INTRODUCTION

PAGE

A RESPONSE SURFACE METHODOLOGY APPROACH IN THE OPTIMIZATION OF COFFEE ROASTING PROCESS Ruel M. Mojica1, Edgardo V. Casas2Jessie C. Elauria3, , Engelbert K. Peralta4 and Marilyn C. Elauria5ABSTRACT

Optimization is a vital tool in agricultural and food engineering for the efficient operation of processing systems and unit processes yielding a highly acceptable product. The response surface methodology approach is a statistical technique that was used by authors in most studies involving optimization. The same methodology was used to optimize several unit operations in agricultural process engineering using fractional factorial experimental designs. The coffee roasting process operation was optimized with parameters affecting the process as independent variables while the responses, designated as dependent variables. An analysis of variance (ANOVA) was performed to determine which of the parameters significantly affected the independent variables. Second order polynomial (SOP) models as functions of the independent variables generated response surface and contour plots. Optimum regions were derived by superimposition of the contour plots based on the industry standards. Optimum operating conditions of 204.50C temperature, 20 min time of roasting and 13% initial moisture content of green beans were established.Separate validation experiments conducted at optimum conditions verified predictions and adequacy of the SOP models. Keywords: coffee roasting, optimization1. INTRODUCTIONCoffee, both as beverage and as a plant originates from northeastern Africa; the plant is a woody perennial evergreen and produce mainly economically in developing countries. Coffee beans are initially processed by removing the outer layer of the fleshy pulp that may be accomplished by a dry or a wet procedure. The wet (or washing) process is the more complex and time consuming procedure but leads generally to a higher quality of final product ( Dart and Hursten, 1985[4] and Belitz, 1999)[2] . Green coffee beans cannot be consumed as such but need to undergo a process of roasting that is essential in the formation of flavor and aroma. The different degrees of roasting (light, medium, medium-light, dark, medium dark, and very dark) produce different coffee aroma profiles and thus, a variety of coffee beverages (Modello et. al. 2005)[8].Statistics is a science dealing with the analysis of experimental data or information and drawing conclusions from such obtained information. Information or data are only beneficial when it can be examined, analyzed and findings can be recommended for intended users. Statistics is then considered as a universally accepted essential tool for all types of research and resulted in diversified statistical procedures (Gomez and Gomez, 1984) [5] for different applications. One of the statistical procedures developed was the response surface methodology (RSM).Rapid food engineering operations such as roasting reduces the overall cost of operation or processing. However, adverse effects happen to biological products being roasted. These are development of off flavors, undesirable colors, volatilization of flavor compounds and loss of essential vitamins and amino acids. Optimization of the roasting process is performed to ensure rapid processing conditions yielding an acceptable quality product and a high throughput capacity. For instance, the coffee quality aspects may include final moisture content as a measure of flavor, aroma, body and degree of roast which are important quality factors of roasted coffee. On the other hand, process parameters to be optimized may include: temperature, time, initial moisture content, speed of the auger and many other related criteria. RSM is a statistical procedure frequently used for optimization studies. It uses quantitative data from an appropriate experimental design to determine and simultaneously solve multivariate problems. The equations describe the effect of the test variables on the responses, determine interrelationships among test variables and represent the combined effect of all test variables in the response. This approach enables an experimenter to make efficient exploration of a process or system. The coffee roasting process consists primarily of cleaning, roasting, cooling, grinding, and packaging operations. Bags of green coffee beans are hand or machine opened, dumped into a hopper, and screened to remove debris. The green beans are then weighed and transferred by belt or pneumatic conveyors to storage hoppers. From the storage hoppers, the green beans arfe conveyed to the roaster operating at temperatures between 370o and 540oC and the beans roasted for a period of time ranging from a few minutes to about 30 minutes. Roasters are typically horizontal rotating drums that tumble the green coffee beans in a current of hot combustion gases; the roasters operate in either batch or continous modes and can be indirect-or direct-fired. Indirect-fied roasters are roasters in which the burner flame does not contact the coffee beans, although the combustion gases from the burner do contact the beans. Direct-fired roasters contact the beans with the burner flame and combustion gases. At the end of the roasting cycle, water sprays are used to quench the beans. Following the roasting, the beans are cooled and run through a destoner. Destoners are air classifiers that remove stones, metal fragments, and other waste not removed during initial screening fomr the beans. The stoners pneumatically convey the beans to a hopper, where the beans are stabilized and dry (small amounts of water from quenching exist on the surface of the beans. This stabilization process is called equilibration. Following this, the roasted beans are ground, usually by multi-stage grinders. Some roasted beans are packaged and shipped as whole beans. Finally, the ground coffee is vacuum sealed and shipped. Additional operations associated with processing green coffee beans include decaffeination and instant (soluble) coffee production. Decaffeination is the process of extracting caffeine from green coffee beans prior to roasting. The most common method of decaffeination process used in the US is supercritical carbon dioxide (CO2) extraction. In this process, moistened green coffee beans are contacted with large quantities of supercritical CO2 pressure maintained at about 4000 PSI and temperatures between 90o and 100oC that removes about 97% of the caffeine from the beans. The caffeine is then recovered from CO2 using activated carbon adsorption system. Another method is commonly by solvent extraction method, using oil (extracted from roasted coffee) or by ethyl acetate as a solvent. In this process, solvent is added to moistened green coffee beans to extract most of the caffeine from the beans. After the beans are removed from the solvent, they are steam-stripped to remove any residual solvent. The caffeine is then recovered from the solvent, and solvent is re-used. Decaffeinated coffee beans have a residual caffeine content of about 0.1 percent on a dry basis. Not all facilities have decaffeination operations and decaffeinated green coffee beans are purchased by many facilities that produce decaffeinated coffee.For example in the optimization of the roasting process, the roasting temperature, roasting time and to some extent initial moisture content of green beans are considered important factors affecting the quality of roasted beans. The following responses can be investigated: flavor, aroma, body, and aftertaste. A three-level five-parameter experimental design can be used to evaluate the optimum roasting process conditions. The number of functions is dependent on the number of response variables. In the following case, three mathematical functions of (k are assumed to exist for Yk:

