore becomes a two-factor fullyested design with two instrumental replicates per run in whichhe variances are calculated according to Tables 1 and 2.

The sSL or the now called sISL is then calculated according tohe the following equation:

ISL =√(

s2r

nrpr+ s2

run

pr

)+

(s2

r

np+ s2

run

p

)(3)

264 E. Trullols et al. / Analytica Chimica Acta 569 (2006) 260–266

Table 2Variances for a two-factor fully nested design

Variance Expression Degrees offreedom

Repeatability variance, s2r MSE (pn) − 1

Between-run variance, s2run

MSrun − MSE

n

Run-different intermediate variance, s2I s2

r + s2run

As nr and pr are the number of replicates and the number ofruns performed over the unknown sample, both are usually equalto 1. Both n and p are the number of replicates and runs used inthe experimental design (Fig. 3), so it becomes even simpler tocalculate sISL from the following equation:

sISL =√

s2r

(1 + 1

np

)+ s2

run

(1 + 1

p

)(4)

The value obtained is substituted in Eqs. (1) and (2) for eachanalyte. The effective number of degrees of freedom of theStudent t-test must be computed using the Satterthwaite [17]approach.

4. Results and discussion

Following the experimental design shown in Fig. 3, two oper-ators twice analysed two different validation standards for 22days, thus leading to 88 runs. From these analyses performedat the specification limits of the surfactant and mineral oil,both responses were recorded and, from the standard deviationsin intermediate precision conditions, the cut-off and screeningresponses were calculated (Table 3).

We can estimate the performance parameters by taking intoaccount the decision values shown in Table 3. Sensitivity wasassessed by measuring 20 times a sample with a concentration ofswte0(vroc

The unreliability region is the interval of responses or con-centrations where the probability of obtaining false responses orresults obtained is higher [6]. In the present case, this region isplaced between the specification limit response and the screen-ing response of the analyte because is where these probabili-ties of committing false responses are higher. Once calculatedthese two response values, (i.e. specification limit response andscreening response), the unreliability region is estimated eas-ily. For the surfactant, the unreliability region lies between theresponse values of 2.61 mV (specification limit) and 1.89 mV(screening response). For the mineral oil content, the unreliabil-ity region lies between response values of 0.53 mV (specificationlimit) and 0.67 mV (screening response). In both cases, withinthe unreliability region the probability of a type I error is themost important.

False positive and false negative rates are interesting in thepresent application because the decisions depend on them. Forthe mineral oil, the false positive rate is assessed using a samplethat contains 0.707 g/l of mineral oil. None of the 20 responsesrecorded provided a value above rscreening = 0.67 mV, which is afalse positive rate of 0% at this concentration level. In this case,there is just one analyte to provide the false response rate. If weconsider both analytes, several situations arise:

(a) a false positive result for the mineral oil content but a true

(

(

rmsr0t

TV nd th

MRBRErr

A

urfactant below 0.39 g/l (0.099 g/l). All 20 responses recordedere below rscreening (i.e. 1.89 mV), so the sensitivity rate at

his concentration level was 100%. Similarly, specificity wasstimated from a sample with a surfactant concentration above.39 g/l (0.619 g/l) and a mineral oil concentration below 1 g/l0.707 g/l). All of the 20 responses recorded showed a responsealue for the surfactant above rscreening (i.e. 1.89 mV) and aesponse value below rscreening (i.e. 0.67 mV) for the mineralil. This implies a specificity rate of 100% at both levels ofoncentration.

able 3ariances, effective degrees of freedom, rcut-off and rscreening for the surfactant a

ean response at the specification limit, rSL (mV)epeatability variance, s2

retween-run variance, s2

runun-different intermediate variance for the specification limit, s2

ISL

ffective degrees of freedom, νeff

cut-off (α = 1%) (mV)

screening (α = 1%, β = 10%) (mV)

ll values are calculated in response terms.

negative result for the surfactant content, which means thatthe bath can still be used since there is enough surfactant,

b) a false positive result for the surfactant but a true negativeresult for the mineral oil, which means that the bath can stillbe used if a small amount of surfactant is added,

(c) both results are false positives, which means that thedegreasing bath must be replaced. This situation will nothappen often because the probability of a type I error hasbeen set at 1%,

d) both results are true negative, which means that the bath canstill be used.

