Hough Et Al 2004 Defects

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Determination of consumer acceptance limits to sensory defectsusing survival analysis

Guillermo Hough *, Lorena Garitta, Ricardo Sanchez 1

Instituto Superior Experimental de Tecnolog ıa Alimentaria, 6500 Nueve de Julio, Buenos Aires, Argentina

Available online 19 March 2004

Abstract

Survival analysis concepts and calculations were applied to consumers’ acceptance/rejection data of samples with different levels

of sensory defects. The following defects in UHT milk were studied: acid, caramel, cooked, dark color, lipolytic and oxidized. For

each defect a series of nine concentrations were prepared and tested by 50 member consumer panels. The lognormal parametric

model was found adequate for most defects and allowed prediction of concentration values corresponding to 10% probability of

consumer rejection. For cooked flavor the model was not adequate due to a large number of right censored data, consumers did not

find this defect objectionable. For oxidized flavor there were also many right censored values, but this was due to an inadequate

concentration range.

2004 Elsevier Ltd. All rights reserved.

Keywords: Sensory; Quality control; Survival analysis; Statistics; UHT milk; Sensory defects

1. Introduction

Most textbooks refer to quality in the sense of

meeting or exceeding consumer’s expectations, thus

quality implies understanding and quantifying these

expectations. A basic requirement of any sensory quality

control (QC) system is the definition of standards or

tolerance limits on a sensory basis for the product

(Lawless & Heyman, 1998). Recently Food Quality and

Preference (Vol. 13, No. 6), published a special issue on

‘‘Advances in Sensory Evaluation for QC’’, where most

of the papers (e.g., Costell, 2002; Mu~noz, 2002; Weller &

Stanton, 2002) emphasized the importance of estab-

lishing sensory specifications through consumer input.

One method for obtaining sensory specifications,

outlined by Mu~noz, Civille, and Carr (1992), is to present

consumers with samples covering a range of a specific

sensory attribute. Consumers measure the acceptability

of these samples by scoring on a hedonic scale, and then

these scores are correlated versus intensity measurements

of the same samples given by a trained sensory panel.

Alternatively, the trained panel measurements can be

replaced by a chemical or physical index of the samples.

The specification is obtained by choosing a minimumlevel of acceptability on the chosen hedonic scale.

In the routine consumption of a food product, con-

sumers do not measure acceptability on a scale, saying

for example: ‘‘this biscuit has a six, therefore I’ll phone

up and complain’’. Rather, their judgments are accep-

tance or rejection of the product. In this context the

question is: how high can the intensity or concentration

of a sensory defect be, before a consumer rejects the

product? In the present paper, survival analysis statistics

are presented as a tool to answer this question.

2. Survival analysis concepts

Methods of survival analysis have been developed to

evaluate times until an event of interest, often called

survival times, taking into account the presence of cen-

sored data (Gomez, 2002). These methods have been

applied to shelf life of foods (Hough, Langohr, Gomez,

& Curia, 2003). Time can be replaced by other variables

in the system under study, for example distance to fail-

ure in vehicle shock absorbers (Meeker & Escobar,

1998) or, as in the present case, concentration of a

sensory defect. Assume that we define a random variable

* Corresponding author. Fax: +54-2317-431309.

E-mail address: [email protected] (G. Hough).1 Deceased May 11 2003.

0950-3293/$ - see front matter 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.foodqual.2004.02.006

Food Quality and Preference 15 (2004) 729–734

www.elsevier.com/locate/foodqual

http://mail%20to:%[email protected]/

http://mail%20to:%[email protected]/



C as the concentration at which a consumer rejects the

sample. The failure function F ðcÞ can be defined as the

probability of a consumer (or proportion of consumers)

rejecting a food with the level of a sensory defect < c,

that is F ðcÞ ¼ P ðC < cÞ.

In quality control studies, samples with different

concentrations of a defect are presented to consumers.For example, concentrations could be 0, 5, 10 and 15. If a

consumer accepts the sample with concentration ¼ 5, and

rejects it with concentration ¼ 10, the exact concentra-

tion of rejection could be any value between 5 and 10.

This is defined as interval censoring. A special type of

interval censoring is when a consumer rejects the sample

with concentration ¼ 5, thus rejection concentration is

6 5 and this is called left censoring. If the consumer ac-

cepts all concentrations, rejection would occur for a

concentration >15 and the data is right censored.

The likelihood function, which is used to estimate the

failure function, is the joint probability of the given

observations of the n consumers (Meeker & Escobar,

1998):

L ¼Yi2 R

ð1 F ðr iÞÞYi2 L

F ðliÞYi2 I

ð F ðr iÞ F ðliÞÞ ð1Þ

where R is the set of right-censored observations; L, the

set of left-censored observations; and I , the set of

interval-censored observations. Eq. (1) shows how each

type of censoring contributes differently to the likeli-

hood function.

