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Estimating Shelf-Life of Cottage Cheese Using Hazard Analysis
Estimating Shelf-Life of Cottage Cheese Using Hazard Analysis KAREN SCHMIDT
Departmenl of Food Science and Technology University of Georgia Athens :nlO2 JAN BOUMA
6708 ABSTRACT
Cottage cheese samples were stored at three temperatures: 0, 4, and 7°C. Microbial counts, pH, percentage of free whey, and sensory characteristics were analyzed over time to determine the shelf-life. Weibull hazard analysis was used to fit the shelf-life data to different statistical models. From the Weibull graphs, cottage cheese stored at 4°C had a nominal shelf-life of 19 d, whereas cottage cheese stored at 7°C had a nominal shelf-life of 6.5 d. Physical and microbial measurements suggest different deterioration mechanisms that are dependent on storage temperature of the samples. (Key words: cottage cheese, shelf-life, hazard analysis) INTRODUCTION
Estimation of shelf-life is difficult but critical to the successful marketing of a food product. Gacula and Kubula (1) described the distribution function of shelf-life by using different statistical methods. One of these methods, hazard analysis, is a plotting technique that allows selection of the proper data distribution. With the proper data distribution, accurate predictions can be made concerning the probability of end of shelf-life for products. The median and mean ages for shelf-life can also be determined. One hazard analysis method in particular that may apply widely is the Weibull distribution (9). This distribution is for "failed" products, products that have reached the end of
Received January 24, 1991. Accepted June 17, 1992. 1992 J Dairy Sci 75:2922-2927
as
Thorbeckestraat 76 Wageningen, The Netherlands
their shelf-lives. Shelf-life for food products potentially fits the Weibull distribution. The basis of using this distribution is to evaluate a number of products and then determine the time to failure for each unit. The time information is then tabulated, and cumulative hazard percentages are calculated. These cumulative hazard percentages are then plotted against time on different plotting papers until the best fitting distribution is found (6, 7). The hazard analysis technique has been successfully used to predict shelf-life for many different products, such as fans, electrical motors, and some food products (1, 6). Wittinger and Smith (10) used this technique to analyze the shelf-life of ice cream made with different combinations of sweeteners and stabilizers and recommended this technique to estimate the shelf-life of other dairy products. In the last two decades, consumption of cottage cheese in the United States has decreased for several reasons, including inconsistent product quality, decreased ratios of curd to dressing, and lack of marketing support (2). Variation in shelf-life may contribute to inconsistent product quality. Various factors, such as raw material, production, and storage temperature, can influence the overall quality of cottage cheese as perceived by the consumer. The objective of this study was to evaluate the feasibility of determining the shelf-life of cottage cheese stored at various refrigerated temperatures using hazard analysis technique. MATERIALS AND METHODS
Samples of cottage cheese were obtained on the day of production from the University of Georgia Creamery. Samples were collected in 227-ml plastic containers and were immediately stored at 0, 4, or 7°C. Storage temperatures varied ± I·C except for storage at O°C,
2922
SHELF-LIFE OF COlTAGE CHEESE
which remained between 0 and SC. For each day of sampling, microbiological quality, pH, percentage of free whey, and sensory evaluation were determined. Microbiology
Total plate count, yeasts and molds. and psychrotroph counts of the cottage cheese samples were measured as outlined in Standard Metlwds for the Examination of Dairy Products (3). Samples were analyzed on the day of production, at 3, 5, 7, and 14 d after production, and then on every other day until the end of shelf-life was determined. For total counts, plate count agar and an incubation time of 2 d at 32"C were used. For psychrotrophic organisms, tartaric acid was added at a concentration of .9% to potato dextrose agar prior to pouring, and the incubation time was 5 d at 25°C. pH
A 20-g sample was equilibrated to room temperature (22°C) in a closed container in 20 to 25 min and then stirred. The pH was measured on d I, 3, 5, 7, and 14 and on every other day thereafter until the end of the study with an Orion 701 digital pH meter (Orion Research, Boston, MA). Percentage of Free Whey
The method described by Mohamed and Morris (5) was modified for free whey determinations. A 20-g sample of cottage cheese was vacuum filtered through Whatman number 1 filter paper (Whatman Ltd., Maidstone, England) fitted into a to-cm diameter Buchner style funnel (Coors Ceramicon Designs, Golden, CO). The curds were spread in a thin layer covering the surface. After 10 min, the funnel and curd were weighed. The percentage of free whey was calculated using the following formula: [(initial sample weight - curd weight)/(initial sample weight)] x 100 = percentage of free whey. The percentage of free whey content was evaluated on d 1, 3, 5, 7, and 14 and on every other day thereafter until the end of the study. Sensory Evaluation