Yk = (k (T, t, MC) Eqn [1]where T for instance is the roasting temperature, t is the time of roasting and MC is the initial moisture content of green beans. RSM was employed by several authors including Dilidili (2001) and Madamba, 1997[6] (2002)[6] to optimize unit operations resulting in acceptable responses. Other authors used RSM in optimization studies for biotechnology, drug preparation, ultra-filtration, and surveying.The objective of the paper was to determine the best operating conditions for automatic mechanical coffee roaster developed for small farmers and optimize the coffee roasting process.

2. MATERIALS AND METHODS2.1 The Coffee Roasting Machine

The coffee roasting machine used was the automatic mechanical roaster developed by Dr. Ruel Mojica, 2003[7] intended for small scale farmers. The roaster consisted of the following parts: (a) hopper for loading of green beans; (b) roasting chamber where actual roasting took place; (c) casing assembly; (d) heater; (e) insulation; (f) frame support; (g) electric motor support; (h) power transmission assembly; and (i) discharge outlet (Figure 1). The roaster is made of stainless steel except for the roasting chamber and the auger made up of G.I. sheet (gauge #16). The roaster operates with a microcontroller to maintain and control the temperature setting inside the rotating drum and the time of roasting. The microcontroller served as the heart in the operation of the machine. It controlled the time of operation and the required temperature inside the roasting chamber. Electric heater serves as stable source of heat during roasting. Once the roasting process was completed, the beans must immediately move from the chamber to avoid production of burnt beans. This was the very reason why most of the roasting machines used in large-scale operation had its cooling equipment attached to the machine. To facilitate the unloading operation, a circular opening at the bottom of the roasting chamber was provided. The cap was provided with threads to ensure safety while the machine was in operation.

2.2 The Response Surface SoftwarePROC RSREG (response surface regression) of Statistical Analysis System, SAS v.8.1 (2001) was used for optimization studies of coffee roasting. Equation [2] was used for the model of RSREG that also draws the contour as well as the surface plots produced. Contour plots of the responses can also be drawn using the more user-friendly Statistica for Windows Ver. 7.0.

Figure 1. microprocessor controlled coffee roaster2.3 The Experimental Analysis

In the analysis of the roasting process, a fractional three-level-three-factor factorial experiment was used to establish the optimum operating conditions of the machine. Table 1 shows the design matrix developed using the Design Number 1 of Box and Behnken (1960) [2]. The design had 15 runs as contrasted with the 27 runs which a 3 x 3 x 3 complete factorial design would have. Independent variables were coded as X1 (roasting temperature, 0C), X2 (roasting time, min), and X3 (initial moisture content, % dry basis). Corresponding levels were designated -1, 0, and +1, 0 being the center point. Table 2 presents the independent variables as they were coded in the optimization study. The corresponding values of L1, L2 and L3 were based on the results of the preliminary test runs.

Table 1. A Box and Behnken design matrix for an incomplete three-factor factorial experimental designBOX AND BEHNKEN RUN NUMBERSX1X2X3

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15+1

+1

-1

-1

0

+1

+1

-1

-1

0

0

0

0

0

0+1

-1

+1

-1

0

0

0

0

0

0

+1

+1

-1

-1

00

0

0

0

0

+1

-1

+1

-1

0

+1

-1

+1

-1

0

Table 2. Independent variables used in the optimization study.