Usually, failure times are not normally distributed,

instead their distribution is often right skewed. Often, a

loglinear model is chosen:Y ¼ lnðC Þ ¼ l þ rW ;

where W is the error term distribution. That is, instead of

the failure concentration C , its logarithmic transforma-

tion is modeled. In Klein and Moeschberger (1997) or

Lindsay (1998) different possible distributions for C are

represented, for example the lognormal or the Weibull

distribution. In case of the former, W is the standard

normal distribution, in case of the Weibull distribution,

W is the smallest extreme value distribution.

If the lognormal distribution is chosen for C the

failure function is given by:

F ðcÞ ¼ UlnðcÞ l

r

; ð2Þ

where UðÞ is the standard normal cumulative distribu-

tion function, and l and r are the model’s parameters.

If the Weibull distribution is chosen, the survival

function is given by:

F ðcÞ ¼ 1 S sev

lnðcÞ l

r

; ð3Þ

where S sevðÞ is the survival function of the smallest ex-

treme value distribution: S sevðwÞ ¼ expðewÞ, and l and

r are the model’s parameters.

The parameters of the loglinear model are obtained

by maximizing the likelihood function (Eq. (1)). The

likelihood function is a mathematical expression which

describes the joint probability of obtaining the data

actually observed on the subjects in the study as a

function of the unknown parameters of the model being

considered. To estimate l and r for the lognormal or theWeibull distribution, we maximize the likelihood func-

tion by substituting F ðcÞ in Eq. (1) by the expressions

given in Eqs. (2) or (3), respectively.

Once the likelihood function is formed for a given

model, specialized software can be used to estimate the

parameters (l and r) that maximize the likelihood

function for the given experimental data. The maximi-

zation is obtained by numerically solving the following

system of equations using methods like the Newton–

Raphson method (Gomez, 2002):

o ln Lðl;rÞ

ol ¼ 0

o ln Lðl;rÞ

or¼ 0

For more details on likelihood functions see Klein and

Moeschberger (1997), Lindsay (1998) or Gomez, Calle,

and Oller (2001).

3. Materials and methods

A commercial whole fat UHT milk was provided by a

local manufacturer in 1 l cartons all from the samebatch. Both the manufacturer’s in-plant quality control

sensory panel and a panel trained in descriptive analysis

of dairy products found the batch to be free of sensory

defects.

The following defects in UHT milk were studied:

acid, caramel, cooked, dark color, lipolytic and oxi-

dized. These are well known sensory defects that can

be present in UHT milk, either due to processing or

storage problems and were chosen to illustrate the

methodology. Other defects can also be present (Inter-

national Dairy Federation, 1997) but are not covered in

the present work. Preparation of the stock solutions for

these defects is in Table 1. These stock solutions were

diluted with UHT milk to obtain a series of nine con-

centrations for each defect, as shown in Table 2. A

previous work on reconstituted milk powder was taken

as a guide in preparing these solutions (Hough et al.,

2002).

For each defect the nine concentrations were tested

by a 50 member consumer panel, that is a total of 300

consumers were used (50 consumers· 6 defects). All

consumers had drunk milk at least once in the last week,

and were between 18 and 25 years old. The consumers

were presented with the nine samples monadically in

730 G. Hough et al. / Food Quality and Preference 15 (2004) 729–734



random order. Thirty ml of each sample was presented

in a 70 ml plastic glass. Time between each sample was

approximately 1 min. Water was available for rinsing.

For each sample they had to taste it and answer the

question: ‘‘Would you normally consume this product?

Yes or No?’’. It was explained that this meant that if

they bought the product to drink it, or it was served to

them at their homes, whether they would consume it or

not. The tests were conducted in a sensory laboratory

with individual booths with artificial daylight type illu-

mination, temperature control (between 22 and 24 C)

and air circulation.

The CensorReg procedures from S-PLUS (Insightful

Corporation, Seattle, USA) were used to estimate the

parameters l and r, and the F ðcÞ ¼ 10% quantile.

4. Results and discussion

4.1. Raw data and censoring considerations

To illustrate the data treatment we shall refer to the

lipolytic data. Table 3 presents the data for 5 of the 50subjects to illustrate the interpretation given to each

subject’s data.

Subject 1 was as expected, that is he/she accepted the

samples up to a certain concentration and then consis-

tently rejected them. Their data are interval censored

because we do not know at exactly what concentration

between 13% and 20% the consumer would start

rejecting the product. For the lipolytic defect 21 subjects

presented this type of data.