An experienced panel of five to seven members determined the end of shelf-life of the
2923
cottage cheese samples. Panelists were trained in 12 to 15 sessions that concentrated on cottage cheese characteristics. They were familiarized with off-flavors associated with the end of shelf-life. All panelists were employees of the University of Georgia and ranged in age from 25 to 55 yr. Each panelist was presented with 15-g samples in 58-ml plastic cups that were coded with randomly generated threedigit numbers. A "just noticeable difference" test was utilized for the study (4). The samples stored at 4 and 7°C were paired with samples stored at O°C, which was considered to be the reference. The panelists were asked to identify which sample had more "fruity fermented offflavor" development and then to indicate whether or not it was objectionable. Panelists received at the most three pairs of samples. Samples were rated on d 1, 3, 5, 7, and on every other day thereafter until the end of shelf-life was determined. The end of shelf-life was defined as follows: when at least 60% of the panelists identified the stored sample as objectionable in two consecutive sessions. The first of the two sessions was considered to be the end of shelf-life (10). experimental Plan
The experiment was repeated three times from May through July to gather sufficient data points for hazard analysis. For each experiment, 28 containers were stored at the appropriate temperature. Data were analyzed using hazard analysis to determine the shelf-life. As described by Nelson (6), each carton of cottage cheese (prior to the end of shelf-life) can be used as a data point to identify the appropriate distribution of the shelf-life of the stored cottage cheese. Hazard plots were performed on different distribution plots (Team Electronics, Tamworth, NH) from which the appropriate distribution and the shape of the distribution itself (e.g., bell, skewed) can be determined. This information can be obtained from the plotting paper itself. In addition, data were analyzed using regression analyses on PC-SAS (8) to determine the distribution fit of the data. After the data were analyzed, the results were verified in December of the same year to check the validity of the shelf-life models. Journal of Dairy Science Vol. 75. No. 11. 1992
2924
SCHMIDT AND BOUMA
8.0C
~7.00 ~ 6.00
<:; a
D
1
:E 500 T a 0; 4. 00 $ 0-
S! 3.00 2.00+----+----,-----+----~ 12 16 8
o
days
2.50 1-------+-----+----.--j-.~.C 8·2 days
Figure 1. Log (aerobic bacteria per gram) versus time in days for cottage cheese stored at three temperatures: O'C (0), 4'C (e), and 7'C (~). Data represent the means of three trials.
Figure 3. Log (psychrotrophs per gram) versus time in days for cottage cheese stored at three temperatures: O°C (0), 4'C (e), and 7'C (~). Data represent the means of three trials.
RESULTS AND DISCUSSION
Psychrotroph counts are shown in Figure 3. The counts for the samples stored at 0 and 4°C ranged within one log cycle. After 3 d, the counts for the samples stored at 7°C generally increased. This increase coincided with an increase in the total aerobic count, suggesting that increases in total aerobic counts are due to the increase in psychrotrophic microorganisms. The pH data are shown in Figure 4. The pH of the 0 and 4°C stored samples stabilized around 5.2 and remained relatively constant for the remainder of the study. The pH from samples stored at 7°C dropped after 3 d of storage to 4.7 and remained there to the end of study. Measurements for the percentages of free whey are shown in Figure 5. The percentage of free whey remained at approximately 18% during the experiment for the 0 and 4°C samples. The percentage of free whey in the samples stored at 7°C decreased after 2 d and then increased to about 35 to 40% after 7 d. The overall percentage of free whey for samples stored at 7°C, the increase in microbial counts (aerobic and psychrotrophic), and the decrease in pH suggest that an increase in acid-producing microorganisms was responsible for the deterioration over time of samples stored at 7°C, but does not explain the deterioration mechanisms that were occurring in the 4°C samples. The samples stored at 4°C deteriorated beyond the nominal shelf-life (e.g., panelists considered the product to be "objectionable", even through the reference was rated to be "nonobjectionable") but still had pH, percentage of free whey, and microbial counts
Microbiology
Total aerobic counts for the cottage cheese samples are shown in Figure 1. The counts for samples stored at 0 and 4°C varied basically within a log cycle. Samples stored at 7°C showed an increase in total count after 1 to 3 d and generally continued to increase throughout storage. Yeast and mold counts are shown in Figure 2. The counts of yeasts and molds for the samples stored at 0 and 4°C remained generally within a log cycle throughout the testing period. Samples stored at 7°C showed higher counts throughout storage.