INDEPENDENT VARIABLESCODED VARIABLES

Symbol Code -10+1

Roasting temperature (0C)

Roasting time (min)

Initial moisture content (%)X1X2

X3L1

L1

L1L2

L2

L2L3

L3

L3

2.4 Optimization of the Roasting Process

Response Surface Methodology (RSM) is essentially a particular set of mathematical and statistical methods used by researchers to aid in the solution of certain types of problems which are pertinent to scientific and engineering processes. The procedures are a collection of experimental strategy, mathematical methods, and statistical inference which when combined, enable the experimenter to make an efficient empirical exploration of the system in which he is interested. Using the RSM one can (1) find a suitable approximating function for the purpose of predicting future response; and (2) determine what values of the independent variables are optimum values as far as response is concerned (Myers, 1971) [7].In optimizing the roasting process with RSM as a tool, several assumptions were considered:

1. That three input factors (X1, X2, X3) were closely controlled during the entire observation process and were measured with negligible error;

2. That the dependent variables (Y1, Y2, Y3, Y4) defined the system and were experimentally measured;

3. That there were three mathematical functions, fk (k=1,,5) that described the relationship between responses, Yk and the factors Xi that were taken to be both quantitative and continuous, such as Yk = fk (X1, X2,,X3);4. That the functions could be approximated by second-order polynomial equations in the form of:

Eqn [2] where:

Bo, Bi, Bii were regression constants/coefficients which were estimated from the data of the study;

Xi were coded independent variables; and

Yk were the responses generated from the study.The effect of the different levels of temperature, time and initial moisture content was compared using Analysis of Variance (ANOVA). The RSReg Procedure of SAS (version 8) was used in making approximations of the (k functions. RSReg was found suitable to approximate the said functions using the second order polynomials. Likewise, using the same procedure, optimum independent variable values were determined such as would give the best performance and output responses. With the RSReg Procedure, parameters of a complete quadratic response surface were fitted and critical values were determined such that response optimization with respect to factors in the model was effected.

The quadratic model obtained from regression analysis was used to build a 3-dimensional graph in which the different variable Yi was represented by a curvature surface as a function of Xi. The relationship between the response and independent variables was directly visualized from the response surface plot. The information that the 3-dimensional graph conveyed was the same as that from the mathematical equation.

3. RESULTS AND DISCUSSIONS

3.1 Response Surface AnalysisThe Response Surface Analysis using the procedure of Statistical Analysis System (SAS) Institute was conducted to determine the levels of temperature, time and initial moisture content coded as X1, X2 and X3, respectively, that would give optimum values of the dependent parameters namely: final weight (Y1); final moisture content (Y2); overall cup quality (Y3); general acceptability (Y4); and willingness to buy (Y5). The stationary point was identified for each independent parameter to determine its turning points; a maximum, a minimum or a saddle point. Ridge analysis was performed when the stationary point is a saddle point. The optimum operating conditions of the mechanical roaster were sought in order to come up with the performance levels that were deemed as close to the ideal conditions as possible. In the optimization study, Response Surface Analysis using the procedure of Statistical Analysis System (SAS) Institute was used. A Box-Behnken experimental design with three independent variables at three levels was used to study the effects of factor variables on the response variables. A Box-Behnken experimental design has the advantage of requiring fewer experiments (15 runs) than would a full factorial design (27 runs). Factor variables, also known as independent variables, were coded X1, X2, and X3 and represented the roasting temperature, roasting time, and the initial moisture content of the coffee beans, respectively. Different factor variable levels were likewise given codes: -1, 0, +1, as shown in the same table, with their corresponding code (actual) values.Table 3 presents the experimental data on response variables using Box-Behnken design for the response surface analysis obtained during the final testing of the mechanical roaster. The weight of roasted beans ranges from 2.8 kgs to 3.8 kgs from its original weight of 5 kgs. This is in consonance with the findings of Knox and Huffaker (1997) in: Mojica and Peralta (2003)[11] indicating that 12.25% of the total weight of coffee beans was lost due to roasting. Run number 7, together with run number 4, likewise showed to have the highest moisture content as against run number 1s outcome having the lowest value.

