Applying the Boolean algebra approach to summing up qualitative ergonomic data

Transcription

1 Applying the Boolean algebra approach to summing up qualitative ergonomic data Toshiki YAMAOKA Wakayama University 930 Wakayama JAPAN, Abstract: This paper describes a method to sum up or minimize qualitative ergonomic data like user requirements of usability using the Boolean algebra approach and multiple regression analysis(the quantification 1). The correspondence analysis was conducted compared with results of the Boolean algebra approach and the quantification 1. Four pens were selected to be evaluated from view point of usability. A questionnaire was done using (A)feeling of push button feed, (B)weight, (C)balance, (D)thickness, (E)shape, (F)texture as independent variable, and total evaluation of pen as dependent variable. After the items((a)-(f)) were narrowed down by the quantification 1, the Boolean algebra approach was conducted using items narrowed down. Finally results of the Boolean algebra approach and the correspondence analysis were compared to be evaluated the difference of them. Key words: the Boolean algebra approach, ergonomics, correspondence analysis, quantification 1,usability 1. Introduction Usually qualitative ergonomic data like user requirements are difficult to be summed up, classified and weighted. However, the multiple regression or the quantification 1 were done for identifying important data. Ordinarily analysis was finished after employing the multiple regression or the quantification 1. The Boolean algebra approach is employed in order to investigate the relationship among independent variables and the causality between independent variable and dependent variable. This paper describes the algorithm how to sum up or minimize user requirements or evaluation items using the Boolean algebra approach. 2. Method (1) Four pens were evaluated using a questionnaire which comprised the following seven independent variables and a dependent variable. independent variable: (A)feeling of push button feed, (B)weight, (C)balance, (D)thickness, (E)shape,(F)texture dependent variable: total evaluation of pen 13 subjects (university student,m:11,f:2) checked the applicable items of seven independent variables and scored mark from one to ten as total evaluation. 3. Results and Discussions (1) conducting the quantification 1 method Main purpose of using the quantification 1 method is to narrow down important independent variables which

2 influenced the total evaluation of pen. The following items (independent variables) which influenced the total evaluation of pen were extracted using the quantification 1 (table 1.). Mechanical pen (1): (A) feeling of push button feed (weight for the dependent variable: range (2.5),partial correlation coefficient(ppc) (0.62) (C) balance (weight: range(3.6),ppc(0.71)) (E) shape (weight: range(1.6),ppc (0.50)) Mechanical pen (2): (A) feeling of push button feed (weight: range (2.5),PPC (0.61)), (B) weight (weight: range (2.5),PPC(0.59)) (D) thickness (weight: range(3.0),ppc (0.44)) Mechanical pen (3): (A) feeling of push button feed (weight: range (1.7),PPC (0.77)) (B)weight (weight: range(1.4),ppc (0.72)) (E)shape (weight: range (1.3),PPC (0.66)) Mechanical pen (4): (A)feeling of push button feed (weight: range (1.2),PPC (0.58)) (B) weight (weight: range (4.5),PPC (0.80)) (C) balance (weight: range(2.3), PPC(0.79)) (F) texture (weight: range (2.9), PPC(0.63)) Especially (C) balance in pen (1), (D) thickness in pen (2), (A) feeling of push button feed in pen (3) and (B) weight in pen (4) influenced the total evaluation of pen.. feeling of push button feed(a) Table 1. a part of data for pen (1) weight (B) Balance (C) Thickness (D) Shape (E) Texture (F) total evaluation Subject(1) Subject(2) Subject(3) Subject(4) (2) conducting the Boolean algebra approach The extracted items were minimized using the Boolean algebra approach which is created by Charles C. Ragin (table 2.). An algorithm to sum up the items using the Boolean algebra approach based on Quine-McCluskey minimization technique is as follows. 1) The answers which showed score of the total evaluation from 6 to 10 were selected. 2) The Boolean algebra approach was conducted using a matrix of the selected answers and the extracted items by the quantification 1. So, a truth table was made (table 2.) 3) Capital letter checked for items and small letter not clicked were used to calculate based on Boolean laws. Capital letter and small letter mean logical variable (figure 1.). 4) Each combinations of capital letter and small letter by union (OR) and intersection (AND) are minimized

3 using the redundance law of Boolean law (Boolean equation) mainly (figure 1.). 5) Finally redundant terms among prime implicant narrowed down were eliminated using the prime implicant chart. Table 2. truth table of the pen (1) logical variable logical function feeling of push button feed (A) Balance (C) Shape (E) total evaluation (z) subject(2) subject(3) subject(5) subject(6) subject(7) subject(8) subject(9) subject(10) subject(13) From the truth table (table 2.) subject(2): AcE subject(3):ace subject(5): ace subject(6):ace subject(7):ace subject(8): AcE subject(9):ace subject(10): ace subject(13):ace (1: capital letter, 0: small letter) number of capital letter:1 Ace ace number of capital letter:2 AcE ace ace Ac, ce, ae, ac minimization by the Boolean law disjunctive canonical form c(a+e) + a(c+e)= Z the pen (1) Figure 1. calculation process of the Boolean algebra approach