6.50.-----------------,
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~ o
5.50
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u
§ 4.50 ~ ~
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~
3.50
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250 +------j4----8i----+12~--~16 0 days
figure 2. Log (yeasts and molds per gram) versus time in days for cottage cheese stored at three temperatures: O'C (0), 4'C (e), and 7'C (~). Data represent the means of three trials. Iournal of Dairy Science Vol. 75, No. 11, 1992
SHELF-LIFE OF
corrAGE
days
Figure 4. pH versus time in days for cottage cheese stored at three temperatures: O·C (0), 4·C (.), and 7"C (A). Data represent the means of three trials.
similar to those of the reference. Because the physical and microbial measurements were similar and followed the same trends for the samples stored at 0 and 4°C and because the sampl~s st~red at 7°C had different physical a~d nucroblal measurements that did not agree With the reference, deterioration mechanisms f~r the sampl~s st~red at 4 and 7°C may be different. This difference in deterioration mechanisms warrants further study. End of shelf-life was determined from the just noticeable difference test. The mean (± SD) shelf-life in days for the samples stored at 4°C was 17 ± 4.1 d, and 7 ± 2.9 d for the samples stored at 7°C. The large standard deviations reflect differences between batches. The significant differences between batches are not
45.0,.--------------~
,..
40.0
~
35.0
~
.30.0
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~ 250
2925
CHEESE
surprising, because the product was manufactured over a 2-m0 period in the University of Georgia Creamery, starting with different milks and culture. Because the shelf-life of cottage cheese is approximately one-half as long stored at 7°C as at 4°C, storage temperature appeared to have the largest influence on shelf-life. Because days to failure differed, hazard analysis was used to determine whether a statistical model could be fitted that would predict the shelf-life of cottage cheese. To perform hazard analysis, a proper distribution that captured the variance as it occurred in this research needed to be identified. Therefore, all data from the three replications were combined for a specific storage temperature and were pl?tted on several distribution plots to determme which distribution best fitted the data (Team Electronics, Inc.). The data from all three batches were included for hazard analysis calculations as described by Nelson (6, 7). The appropriate distributions from the data were then determined by fitting the best straight line through the data. Hazard plots for the samples stored at 4 and 7°C were made on Weibull hazard paper (9). A log-linear regression was performed on the data plotted in Weibull graphs shown in Figures 6 and 7, and correlation coefficients are presented in Table 1. From these plots, correlation coefficients greater than .90 indicate good linear fit. Several parameters can describe the distribution of a data set. In the case of the Weibull distribution, the shape parameter indicates the shape of the distribution (e.g., bell, skewed). The shape parameter for the sample stored at 4°C was approximately 4.19. This value is obtained from the plot itself; each individual ~lot ~as an anchor point placed at the graph. A line IS then drawn from this point until it intersects the shape parameter line (a top X-
~. 20.0"=.,,,~.c=.'i=~....,"'_=.w=~+-...
c
'50
i lOOl 5.0 . C
~---+_I- - - . . . . - + - I_-.J
o
8
12
days
Figure 5. Percentage of free whey versus time in days for cottage cheese stored at three temperatures: O·C (0) 4·C (.), and 7·C (A). Data represent the means of ~ trials.
TABLE I. Infonnation from Weibull distribution graphs. Storage temperature
Correlation coefficient
Shape parameter
.95
4.1
.93
1.71
rC) 4 7
Nominal shelf-life (d)
19.0 6.5
Journal of Dairy Science Vol. 75, No. 11, 1992
2926
SCHMIDT AND BOUMA 1
Snope Parameter
1 Shape Parornt:ter
2
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b
o o
oaxo
0
10
100
1000
Cumulotive i'H:JZord (X)
10
100
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Cumulative hazard (I)
Figure 6. Weibull hazard analysis plot for cottage cheese stored at 4'C. Line a represents the shape parameter line. Line b represents lhc data line.