In terms of overall cup quality, the highest rating of 89.5% was obtained as against the 72.3% lowest rating. Maximum and minimum general acceptability and willingness to buy values were at 7.9 and 5.2 as well as 8.2 and 4.8, respectively. With the experimental data as sole bases of reference, experimental run number 5 having an actual combination of 200 0C temperature, 20 minutes time of roasting and 13 % initial moisture content outranked all the rest in terms of overall cup quality and general acceptability and willingness to buy the product. 3.2 Effect of Factor Variables on ResponsesTo determine the over-all effect of factor variables such as roasting temperature, roasting time and initial moisture content on the response variables namely: final weight; final moisture content, overall cup quality general acceptability and willingness to buy, the Response Surface Regression of the SAS Institute was conducted. To functionally relate the response variable to factor variables, Box and Behnken[2] have advanced the validity of a second order polynomial as a graduating function to adequately approximate the functional relation between the true response and independent variables. The second degree equation likewise provided information on first and second order effects as well as interaction effects of the variables. Table 3. Experimental data on final weight using Box-Behnken design for the response surface analysis.

SAM RUN

NO.ROASTNG PROCESS

CONDITIONSRESPONSE

VARIABLES

X1X2 X3Y1Y2Y3Y4Y5

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15225

225

175

175

200

225

225

175

175

200

200

200

200

200

20025

15

25

15

20

20

20

20

20

20

25

25

15

15

2013

13

13

13

13

16

10

16

10

13

16

10

16

10

132.8

3.1

3.4

3.9

3.5

3.4

3.2

3.8

3.6

3.5

3.5

3.2

3.2

3.1

3.43.8

5.0

7.6

8.2

5.8

5.6

5.1

8.2

8.1

5.9

4.9

5.0

5.6

5.2

5.883.6

84.0

76.1

72.3

89.5

82.9

85.9

78.1

73.2

87.5

80.6

81.1

82.7

83.8

88.56.4

7.3

6.0

6.6

7.9

5.4

7.0

5.2

6.5

7.7

6.4

6.2

4.6

7.4

7.66.3

6.7

7.2

6.7

8.2

6.0

7.1

5.2

6.5

7.5

5.8

6.5

4.8

6.7

7.4

where:

Factor Variables

X1 = Roasting temperature, 0C

Y1 = Final weight, kg

X2 = Roasting time, min; and

X3 = Initial moisture content, % d.b.

Response VariablesY2 = Final moisture content, % d.b.

Y3 = Overall cup quality

Y4 = General acceptability, in percent rating (%)

Y5 = Willingness to buy, in percent rating (%)

Meanwhile, Table 4 presents the Analysis of Variance (ANOVA) showing the significance of response surface models; the effect of treatment variables as linear, quadratic or interaction (cross-product) terms. A second-order polynomial equation was used to obtain the different models that would fit the mathematical function (k for the five response variables Y1 to Y5.The ANOVA showed meaningful response surface regression models for all the response variables, having a highly significant effect on final weight, final moisture content, overall cup quality, general acceptability and at 5% significance level on willingness to buy. These significant values were largely generated by the highly consequential contribution imparted by both the linear and quadratic components of all response regression models, and more so, by the total regressed model itself.Table 4. Analysis of Variance (ANOVA) table showing the significance of surface regression model and factor variables as linear, quadratic, and interaction terms (cross product) on each of the response variables.

DEGREE OF FREEDOMSUM OF SQUARES

Y1Y2Y3Y4Y5

Model

Linear

Quadratic

Cross product

Total

Residual

Lack-of-fit

Pure error

Total Error

R2Coefficient of Variation (%)3

3

3

9

3

2

5

1.3575***

0.3898***

0.0125ns

1.7598***

0.0375***

4.1709 E-14

0.0375

0.9791

2.5826

20.8575***

5.1432***

0.1925ns26.1932***

0.3575*

0.00667

0.3642

0.9863

4.5080168.6175***

178.3598***

20.1025ns367.0798***

10.2975ns

2.0000

12.2975

0.9678

1.91284.2875**

5.9457***

2.2950**

2.5282***

0.5825ns0.0467

0.6292

0.9522

5.41853.2575**

6.0118**

0.5725 ns9.8418*

0.7275ns0.3800

1.1075

0.8989

7.1598

*** significant at 1%

** significant at 5%

* significant at 10%

ns not significant

It can also be noted in Table 4 the residual variance that is comprised of lack-of-fit and pure experimental error. Lack-of-fit test measures the failure of the model to represent data in the experimental domain at points which are not included in the regression. The coefficient of determination (R2) is the proportion of variability in the data explained or accounted for by the model while the coefficient of variance (CV) is the ratio of the standard error to the mean value of observed response expressed as percentage. It is a measure of reproducibility of the model. As a general rule, a model can be considered as highly as reproducible if its CV is not greater than 10% (Tanquilut, 2007 citing Miranda 1991).It is evident that the model developed for the three response variables Y3, Y4 and Y5 appeared to be very adequate having possessed no lack of fit and a satisfactory R2 value of 0.9678, 0.9522 and 0.8989, respectively. The results indicated that more than 90% of the variation in the response was accounted for by the function. Moreover, its significant lack of fit suggested fitted y values as having approached close to Y values, which would be indicative of a linear regression function (Myers[7] and Montgomery, 1995[6] as cited by Rafosala, 2000). Insignificant lack of fit indicated that variations in the models were due to random error.