Subject 2 accepted all samples. Supposedly at a suf-

ficiently high concentration the sample would be re-

jected and thus the data is right censored. Two subjects

presented this type of data.

Subject 3’s data were considered as left censored. Left

censoring can be considered as a special case of interval

censoring with the lower bound equal to time ¼ 0

(Meeker & Escobar, 1998). But as the literature and

statistical software distinguish it, we have also done so.

Thirteen subjects were left censored.

Subject 4 was rather inconsistent, rejecting the sample

with C ¼ 9%, accepting with C ¼ 13% and 20%, and

rejecting from C ¼ 30% onwards. Censoring could be

interpreted in different ways. One possibility would be to

consider the data as interval censored between 6% and

9% C , that is ignoring the subject’s answers after the first

Table 1

Stock solutions used to prepare UHT milk samples with different defects

Defect Stock solution

Acid 3 ml lactic acid/1 l UHT milk

Caramel 8 g flavoringa/1 l UHT milk

Cooked UHT milk heated 15 min in a boiling water bath

Dark color 100 ml of 2% coloringb solution completed to 1 l with UHT milk

Lipolysis Fatty acid mixturec + 5 g of Vaseline + 2 g Tween 80, heated to 50 C for dissolution, added to 1 l UHT milk at 35 COxidize d 1 ml of 1% copper sulfat e solution+6·6 cm copper foil strip added to 1 l UHT milk, stored 24 h at 4 C

a Givaudan Roure (Munro, Argentina) caramel essence code 73865-33.b SICNA (Milan, Italy) caramel coloring.c 46 mg of butyric + 30 mg of caproic + 23 mg of caprilic + 28 mg of capric+ 30 mg of lauric; all acids were analytical grade.

Table 2

Concentrations (percentage of stock solution; Table 1) in UHT milk

used to determine concentration limits of defects

Conc ent ration Conc. % v/va Conc. % v/vb

1 0 0

2 6 10

3 9 13

4 13 19

5 20 26

6 30 36

7 44 51

8 67 71

9 100 100

a Concentration of color, caramel, cooked and lipolysis defects.b Concentration of acid and oxidized defects.

Table 3

Acceptance/rejection data for five subjects who tasted UHT milk samples with different lipolytic concentrations

Subject Concentration Censoring

0 6 9 13 20 30 44 67 100

1 Yes Yes Yes Yes No No No No No Interval: 13–20

2 Yes Yes Yes Yes Yes Yes Yes Yes Yes Right: >100

3 Yes No No No No No No No No Left: <6

4 Yes Yes No Yes Yes No No No No Interval: 6–30

5 No No No Yes Yes No No No No Not consider

G. Hough et al. / Food Quality and Preference 15 (2004) 729–734 731



time he/she rejected the milk. In the present study we

considered the data to be interval censored between 6%

and 30% as shown in Table 3. Nine subjects presented

this type of data.

Subject 5 rejected the fresh sample, he/she was either:

(a) recruited by mistake, that is they did not like milk, or

(b) they preferred the lipolytic milk to the unalteredcontrol, or (c) they did not understand the task. It would

not be reasonable to consider the results of these sub-

jects in establishing the concentration limit for quality

control. For example, for consumers who preferred the

lipolytic to the unaltered control, a company would

have to produce a milk with this particular flavor, a

highly unlikely policy. Five subjects presented this

behavior of rejecting the unaltered control and their

results were not considered. In a study on sensory shelf-

life of yogurt, Hough et al. (2003) found that 4 out of 50

consumers rejected the fresh product and their results

were not included in the sensory failure calculations.

4.2. Failure probability calculations

To date, there are no statistical tests to compare the

goodness-of-fit of different parametric models used for

interval-censored data. Therefore, visual assessment of

how parametric models adjust to the non-parametric

estimation is the common practice in choosing the most

adequate model. Fig. 1 shows how six standard distri-

butions were fitted to the lipolytic data. Details about

each one of these distributions can be found in the

literature (Klein & Moeschberger, 1997; Meeker &

Escobar, 1998). Both the lognormal and loglogistic

distributions had adequate fits, the lognormal was cho-

sen for simplicity. For the rest of the defects, except

cooked and oxidized which shall be discussed further

ahead, the lognormal was also adequate. The maximum

likelihood estimates of the parameters of the lognormal

distribution are in Table 4.