Figure 7. Weibull hazard analysis plot for cottage cheese stored at 7'C. Line a represents the shape parameter line. Line b represents the data line.
axis) that is parallel to the data line. This intersecting value is then the shape parameter. When the shape parameter varies between 2 and 5, the corresponding distribution is nearly bell-shaped. This symmetry makes the 50th percentile a good estimator for the nominal shelf-life (1). The nominal shelf-life for cottage cheese stored at 4'C could be detennined from Figure 6 and was approximately 19 d. To determine the nominal shelf-life from the hazard plot, a perpendicular line was drawn from the top X-axis at the 50 percentile to the data line, and the corresponding nominal shelf-life (in days) was read from the Y-axis. The number (19 d) agreed with the sensory data of 17 ± 4.1 d as found by the panel because 19 d was within a 95% confidence interval. The shape parameter for the Weibull distribution was approximately 1.7 for the samples stored at 7·C. In this case, the shape parameter of 1.7 indicated a skewed distribution, which was supported by how quickly these cottage cheese samples became objectionable to the judges. Because of this skewness, the 50th percentile was not a good estimator for nominal shelf-life. In these cases, a median value, which corresponds to the 37.5 or 62.5 percentile, is a better estimator (6, 7). Because of the right skewness of this distribution, perhaps values lower than 50% (37.5%) would indicate nominal shelf-life more accurately. For example, the 37.5 percentile, which corresponded to a nominal shelf-life of 5 d, was more realistic
for cottage cheese stored at 7°C and agreed with the sensory panel more than for the nominal shelf-life at the 50 percentile (9 d). These data were verified 5 mo later. Cottage cheese samples were prepared as described earlier and stored at 0, 4 and 7°C. Verification data showed that cottage cheese stored at 4°C had a shelf-life of 17 d, whereas the samples stored at 7'C had a shelf-life of about 7 d. The samples stored at 7"C again showed the right skewness distribution for the cottage cheese samples. These shelf-life data agreed with the previous work conducted during May through July. The hazard analysis is a useful, inexpensive, and easy technique to determine the shelf-life of cottage cheese. Once the distribution is determined on the appropriate hazard plots, an accurate idea of the shelf-life can be realized. For a manufacturer, this infonnation would be useful so that shelf-life can be labeled more accurately, thus reducing waste and loss of consumer trust.
Journal of Dairy Science Vol. 75, No. 11, 1992
CONCLUSIONS
Hazard analysis was a suitable technique to evaluate the shelf-life of cottage cheese stored at different temperatures. Shelf-life of cottage cheese refrigerated at 4°C was about 19 d, whereas cottage cheese stored at 7°C had a shelf-life of about 7 d. In addition to sensory deterioration, changes in percentage of free whey, pH, and microbial quality also sup-
SHELF·LIFE OF COTTAGE CHEESE
ported these differences in shelf-life. However, the deterioration mechanisms for the samples stored at 4 and the 7°e appeared to be different and to warrant further investigation. Based on this experiment, these plotting techniques appear to have wide applications for other dairy and food produc~.
REFERENCES 1 Gacula, M. C., and 1. 1. Kubula. 1975. Statistical models for shelf-life failures. 1. Food Sci. 40:404. 2 Honer, C. 1990. Cheese Market News 10 (May 11):4. 3 Marshall, R. T., D. M. Adams, D. R. Morgan, N. F. Olsen, and C. H. White. 1985. Microbiological methods for dairy products. Pages 133-146, 194-198 in Standard Methods for the Examination of Dairy Products. 15th ed. G. H. Richardson, ed. Am. Publ. Health Assoc., Washington, DC.
2927
4 Meilgaard, M., G. V. Civille, and B. T. Carr. 1987. Sensory Evaluation Techniques. CRC Press, Inc., Boca Raton, FL. 5 Mohamed, M. 0., and H. A. Morris. 1987. Textural and microstructural properties of rennet-induced milk coagulum as affected by the addition of soy protein isolate. 1. Texture Stud. 18:137. 6 Nelson, W. 1969. Hazard plotting for incomplete failure data. J. Quality Techno!. 1:27. 7 Nelson, W. 1972. Theory and application of hazard plotting for censored failure data. Technometrics 4: 945. 8 SAS~ User's Guide: Statistics, Version 5 Edition. 1985. SAS Inst., Inc., Cary, NC. 9 Weibull, W. 1951. A statistical distribution of wide application. J. App!. Mechanics 18:293. 10 Wittinger. S. A., and D. E. Smith. 1986. Effect of sweeteners and stabilizers on selected sensory attrib· utes and shelf·life of ice cream. 1. Food Sci. 51:1463.