Response variable final weight exhibited a highly significant lack of fit values while final moisture showed evidence of significant lack of fit values. A significant lack of fit would indicate that the regression function would not be linear. A number of significant variations which the random error might account for can occur, variations which might be caused by an unknown factor which the response surface model did not take into account. As such, careful thought should be done for conclusions arising from this process that other forms of the model should be investigated.

The coefficient of variation (CV) relates experimental error as a percentage of the mean indicating the degree of precision when comparing treatments and serving as a sufficient index of the reliability of the experiment being conducted (Gomez and Gomez, 1984)[3]. CV values listed in Table 9 showed relatively low values of 2.58, 4.51, 1.91, 5.42 and 7.16 for Y1, Y2, Y3, Y4 and Y5 response variables, respectively. The same way all the response variables had sufficiently high R2 values which measured the degree of reduction in the variability of the responses obtained when subjected to regressor variables X1, X2 and X3.

A highly significant effect of temperature and time on final weight, final moisture content and overall cup quality is in consonance with the study of Mojica and Peralta (2003). The higher the roasting temperature and the longer the time of roasting the lower the weight of the roasted beans, and consequently, the lower the final moisture is. The result also proves the claim of Sivetz (1983)[8] that among the factors that affect the roasting process are temperature and time of roasting.

On the other hand, initial moisture content had no significant effects on the final weight, final moisture content and willingness to buy. This explains the fact that the ranges of values of initial moisture content that have been used as factor levels were so closed to each other (10%, 13% and 16%). But it should also be noted that the selected values were based on the recommended moisture content of the green beans, that is, 12 13 % dry basis.

3.3 Contour Plots of Response VariablesIt is convenient to visualize the relation between response and factor levels geometrically. The three dimensional strategy gave a clear understanding on the behavior of the response variables throughout the total operating region. A very useful representation of the surface was obtained by drawing lines of equal response on a graph whose coordinates denoted the levels of the factors. The response curves (Figures 2a to 2e) show the influence of temperature and time on the response variables Y1, Y2, Y3, Y4 and Y5. Figures 2a and 2b show a saddle point which implied the existence of two distinct regions of maximum response. This means that a decrease in final weight and final moisture content will occur by moving away from the axis of roasting temperature (X1) and taking the forward direction of time (X2). Thus a minimum weight and moisture content can be realized at a maximum roasting temperature and longer roasting time.

On the other hand, response curve of X1 and X2 (Figures 2c to 2e) formed a maximax system for response variable Y3, Y4 and Y5. The center point of the curve represents the maximum point. This means that a decrease in responses will take place in the backward move in X1 and X2 directions. Thus, an increase in overall cup quality, general acceptability and willingness to buy could be realized on a move toward the directions of temperature and time.

3.4 Canonical Analysis of the Response SurfaceThe eventual goal of canonical analysis is to be able to determine the nature of the stationary point and the entire response system. The analysis begins with a translation of the response function from the origin O (X1 = 0, X2 = 0, X3 = 0) to a new origin at the center of the system at S, i.e. at the stationary point. The response function then is expressed in terms of new variables W1, W2, W3, the axes of which corresponds to the principal axes of the contour system. The calculation procedures are given by Dilidili (1983) citing Davies, et. al. (1963) and Myers (1971).The general representation of the canonical form is given by:

Y = YS + 1W12 + 2W22 + . + kWk2 Eqn [3]Where YS denotes the response at the stationary point S, and the center of the system is at X1S, X2S, and X3S. The coordinates of the stationary point can be found by taking the partial derivatives of the fitted response surface with respect to X1, X2, .. XK, equating to zero, and solving for the XKS. Substituting the values of the coordinates to the estimating equation gave YS.

The coefficient (1, 2, k) of the canonical equation, sometimes called as eigenvalues, aids in determining the nature of the stationary point and the response system by observing the sign and magnitude of s. For instance, if the eigenvalues are all negative, then the solution is maximum; if eigenvalues are all positive, then solution is minimum; and in case where s differ in sign, the stationary point is a saddle point. If one of the values turns out to be very small in comparison with the others, then the system approximates that of a ridge. Thus, the eigenvalues () indicate the degree of sensitivity of the system if one has to depart from the stationary point.