Fig. 2 shows the failure function for the lipolyticdefect. This graph can be used to fix a value of percent

consumers rejecting the milk, for example 10% and

estimate the lipolysis concentration to be 4%. If the

lipolysis concentration is known, then the percent

consumers rejecting the product can be estimated. In

shelf-life studies the storage time has been estimated

considering 50% consumers rejecting the product

(Cardelli & Labuza, 2001; Hough et al., 2003). It should

be noted that this means that of the few consumers who

taste the product close to the end of its shelf-life, 50% of

these will reject the product. In quality control the sit-

uation is different. If a batch is tested to have a lipolysis

concentration such that 50% of consumers will reject it,

this would be unacceptably high as all consumers would

be tasting the batch with this lipolysis concentration. A

10% rejection limit is suggested as shown in Table 4. The

confidence bands of these percentiles are relatively wide,

reflecting the uncertainty inherent to the censored data.

It should be noted that 50 consumers were used for each

defect, a larger consumer panel would have reduced the

confidence bands.

The concentrations shown in Table 4 can be used for

routine quality control. For example a panel can be

trained in detecting acid flavor in UHT milk using

concentrations shown in Table 2, and specifically learn

.1

.2

.5

.9

0 10 20 30 40 50

Smallest Extreme Value Probability Plot

.1

.3

.6

.9

.98

0 10 20 30 40 50

Normal Probability Plot

Concentration %

.1

.4

.8.95

.99

0 10 20 30 40 50

Logistic Probability Plot

.1

.2

.5

.9

5 10 15 20 30 40

Weibull Probability Plot

.05.2.5

.8.95

5 10 15 20 30 40

Lognormal Probability Plot

Concentration %

.05.2.5.8

.95

.99

5 10 15 20 30 40

Loglogistic Probability Plot

F a i l u r e p

r o b a b i l i t y

Fig. 1. Probability of consumer rejecting the UHT milk with different lipolytic concentrations for six distribution models.




the concentration of 14% from Table 4 as a specification

limit. The panel would compare the daily productionwith this limit and thus decide whether the product is in

or out of specification.

For the oxidized defect 41% of the consumers were

right censored, that is a large proportion of consumers

either found the maximum concentration of this defect

acceptable, or found it to be below their threshold. With

this type of data the model’s parameters can be calcu-

lated, but their confidence intervals are too wide. For

example, for 10% rejection, the calculated concentration

was 12% with lower and higher 95% confidence limits of

5% and 28%, respectively. What occurred for this defect

was that the concentration range chosen was too low,

probably below the threshold for many consumers; the

stock solution in Table 1 would have to be modified to

increase the oxidized flavor intensity.

For the cooked defect 80% of consumers were right

censored. The stock solution (100% concentration) was

prepared by boiling UHT milk during 15 min. It is

highly unlikely that consumers will ever find a sample of

UHT milk with a higher cooked flavor than this. Thus

modifying the stock solution in Table 1 to increase the

cooked flavor would not be of practical importance.

Consumers do not seem to mind an increase in cooked

flavor within reasonable limits.

5. Conclusions

To determine the concentration limits of sensory de-

fects the focus has been set on the probability of a

consumer rejecting a product with a certain concentra-

tion. Survival analysis statistics have been used replacing

the time variable with concentration. It has been shown

that different types of censoring have to be considered in

determining a concentration limit. An important aspectof this methodology is that experimental sensory work is

relatively simple as no trained sensory panel work is

necessary. In this work, for each defect, 50 consumers

tasted nine UHT samples with different concentrations

of the defect, answering yes or no to whether they would

consume the samples. This information was sufficient to

model the probability of consumers rejecting the prod-

ucts with different concentrations. The choice of the

concentration range used to estimate the limits needs

special attention. If the concentration range is too low

(as occurred for the oxidized flavor) a large proportion

of consumers will present right censored data and esti-mations will lack precision. A large proportion of right

censored data also occurs when the defect does not

produce consumer rejection within reasonable concen-

tration limits, as occurred for the cooked flavor. Future

research in the application of survival analysis statistics

to concentration limit studies should cover: cases where

it is advisable for each consumer to try only one sample,

this would lead to the analysis of current status data

(Gomez, 2002); and how covariates related to the con-

sumers, such as age or gender, influence concentration

limit estimations.

Acknowledgements

Agencia Nacional de Promocion Cientıfica y Tec-

nologica PICT 98-09-04827.

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Table 4

Estimates of the lognormal distribution parameters (l, r) and the concentrations corresponding to 10% of consumers rejecting the product for acid,

caramel, color and lipolysis defects

Defect l se r se 10% quantile

95% lower limit Estimated quantile 95% upper limit

Acid 3.3 ± 0.1 0.5 ± 0.1 11 14 19

Caramel 3.6 ± 0.2 0.9 ± 0.1 6 11 18Color 3.5 ± 0.1 0.7 ± 0.1 9 13 18

Lipolysis 2.5 ± 0.1 0.8 ± 0.1 3 4 7

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G. Hough et al. / Food Quality and Preference 15 (2004) 729–734 733



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