lournal of Dairy Science Vo!. 75, No. 11, 1992
Departmenl of Food Science and Technology University of Georgia Athens :nlO2 JAN BOUMA
6708 ABSTRACT
Cottage cheese samples were stored at three temperatures: 0, 4, and 7°C. Microbial counts, pH, percentage of free whey, and sensory characteristics were analyzed over time to determine the shelf-life. Weibull hazard analysis was used to fit the shelf-life data to different statistical models. From the Weibull graphs, cottage cheese stored at 4°C had a nominal shelf-life of 19 d, whereas cottage cheese stored at 7°C had a nominal shelf-life of 6.5 d. Physical and microbial measurements suggest different deterioration mechanisms that are dependent on storage temperature of the samples. (Key words: cottage cheese, shelf-life, hazard analysis) INTRODUCTION
Estimation of shelf-life is difficult but critical to the successful marketing of a food product. Gacula and Kubula (1) described the distribution function of shelf-life by using different statistical methods. One of these methods, hazard analysis, is a plotting technique that allows selection of the proper data distribution. With the proper data distribution, accurate predictions can be made concerning the probability of end of shelf-life for products. The median and mean ages for shelf-life can also be determined. One hazard analysis method in particular that may apply widely is the Weibull distribution (9). This distribution is for "failed" products, products that have reached the end of
Received January 24, 1991. Accepted June 17, 1992. 1992 J Dairy Sci 75:2922-2927
as
Thorbeckestraat 76 Wageningen, The Netherlands
their shelf-lives. Shelf-life for food products potentially fits the Weibull distribution. The basis of using this distribution is to evaluate a number of products and then determine the time to failure for each unit. The time information is then tabulated, and cumulative hazard percentages are calculated. These cumulative hazard percentages are then plotted against time on different plotting papers until the best fitting distribution is found (6, 7). The hazard analysis technique has been successfully used to predict shelf-life for many different products, such as fans, electrical motors, and some food products (1, 6). Wittinger and Smith (10) used this technique to analyze the shelf-life of ice cream made with different combinations of sweeteners and stabilizers and recommended this technique to estimate the shelf-life of other dairy products. In the last two decades, consumption of cottage cheese in the United States has decreased for several reasons, including inconsistent product quality, decreased ratios of curd to dressing, and lack of marketing support (2). Variation in shelf-life may contribute to inconsistent product quality. Various factors, such as raw material, production, and storage temperature, can influence the overall quality of cottage cheese as perceived by the consumer. The objective of this study was to evaluate the feasibility of determining the shelf-life of cottage cheese stored at various refrigerated temperatures using hazard analysis technique. MATERIALS AND METHODS
Samples of cottage cheese were obtained on the day of production from the University of Georgia Creamery. Samples were collected in 227-ml plastic containers and were immediately stored at 0, 4, or 7°C. Storage temperatures varied ± I·C except for storage at O°C,
2922
SHELF-LIFE OF COlTAGE CHEESE
which remained between 0 and SC. For each day of sampling, microbiological quality, pH, percentage of free whey, and sensory evaluation were determined. Microbiology
Total plate count, yeasts and molds. and psychrotroph counts of the cottage cheese samples were measured as outlined in Standard Metlwds for the Examination of Dairy Products (3). Samples were analyzed on the day of production, at 3, 5, 7, and 14 d after production, and then on every other day until the end of shelf-life was determined. For total counts, plate count agar and an incubation time of 2 d at 32"C were used. For psychrotrophic organisms, tartaric acid was added at a concentration of .9% to potato dextrose agar prior to pouring, and the incubation time was 5 d at 25°C. pH
A 20-g sample was equilibrated to room temperature (22°C) in a closed container in 20 to 25 min and then stirred. The pH was measured on d I, 3, 5, 7, and 14 and on every other day thereafter until the end of the study with an Orion 701 digital pH meter (Orion Research, Boston, MA). Percentage of Free Whey
The method described by Mohamed and Morris (5) was modified for free whey determinations. A 20-g sample of cottage cheese was vacuum filtered through Whatman number 1 filter paper (Whatman Ltd., Maidstone, England) fitted into a to-cm diameter Buchner style funnel (Coors Ceramicon Designs, Golden, CO). The curds were spread in a thin layer covering the surface. After 10 min, the funnel and curd were weighed. The percentage of free whey was calculated using the following formula: [(initial sample weight - curd weight)/(initial sample weight)] x 100 = percentage of free whey. The percentage of free whey content was evaluated on d 1, 3, 5, 7, and 14 and on every other day thereafter until the end of the study. Sensory Evaluation
