8. STATISTICAL ANALYSIS

The average production might be indicative of what could be expected for the logging operation by construction crane but it is worth examining the different study areas and settings. The equation to calculate productivity is: Productivity = volume : cycle time.

The productivity on study area A amounted to 11.15 m³ per hour and increased to 15.49 m³ per hour on study area B although the load volume was only about two-thirds of area A and the assortments were about one-quarter longer than at area A (for details see Table 2). Comparing the number of loads - 75 loads in 9.96 hours on study area A and 69 loads in 4.33 hours on study area B - seem to necessitate further statistical analysis.

The analysis of the cycle time variance was a result of assuming that there is a significant difference at the 0.05 level for the mean cycle time. The next step was to question which input has the greatest influence on the cycle time.

With this in mind a multiple regression was computed. The stepwise method was used with cycle time as dependent variable and length of load, load volume, load size and logging distance as independent variables.

The influence of the other recorded information - such as the method of transport and type of load - can only be shown by an analysis of variance, but their contribution of explanation to the proportion of the variation in the dependent variable, explained by a regression model, cannot be quantified because values of a nominal scale cannot be run by regression procedures.

In accordance with this regression procedure the highest degree of explanation for the cycle time is given by the load volume entered first in the equation followed by the logging distance. All other independent variables were not entered into the equation because they did not meet the entry criterion.

Dependent variable	Independent variables Multiple R R Square
cycle time	load volume logging distance 0.68255 0.46587

The R square coefficient, sometimes called the coefficient of determination, is a used measure of appropriate fit of a particular regression model. If all the observations fall on the regression line, R square is 1, and, in case there is no linear relationship between dependent and independent variables, R square is 0.

The multiple linear regression, as extension of bivariate regression by incorporating multiple independent variables, provides the following equation for the dependent variable cycle time:

cycle time = - 3.59901 + 3.30175 * (load volume) + 0.18187 * (logging dis-tance).

Assuming the load volume and logging distance as main influences to the cycle time, the attempt was made to find the optimal load volumes and logging distances which provide the highest logging performances. With this in mind the independent variables were subdivided into groups and the hypotheses that several group means are equal were examined by the statistical procedure of analysis of variance.

This statistical procedure indicates if the group means are probably unequal, but it does not pinpoint where the differences are. The Scheffe method, one of many available multiple comparison tests, was used for determining which group means are different from each other because its application is recommended to groups of unequal sample sizes. According to the range of volume per load (see Table 2) and number per formed group the following classification was chosen:

The Scheffe test showed that groups 2 and 3 are significantly different from group 1 at the 0.05 significance level. This means that if the volume per load is greater than 1.5 m³ there is a significant increase in the mean cycle time. Despite the higher cycle time there will not be a decrease in the productivity of the construction crane because the higher cycle time will then be compensated by the higher load volume.

The following grouping was chosen for the logging distances:

The Scheffe procedure revealed that the cycle time of group three is significantly different at the 0.05 level from the other two groups which suggests the most suitable logging distances. This means that if the logging distance exceeds 35 m there is a significant increase in the mean cycle time and consequently a decrease in the logging performance.

The Scheffe test for groups formed by the length of assortments did not show any significant difference in the cycle time between the groups, which might be caused by superimpos-ing effect of load volume. This effect might also cause no significant difference in the cycle time between groups formed by the type of load.

Different methods of transportation occurred only on study area B. The three formed groups were "load transported horizontal", "load transported vertical" and "load rehooked from vertical to horizontal". The cycle time of the third variant was significantly different at the 0.05 level and was two times higher than variant 1 and three times higher than variant 2 which suggests the sequence of operation.

Another reason for the higher logging performance on study area B became obvious but this influence could not be evaluated, either by an analysis of variance or by a regression procedure. This influence is the crane operator's view of the felling site. It is much easier for the crane driver to operate the crane by sight than only by radio contact, as on study area A, where the height of the young trees forming the natural regeneration reduced the view for the crane operator.

Figure 5 shows the correlation between cycle time and load volume and Figure 6 between cycle time and logging distance. The low degree of explanation by only one independent variable demonstrates, therefore, the large variety of influences responsible for cycle time and logging performance.



Correlation 0.59835 S.E. of Est 3.11384 Sig. 0.0000

R Squared 0.35802 Intercept 1.44459 Slope 3.64540

Figure 5. Correlation between cycle time and load volume.



Correlation 0.42495 S.E. of Est 3.51793 Sig. 0.0000

R Squared 0.18059 Intercept -1.02058 Slope 0.23194

Figure 6. Correlation between cycle time and logging distance.