The relationship between the canonical axes Ws and the original axes Xs serve also as a valuable piece of information. It can be determined by using the transformation given by W = M (X XS), with the columns of matrix M being the normalized eigenvectors associated with the eigenvalues 1, 2, k. The eigenvector for the largest eigenvalue gives the direction of steepest ascent if positive, or steepest descent if negative. The eigenvectors corresponding to small or zero eigenvalues point in directions of relative flatness.

The canonical properties of the fitted surfaces are shown in Table 5. The eigenvalues () or the coefficient of canonical variables (W) indicates the nature of surface occurring in the system under consideration. The eigenvalues of the eigenvectors for final weight are 1 = 0.223022; 2 = -0.083195; 3 = -0.217328, which indicates that the stationary point is a saddle point, since the eigenvalues had different signs (+ and -) and the predicted final weight value at stationary point is 3.27. Moreover, the final weight eigenvalue of 0.223022 shows that the orientation of the valley is less curve than the hill orientation of the response curve for final weight is more aligned with roasting temperature and the hill with time. The largest eigenvalue (absolute value) of 0.223022 for temperature indicates that temperature effect is more pronounced and the curvature of the response surface was in its direction. The surface for final weight is more sensitive to roasting temperature. A saddle point also occurred for final moisture content with eigenvalues 1 = 0.952256; 2 = -0.28091; 3 = -0.638665 and a predicted value at its stationary point of 5.799615. As the orientation of the valley and the hill, the final moisture content has similar scenario with that of the final weight, that is, the valley orientation of the response curve is more aligned with roasting temperature and the hill with time. The largest eigenvalue of 0.952256 for temperature indicates that temperature effect is more pronounced and the curvature of the response surface was in its direction. It is evident that the surface for final moisture content is more sensitive also to roasting temperature. Figure 3 represents the response surface plots of overall cup quality. Since all the eigenvalues possessed negative signs, it is indicative that the stationary point of all the response variables is a maximum. In this case, the maximum values are the optimum values.

Table 5. Canonical property of fitted response surfaces.

RESPONSE VARIABLESFACTOR VARIABLESEIGEN VALUESCRITICAL VALUEPREDICTED VALUE AT STATIONARY POINTRESULT OF RESPONSE SURFACE

Final Weight

Temp

Time

Initial MC

0.2213022

-0.083195

-0.217328221.932049

18.184584

14.7586213.271038Stationary point is a saddle point

Final Moisture Content

Temp

Time

Initial MC

0.952256

-0.026091

-0.638665213.305768

16.100585

26.5364345.799615Stationary point is a saddle point

Overall Cup QualityTemp

Time

Initial MC

-2.382970

-3.678358

-6.151172210.804549

19.564069

12.54149189.496081Stationary point is a maximum

General AcceptabilityTemp

Time

Initial MC

-0.318766

-0.0649096

-1.257138205.835407

17.545285

11.4907937.960138Stationary point is a maximum

Willingness To BuyTemp

Time

Initial MC

-0.318103

-0.613551

-1.180846201.580508

20.068644

12.1854247.787600Stationary point is a maximum

3.5 Optimal Processing ConditionIt is the main object of this experiment to obtain the optimum operating conditions of the mechanical roaster that would give maximum response. To realize this, contour plots of statistically significant responses were superimposed to obtain the optimum region of the independent parameters. Superimposition yielded the optimum experimental region shown in (Figure 4). Considering the nature at which roasting temperature values were chosen with their accompanying limitations and the ranges of the different levels of time and initial moisture content, the optimum region point was derived by determining the centroid by midpoint analysis. As such, the optimum values are 204.5 0C roasting temperature; 19.75 min roasting time; and 12.25 % moisture content dry basis.

To validate the mathematical model for the optimum process region, another roasting operation was performed using the above optimum values. A comparative analysis was done on the values of the predictive model for each parameter and the validated experiment.

3.6 Verification of the Optimum Process ConditionsAfter having established the optimum point, verification test was performed using the optimum values (204.5 0C roasting temperature, 19.75 min roasting time, and 12.25 % moisture content) to verify the adequacy of the response. A comparative analysis was done on the values of the predictive model for each parameter and the validated experiment. Table 6 shows the experimental results where corresponding standard deviation value and coefficient of variation are likewise shown. It also presents a comparison between predicted and actual experimental values. Among the five second-order polynomial models, the model for Y1 (final weight) and Y2 (final moisture content) had come up with a predictive value that was lower (5.44% and 17.02%, respectively) than the actual experimental value. This is in spite of the fact that the model along with those of Y1 and Y2 did exhibit a lack of fit which was notably significant.