An experienced panel of five to seven members determined the end of shelf-life of the
2923
cottage cheese samples. Panelists were trained in 12 to 15 sessions that concentrated on cottage cheese characteristics. They were familiarized with off-flavors associated with the end of shelf-life. All panelists were employees of the University of Georgia and ranged in age from 25 to 55 yr. Each panelist was presented with 15-g samples in 58-ml plastic cups that were coded with randomly generated threedigit numbers. A "just noticeable difference" test was utilized for the study (4). The samples stored at 4 and 7°C were paired with samples stored at O°C, which was considered to be the reference. The panelists were asked to identify which sample had more "fruity fermented offflavor" development and then to indicate whether or not it was objectionable. Panelists received at the most three pairs of samples. Samples were rated on d 1, 3, 5, 7, and on every other day thereafter until the end of shelf-life was determined. The end of shelf-life was defined as follows: when at least 60% of the panelists identified the stored sample as objectionable in two consecutive sessions. The first of the two sessions was considered to be the end of shelf-life (10). experimental Plan
The experiment was repeated three times from May through July to gather sufficient data points for hazard analysis. For each experiment, 28 containers were stored at the appropriate temperature. Data were analyzed using hazard analysis to determine the shelf-life. As described by Nelson (6), each carton of cottage cheese (prior to the end of shelf-life) can be used as a data point to identify the appropriate distribution of the shelf-life of the stored cottage cheese. Hazard plots were performed on different distribution plots (Team Electronics, Tamworth, NH) from which the appropriate distribution and the shape of the distribution itself (e.g., bell, skewed) can be determined. This information can be obtained from the plotting paper itself. In addition, data were analyzed using regression analyses on PC-SAS (8) to determine the distribution fit of the data. After the data were analyzed, the results were verified in December of the same year to check the validity of the shelf-life models. Journal of Dairy Science Vol. 75. No. 11. 1992
2924
SCHMIDT AND BOUMA
8.0C
~7.00 ~ 6.00
<:; a
D
1
:E 500 T a 0; 4. 00 $ 0-
S! 3.00 2.00+----+----,-----+----~ 12 16 8
o
days
2.50 1-------+-----+----.--j-.~.C 8·2 days
Figure 1. Log (aerobic bacteria per gram) versus time in days for cottage cheese stored at three temperatures: O'C (0), 4'C (e), and 7'C (~). Data represent the means of three trials.
Figure 3. Log (psychrotrophs per gram) versus time in days for cottage cheese stored at three temperatures: O°C (0), 4'C (e), and 7'C (~). Data represent the means of three trials.
RESULTS AND DISCUSSION
Psychrotroph counts are shown in Figure 3. The counts for the samples stored at 0 and 4°C ranged within one log cycle. After 3 d, the counts for the samples stored at 7°C generally increased. This increase coincided with an increase in the total aerobic count, suggesting that increases in total aerobic counts are due to the increase in psychrotrophic microorganisms. The pH data are shown in Figure 4. The pH of the 0 and 4°C stored samples stabilized around 5.2 and remained relatively constant for the remainder of the study. The pH from samples stored at 7°C dropped after 3 d of storage to 4.7 and remained there to the end of study. Measurements for the percentages of free whey are shown in Figure 5. The percentage of free whey remained at approximately 18% during the experiment for the 0 and 4°C samples. The percentage of free whey in the samples stored at 7°C decreased after 2 d and then increased to about 35 to 40% after 7 d. The overall percentage of free whey for samples stored at 7°C, the increase in microbial counts (aerobic and psychrotrophic), and the decrease in pH suggest that an increase in acid-producing microorganisms was responsible for the deterioration over time of samples stored at 7°C, but does not explain the deterioration mechanisms that were occurring in the 4°C samples. The samples stored at 4°C deteriorated beyond the nominal shelf-life (e.g., panelists considered the product to be "objectionable", even through the reference was rated to be "nonobjectionable") but still had pH, percentage of free whey, and microbial counts
Microbiology
Total aerobic counts for the cottage cheese samples are shown in Figure 1. The counts for samples stored at 0 and 4°C varied basically within a log cycle. Samples stored at 7°C showed an increase in total count after 1 to 3 d and generally continued to increase throughout storage. Yeast and mold counts are shown in Figure 2. The counts of yeasts and molds for the samples stored at 0 and 4°C remained generally within a log cycle throughout the testing period. Samples stored at 7°C showed higher counts throughout storage.