A similar situation occurs with regard to the false negativeate since it is assessed by measuring a sample with 1.246 g/lineral oil but a rather low concentration of surfactant. Twenty

amples were measured but no response recorded was belowscreening = 0.67 mV, which means that the false negative rate was%. Again, if we consider both analytes (mineral oil and surfac-ant), several situations arise:

e mineral oil

Surfactant Mineral oil

2.6 0.534.5 × 10−4 1.3 × 10−4

3.8 × 10−2 1.4 × 10−3

3.9 × 10−2 1.5 × 10−3

89 1032.1 0.621.9 0.67

E. Trullols et al. / Analytica Chimica Acta 569 (2006) 260–266 265

Table 4Results of the analysis of the real samples using the reference method and thequalitative method

Mineral oil (referencemethod)

Mineral oil ri (qualitativemethod of analysis)

Final result

Negative 0.25 NegativeNegative 0.22 NegativeNegative 0.37 NegativeNegative 0.40 NegativeNegative 0.52 NegativePositive 0.61 NegativeNegative 0.51 NegativeNegative 0.46 NegativeNo information 0.50 NegativeNo information 0.47 Negative

(a) a false negative result for the mineral oil but true positiveresult for the surfactant, which means that, even though it isfalsely assumed that there is not enough mineral oil, the bathcan still be used if a small amount of surfactant is added.

(b) a false negative result for the surfactant but true positiveresult for the mineral oil. We can decide to longer use thebath if removing a small part of the mineral oil on the surface.

(c) a true positive result for both analytes, which means that thedegreasing bath must be replaced.

(d) a false negative result for both, which means that we cancontinue to use the bath if we add more surfactant. Thissituation will not happen often because the probability of atype II error is set at 10%.

To properly validate this method, we analysed 10 samplesprovided by a specialized industry. These samples were collectedfor 5 days and every 12 h from a degreasing bath with a lifetimeof 1 week.

Table 4 shows the results for mineral oil content measuredwith the reference method of analysis [18] and with the qualita-tive method. We can see that, with the reference method, all theresults except one were clearly negative. Note that the mineral oilconcentration of the sample with the positive result was close tothe one corresponding to rscreening. When we analyse the sampleswith the qualitative method, a sample is positive if the instru-mamswtttmt

5

vy

exhaustion of a degreasing bath, which is used in the automobileindustry. Two components were considered (the content of min-eral oil and the content of surfactant) in order to decide whetherthe bath should be replaced.

The statistical intervals are defined in response terms and forboth measurands simultaneously. As the specification limit isconsidered in terms of response, the one-sided prediction boundsare defined around the corresponding responses at the specifica-tion limit concentration because the probabilities of committinga type I error and a type II error are considered. On the basis ofthe rscreening responses for the two analytes, the sample is consid-ered positive or negative. When the two responses are combined,however, the considerations may be different.

Our results, obtained with a set of 10 real samples, show thatthe method classified correctly at low concentrations of mineraloil and close to the concentration value for the specification limit.In the region near the concentration of the rscreening, however, onefalse negative result was obtained. No information is availableon the surfactant content, so this cannot be checked.

Although the validation procedure considered only two com-ponents of the degreasing baths, it can be extended to the contentof alkaline salts provided the method of analysis is suitable forthese analytes. These salts are another valid indicator for thereplacement of the degreasing bath.

Future proposals are to perform the validation study at otherconcentrations of these analytes and to determine robustness andrf

A

(lf0Sa

R

ental response ri is higher than the rscreening. On the other hand,sample is negative whenever the instrumental response of theineral oil is lower than the corresponding rscreening. As we can

ee, all the samples analysed – including the one that was positiveith the reference method – provided negative results. This is

herefore a false negative result and is acceptable if we considerhat its mineral oil concentration (1.31 g/l) is extremely close tohe corresponding concentration of the rscreening (1.246 g/l). Theethod of analysis therefore performed accurately with respect

o mineral oil.

. Conclusions

We have described how to use the statistical intervals in thealidation procedure of an innovative qualitative method of anal-sis. The screening method we have validated determines the

uggedness. Control charts are also a feature to consider in theuture.

cknowledgments

The authors acknowledge economic support from the MCyTprojects no BQU2003-500 and BQU2003-1142). Esther Trul-ols would like also to thank the URV for providing a doctoralellowship. This work was also supported by grant CTQ2004-1220 from the MCyT. Special thanks should be given to Dr. A.olans of Henkel Iberica for collaborating on method validationnd supplying specific chemical standards and bath samples.

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