4 The following is results of minimization for the pens. 1) Mechanical pen (1): c(a+e)+a(c+e) (A)feeling of push button feed, (C)balance, (E)shape As the cross section of the pen (1) is triangle, (E)shape is evaluated highly by subjects. 2) Mechanical pen (2): d(a+b) (A)feeling of push button feed, (B)weight As the pen (2) is for drawing, (A)feeling of push button feed and (B)weight seem to be selected. 3) Mechanical pen (3): ab+e+ab (A)feeling of push button feed AND (B)weight The reason for extracting (A)feeling of push button feed and (B)weight is the barrel shape to hold easily. 4) Mechanical pen (4): Abf+aBc+bCf+BcF+ABF (A)feeling of push button feed, (B)weight, (C)balance, (B)weight AND (F)texture, (A)feeling of push button feed AND weight AND (F)texture AND: logical product, A AND B is true if A and B are individually true. [xy, x y] OR: logical sum, A OR B is true if either A or B is true. [x+y, x y] The main features of the pen (4) is that the surface is aluminum and the weight is light. These conditions seems to cause the results by the Boolean algebra approach. Especially, as (F) texture is not evaluated singly and added to another items, it is not so important. (3) conducting the correspondence analysis The data was restructured in order to conduct the correspondence analysis which aim was to compare results of the correspondence analysis with them of the Boolean algebra approach (table 3.). Table 3. frequency of check in case of evaluation from 6 to 10 score Figures of total evaluation show frequency of evaluation from 6 to 10 score pen (1) pen (2) pen (3) pen (4) feeling of push button feed(a) weight (B) balance (C) thickness (D) shape (E) texture (F) total evaluation According to table 3 and figure 2, the following weight down each pen. The pen(1) : shape(e), texture(f) The pen(2) : feeling of push button feed(a), balance(c) The pen(3) : weight(b) The pen(4) : thickness(d) These rough classification was reconfirmed by the cluster analysis.

5 (4) compared results of the correspondence analysis with them of the Boolean algebra approach The differences between results of the correspondence analysis and the Boolean algebra approach are as follows. 1) Mechanical pen (1): (E)shape, (F)texture <correspondence analysis> (A)feeling of push button feed, (C)balance, (E)shape <Boolean algebra approach> As the cross section of this pen is triangle, (E) shape is important item to be evaluated highly. 2) Mechanical pen (2): (A)feeling of push button feed, (C)balance <correspondence analysis> (A)feeling of push button feed, (B)weight <Boolean algebra approach> This pen is for drawing and (A)feeling of push button feed is weighted. 3) Mechanical pen (3): (B)weight <correspondence analysis> (A)feeling of push button feed AND (B)weight <Boolean algebra approach> Although a barrel shape to grip well is adopted, (E) shape is not evaluated highly. 4) Mechanical pen (4): (D)thickness <correspondence analysis> <Boolean algebra approach> (A)feeling of push button feed, (B)weight, (C)balance, (B)weight AND (F)texture (A)feeling of push button feed AND weight AND (F)texture The surface of the pen (4) is aluminum and the weight of it is light. As the correspondence analysis calculates considering the relationship among four pens, the results between them are different. categogy score pen(2) balance(c) push button (A) pen(4) total evaluation weight(b) pen(3) pen(1) shape(e) texture(f) Figure 2. results of correspondence analysis From these differences one may say that the Boolean algebra approach can describe the relationship among

6 items (independent variable) clearly than the correspondence analysis. Although the multiple regression or the quantification 1 can estimate influence on dependent variable, they cannot identify the relationship among items. Especially, as the items used by the Boolean algebra approach are narrowed down and weighted by the quantification 1, objects evaluated can be explained logically and quantitatively by using the items and the Boolean algebra approach. Because the Boolean algebra approach is a holistic method and can show multiple causation by logical sum, conjunctural causation by logical product and multiple conjunctuarl causation by sum of products form. 4. Conclusion The Boolean algebra approach turned out to be able to show the relationship or minimization among items like user requirements or evaluation item. Logical variable and logical function are needed to be identified as prerequisite condition. The relationship between them is the causality. Especially the combination of the Boolean algebra approach and the quantification 1 is effective way to identify the weight and relationship of items. References 1. Ragin CC.The Comparative Method: Moving Beyond Qualitative and Quantitative strategies, University of California Press(1987).