6.50.-----------------,
a,
~ o
5.50
E
u
§ 4.50 ~ ~
o
~
3.50
0-
S!
250 +------j4----8i----+12~--~16 0 days
figure 2. Log (yeasts and molds per gram) versus time in days for cottage cheese stored at three temperatures: O'C (0), 4'C (e), and 7'C (~). Data represent the means of three trials. Iournal of Dairy Science Vol. 75, No. 11, 1992
SHELF-LIFE OF
corrAGE
days
Figure 4. pH versus time in days for cottage cheese stored at three temperatures: O·C (0), 4·C (.), and 7"C (A). Data represent the means of three trials.
similar to those of the reference. Because the physical and microbial measurements were similar and followed the same trends for the samples stored at 0 and 4°C and because the sampl~s st~red at 7°C had different physical a~d nucroblal measurements that did not agree With the reference, deterioration mechanisms f~r the sampl~s st~red at 4 and 7°C may be different. This difference in deterioration mechanisms warrants further study. End of shelf-life was determined from the just noticeable difference test. The mean (± SD) shelf-life in days for the samples stored at 4°C was 17 ± 4.1 d, and 7 ± 2.9 d for the samples stored at 7°C. The large standard deviations reflect differences between batches. The significant differences between batches are not
45.0,.--------------~
,..
40.0
~
35.0
~
.30.0
•
~ 250
2925
CHEESE
surprising, because the product was manufactured over a 2-m0 period in the University of Georgia Creamery, starting with different milks and culture. Because the shelf-life of cottage cheese is approximately one-half as long stored at 7°C as at 4°C, storage temperature appeared to have the largest influence on shelf-life. Because days to failure differed, hazard analysis was used to determine whether a statistical model could be fitted that would predict the shelf-life of cottage cheese. To perform hazard analysis, a proper distribution that captured the variance as it occurred in this research needed to be identified. Therefore, all data from the three replications were combined for a specific storage temperature and were pl?tted on several distribution plots to determme which distribution best fitted the data (Team Electronics, Inc.). The data from all three batches were included for hazard analysis calculations as described by Nelson (6, 7). The appropriate distributions from the data were then determined by fitting the best straight line through the data. Hazard plots for the samples stored at 4 and 7°C were made on Weibull hazard paper (9). A log-linear regression was performed on the data plotted in Weibull graphs shown in Figures 6 and 7, and correlation coefficients are presented in Table 1. From these plots, correlation coefficients greater than .90 indicate good linear fit. Several parameters can describe the distribution of a data set. In the case of the Weibull distribution, the shape parameter indicates the shape of the distribution (e.g., bell, skewed). The shape parameter for the sample stored at 4°C was approximately 4.19. This value is obtained from the plot itself; each individual ~lot ~as an anchor point placed at the graph. A line IS then drawn from this point until it intersects the shape parameter line (a top X-
~. 20.0"=.,,,~.c=.'i=~....,"'_=.w=~+-...
c
'50
i lOOl 5.0 . C
~---+_I- - - . . . . - + - I_-.J
o
8
12
days
Figure 5. Percentage of free whey versus time in days for cottage cheese stored at three temperatures: O·C (0) 4·C (.), and 7·C (A). Data represent the means of ~ trials.
TABLE I. Infonnation from Weibull distribution graphs. Storage temperature
Correlation coefficient
Shape parameter
.95
4.1
.93
1.71
rC) 4 7
Nominal shelf-life (d)
19.0 6.5
Journal of Dairy Science Vol. 75, No. 11, 1992
2926
SCHMIDT AND BOUMA 1
Snope Parameter
1 Shape Parornt:ter
2
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Figure 6. Weibull hazard analysis plot for cottage cheese stored at 4'C. Line a represents the shape parameter line. Line b represents lhc data line.