The model on Y3 (overall cup quality) which was previously adjudged to be having a non-significant lack of fit, produced an experimental output that was almost equal to the predictive value having an error of 0.80% only. The model for Y4 (general and acceptability) and Y5 (willingness to buy) which were also adjudged to be highly adequate models came up with a far 10.32 % and 13.90 % over and above what was predicted by its second-order model, respectively. It was believed that one factor affecting the result was the fact that sensory evaluation, in many instances, was highly subjective. Such subjectiveness might have taken into account in the outcome of the verification tests, particularly on general acceptability and on willingness to buy the product.

Table 6. Predicted and actual experimental data for values at optimum point.

RESPONSE VARIABLE

PREDICTED VALUE

EXPERIMENTAL VALUE

RANGE

% ERROR

Y1Y2Y3Y4Y53.319349

5.546185

89.06050

7.861945

7.7817743.5 ( 0.42

6.4 ( 0.28

88.35 ( 4.17

7.05 ( 1.20

6.7 ( 1.413.0 3.92

6.12 6.68

84.18 92.52

8.85 8.25

5.29 8.11 5.44

17.02

0.80

10.32

13.90

4. CONCLUSION AND RECOMMENDATIONConclusions can be made from the foregoing studies that coffee roasting process is one of the food engineering operations that can be optimized. Optimizing the agricultural processing operations should be performed in order to recommend best conditions for roasting operation resulting in a superior quality product as well as maximizing throughput capacity and reducing processing costs. RSM was found to be a useful approach and it should be recommended that this methodology be adapted to all optimization studies.

5. REFERENCES

[1] BATALON, JUANITO T. 1998. Optimization of Coconut Coir Dust Compaction. A Masteral Thesis. University of the Philippines Los Baos, College, Laguna.

[2] BELITZ, H.D. in: Food Chemistry. Springer-Verlag, Berlin 1999, pp. 87485.

[3] BOX, G.E.P. AND D.W. BEHNKEN. 1960. Some New Three Level Designs for the Study of Quantitative Variables. Technometrics, vol. 2, no. 4. pp. 455-475.[4] DART, S. K. and H. E. HURSTEN in: Coffee, Volume 1, Chemistry, R.J. Clarke, R. Macrae (Eds.). Elsevier, London 1985, pp. 223265.[5] DILIDILI, J[6] GOMEZ, K.A. and GOMEZ, A. A. Statistical Procedures for Agricultural Research, 2nd edition. New York: John Wiley and Sons, Inc.

[7] MADAMBA, P.S. 1997. Optimization of the Drying Process: An Application to the Drying of Garlic. Drying Technology. 15(1). pp. 117-136.

[8] MOJICA, R. M. and PERALTA, E. K. 2003. Design, Construction and Evaluation of A Batch-Type Coffee Roaster for Small-Scale Roasting. Published MS Thesis. University of the Philippines at Los Baos, College, Laguna, Philippines.

[9] MONDELLO, L. COSTA, R. and TANCHIDA, P. Q. 2005. Reliable Characterization of coffee bean aroma profiles by automated headspace solid phase microextraction mass spectrometry. www.ss-journal.de[10] MONTGOMERY, D.C. 1995. Response Surface Methodology. John Wiley and Sons, New Yok, U.S.A.

[11] MYERS, R.H. 1971. Response Surface Methodology. Allyn and Bacon, Inc. Boston, U.S.A.

[12] SIVETZ, MICHAEL. 1983. Coffee Processing Technology. Westport, Connecticut: AVI Publishing Co., Inc.

[13] The Philippines Recommends for Coffee. 1977. Los Baos, Laguna, Philippine Council for Agriculture and Resources Research and Development.Dr. Ruel M. Mojica presently chairs the Department of Agricultural and Food Engineering Cavite State University, Indang, Cavite, Philippines

Dr. Ruel M. Mojica is an Assistant Professor III of agricultural and food engineering and presently chairs of the Department of Agricultural and Food Engineering, Cavite State University, Indang, Cavite. E-mail: ruelmojica@yahoo.comAssistant Prof. Edgardo V. Casas was born in Tiaong, Quezon, Philippines in 1951; received his B. S.C. in Agricultural Engineering in 1975 from the University of the Philippines Los Baos in 1975. Went to University of New South Wales, Australia in 1986 for the Master in Applied Science in Food Engineering, and then enrolled in PhD in Food Science in the same school in 1992. He has worked in the University of the Philippines Los Baos immediately after graduation in 1975as research assistant and training assistant and started teaching crop processing courses in 1977 until to date at the Agricultural and Bioprocess Division, Institute of Agricultural Engineering, College of Engineering and Agro-Industrial Technology, University of the Philippines Los Baos. Email: evcasas04@gmail.comDr. Jessie C. Elauria obtained his PhD. in Energy Engineering and Masters Degree in Mechanical Engineering from the University of the Philippines Diliman, Quezon City in 1993 and 1986 respectively. He graduated from U.P. Los Baos in 1978 with a degree of B.S. Agricultural Engineering.

He is a Professor at the College of Engineering and Agro-Industrial Technology at U.P Los Baos. He also serves as Economic Research Institute of ASEAN and East Asia (ERIA) Working Group Member on Biomass Sustainability in East Asia. He was appointed by former President Fidel V. Ramos as Director of Energy Utilization Management Bureau of the Department of Energy (DOE) from 1995 to 1998. He has published several papers in refereed journals, developed nationally policy papers, monograph, handbook, with several papers published in proceedings and more than 50 papers presented in conferences and workshops here and abroad.

Dr. Marilyn M. Elauria is an Associate Professor in Agricultural Economics and obtained the following degrees: B.S. Agriculture, M.S. Agricultural Economics, and Ph.D. in Management. She has served U.P. Los Baos since 1978 as instructor and has been involved in research and extension activities of the University. Her fields of expertise include Farm Management, Farm Accounting, Agricultural Marketing, Project Analysis, Monitoring and Evaluation, Energy Economics, Agricultural Finance and Investment Management.

Dr. M. M. Elauria is a recipient of the 2010 UPLB Centennial Professorial Chair Award, UPLB United Coconut Planters Bank Professorial Chair Award, UP Diamond Jubilee Faculty Grant and the Asian Regional Research Programme in Energy, Environment, and Climate Research Fellowship at the Asian Institute of Technology, Thailand. She has served as project leader of several foreign and locally funded projects, has five international refereed publications and co-author of Farm Management Book in the Philippines.

ENGELBERT K. PERALTA is an Associate Professor of Agricultural Engineering at the ABPROD, IAE, CEAT, University of the Philippines Los Baos; obtained BS in Agricultural Engineering from the University of the Philippines at Los Baos in 1978; registered as a Professional Agricultural Engineer at the Professional Regulation Commission in the following year. Immediately after graduation, worked as a process engineer and later as an instructor in UPLB; resigned in 1979 to pursue M. Engineering from the Asian Institute of Technology in September 1981 as scholar of the Australian Government. He rejoined the University of the Philippines Los Baos in 1981, became study leader of BIOTECH from 1982 to 1985. E.K. Peralta pursued PhD in Agricultural Engineering at Texas A & M University, 1986.Together with his adviser O.R, Kunze, co-authored Simple Relative Humidity Systems that Fissure Rice and Other Grains at the International Summer Meeting of the American Society of Agricultural Engineers, Rapid City, South Dakota and at the Rice Technical Working Group Meeting, University of California at Davis on June 1988 later published in the ISI Journal Applied Engineering in Agriculture. The American Society of Agricultural Engineers (ASAE) later recognized The Kunze research group for their work on rice fissuring, considered as one of the top outstanding achievements in agricultural engineering of the 20th century in the field of Food and Process Engineering; was a consultant for the Appropriate Technology International Project on State of the Art Study of Coconut By-Product Utilization. was a consultant for the Appropriate Technology International Project on Pilot Plant for Coconut Processing 1991-1993.In 2002, E.K. Peralta with his doctoral student Ritchilda Valerio and Elda B. Esguerra were awarded the Outstanding Scientific Paper award by the National Academy of Science and Technology for their paper Rheological Properties of Mango (Mangifera indica) Fruits in relation to Handling and Transport. PAS 84(3):232-240.

Currently, he is the editor of the Philippine Journal of Agricultural and Biosystems Engineering (PJABE). As Chairman of the IAE Academic Affairs Committee in 2011 led the transformation of the BS Agricultural Engineering curriculum to Agricultural and Biosystems Engineering. His present research interests include applications of nanotechnology on agricultural and Biosystems engineering.2

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Figure 1. The microcontroller-based mechanical coffee roaster.

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Figure 2b. Contour plot for final moisture content (% d.b.) as a function of temperature (0C) and time (min).

Figure 2a. Contour plot for final weight (kg) as a function of temperature (0C) and time (min).

Figure 2e. Contour plot for willingness to buy (scale of 1-10) as a function of temperature (0C) and time (min).

Figure 2d. Contour plot for general acceptability (scale of 1-10) as a function of temperature (0C) and time (min).

Figure 2c. Contour plot for overall cup quality (%) as a function of temperature (0C) and time (min).

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Time (min)

Figure 4. Superimposed contour plots of the response variables showing optimum region.

Temperature

(0C)

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Figure 3. Response surface plot of overall cup quality

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Assistant Professor III and Chair, Department of Agricultural and Food Engineering, Cavite State University, Indang, Cavite. E-mail: HYPERLINK "mailto:ruelmojica@yahoo.com" ruelmojica@yahoo.com;

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