Figure 7. Weibull hazard analysis plot for cottage cheese stored at 7'C. Line a represents the shape parameter line. Line b represents the data line.
axis) that is parallel to the data line. This intersecting value is then the shape parameter. When the shape parameter varies between 2 and 5, the corresponding distribution is nearly bell-shaped. This symmetry makes the 50th percentile a good estimator for the nominal shelf-life (1). The nominal shelf-life for cottage cheese stored at 4'C could be detennined from Figure 6 and was approximately 19 d. To determine the nominal shelf-life from the hazard plot, a perpendicular line was drawn from the top X-axis at the 50 percentile to the data line, and the corresponding nominal shelf-life (in days) was read from the Y-axis. The number (19 d) agreed with the sensory data of 17 ± 4.1 d as found by the panel because 19 d was within a 95% confidence interval. The shape parameter for the Weibull distribution was approximately 1.7 for the samples stored at 7·C. In this case, the shape parameter of 1.7 indicated a skewed distribution, which was supported by how quickly these cottage cheese samples became objectionable to the judges. Because of this skewness, the 50th percentile was not a good estimator for nominal shelf-life. In these cases, a median value, which corresponds to the 37.5 or 62.5 percentile, is a better estimator (6, 7). Because of the right skewness of this distribution, perhaps values lower than 50% (37.5%) would indicate nominal shelf-life more accurately. For example, the 37.5 percentile, which corresponded to a nominal shelf-life of 5 d, was more realistic
for cottage cheese stored at 7°C and agreed with the sensory panel more than for the nominal shelf-life at the 50 percentile (9 d). These data were verified 5 mo later. Cottage cheese samples were prepared as described earlier and stored at 0, 4 and 7°C. Verification data showed that cottage cheese stored at 4°C had a shelf-life of 17 d, whereas the samples stored at 7'C had a shelf-life of about 7 d. The samples stored at 7"C again showed the right skewness distribution for the cottage cheese samples. These shelf-life data agreed with the previous work conducted during May through July. The hazard analysis is a useful, inexpensive, and easy technique to determine the shelf-life of cottage cheese. Once the distribution is determined on the appropriate hazard plots, an accurate idea of the shelf-life can be realized. For a manufacturer, this infonnation would be useful so that shelf-life can be labeled more accurately, thus reducing waste and loss of consumer trust.
Journal of Dairy Science Vol. 75, No. 11, 1992
CONCLUSIONS
Hazard analysis was a suitable technique to evaluate the shelf-life of cottage cheese stored at different temperatures. Shelf-life of cottage cheese refrigerated at 4°C was about 19 d, whereas cottage cheese stored at 7°C had a shelf-life of about 7 d. In addition to sensory deterioration, changes in percentage of free whey, pH, and microbial quality also sup-
SHELF·LIFE OF COTTAGE CHEESE
ported these differences in shelf-life. However, the deterioration mechanisms for the samples stored at 4 and the 7°e appeared to be different and to warrant further investigation. Based on this experiment, these plotting techniques appear to have wide applications for other dairy and food produc~.
REFERENCES 1 Gacula, M. C., and 1. 1. Kubula. 1975. Statistical models for shelf-life failures. 1. Food Sci. 40:404. 2 Honer, C. 1990. Cheese Market News 10 (May 11):4. 3 Marshall, R. T., D. M. Adams, D. R. Morgan, N. F. Olsen, and C. H. White. 1985. Microbiological methods for dairy products. Pages 133-146, 194-198 in Standard Methods for the Examination of Dairy Products. 15th ed. G. H. Richardson, ed. Am. Publ. Health Assoc., Washington, DC.
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4 Meilgaard, M., G. V. Civille, and B. T. Carr. 1987. Sensory Evaluation Techniques. CRC Press, Inc., Boca Raton, FL. 5 Mohamed, M. 0., and H. A. Morris. 1987. Textural and microstructural properties of rennet-induced milk coagulum as affected by the addition of soy protein isolate. 1. Texture Stud. 18:137. 6 Nelson, W. 1969. Hazard plotting for incomplete failure data. J. Quality Techno!. 1:27. 7 Nelson, W. 1972. Theory and application of hazard plotting for censored failure data. Technometrics 4: 945. 8 SAS~ User's Guide: Statistics, Version 5 Edition. 1985. SAS Inst., Inc., Cary, NC. 9 Weibull, W. 1951. A statistical distribution of wide application. J. App!. Mechanics 18:293. 10 Wittinger. S. A., and D. E. Smith. 1986. Effect of sweeteners and stabilizers on selected sensory attrib· utes and shelf·life of ice cream. 1. Food Sci. 51:1463.
lournal of Dairy Science Vo!. 75, No. 11, 1992