Coefficients of repair and maintenance costs for axial and transverse combine harvesters in Argentina

Maintenance and repair cost (M&RC) coefficients were estimated for grain harvesters in Argentina. Two representative machines were selected, the Deutz-Fahr Optima 550 and CASE Axial Flow 2188, both equipped with wheat and maize platforms. Estimated coefficients were 6.685 and 7.143 [10 h] respectively for the Deutz and CASE combines using wheat platforms; and 7.082 and 8.294 [10 h] using maize platforms. The confidence intervals for these values were estimated through regression analysis and Monte Carlo simulation. Finally, in an evaluation of several harvesters (including grain, sugar cane and cotton harvesters), M&RC coefficients were observed to show a mean decreasing tendency of around –1.5% per year.

main points: mean hourly oil lubrication costs, mean hourly grease lubrication costs and mean hourly miscellaneous repair costs. Table 1 shows the costs of these components calculated on these two occasions. The evaluation performed in 1962 refers to a generic machine with a 4.8 m (16 foot) wheat platform, assigned a useful life of 5000 hours. The estimates made in 1978 were based on the costs of a generic harvester used in the Pergamino region (Buenos Aires province) with no specification made of the make or model, nor the working width; its useful life being estimated at 10 years. Neither estimate discriminated between costs generated by the harvester and the platform. Despite both being very general estimates, the M&RCCs were within some 11 [10 -5 h -1 ] of each other.
In the last few years, grain harvesters have increased in their work capacity and new machines with axial threshing systems have emerged. The aim of the present study was: a) to review M&RCCs calculated for transverse cylinder machines and to provide a first M&RCC estimate for an axial cylinder machine in Argentina; b) to establish confidence intervals for these estimates; and c) to determine whether grain, sugar cane and cotton harvesters show any long-term tendency, following the line of work initiated in a previous study by the present author (Frank, 2002).

Material and methods
Two representative harvesters were selected: the Deutz-Fahr Optima 550 which has a transverse cylinder and a 6.9 m (23 foot) platform for wheat/soy or a maize Mainero 2000 platform for 10 furrows at 70 cm, and the CASE Axial Flow 2188 with a wheat/soy 9 m (30 foot) platform or CASE 1083 maize platform 3 for 8 furrows at 70 cm. Based on operation and maintenance manuals and conversations with the technical service heads of both suppliers (AGCO and CASE-New Holland, respectively), repair and maintenance costs were estimated and are provided in annexes to this paper. Prices and salaries were derived from: a) spare part and lubricant prices quoted or recommended by the manufacturer (as effective in July 2001, not including value added tax, VAT); b) new purchase prices for each harvester and their corresponding platforms (harvesting cutterheads) in the same marketing conditions; c) a mean hourly machine operator salary equivalent to the gross salary (i.e., the basic wage plus extras, and company contributions) of the category «tractor operator» stipulated by the Comisión Nacional de Trabajo Agrario (National Agricultural Work Commision) and resolutions of the Administración Federal de Ingresos Públicos, AFIP (Federal Administration of Public Income); d) a modal value was assigned to the workshop-hour (excluding VAT) according to conversations with dealer repair services of the suppliers AGCO and CASE-New Holland. The mean «basic» salary of the «tractor operator» category (including no extras or social security contributions) varied according to the province, thus the simple mean for the  Table 3 provides details of the maintenance and repair costs of the harvesters Deutz-Fahr Optima and CA-SE Axial Flow 2188 according to Central Product Classification (CPC version 1.0 from United Nations) for 1998, and the purchase value of each machine. The ori-  ginal estimates are detailed in the annexes. Given that both machines are sold with a wheat/soy platform, this combination was used as reference. Estimates for the maize platform are separately listed in the annexes. The quotient between the mean hourly maintenance and repair cost and the purchase value of each machine gives an M&RCC for the Deutz-Fahr of 6.685 [10 -5 h -1 ] and a coefficient of 7.143 for the CASE [10 -5 h -1 ], including costs for the wheat platform in both cases.

Results
As already mentioned, this analysis attempts to extend the findings of a previous report on sugar cane and cotton harvesters. In an effort to make both reports comparable, the M&RCC was calculated for machines of different age. This was done by adding mean hourly repair or replacement costs of parts of similar replacement age and dividing this sum by the purchase price of the machine. Table 4 shows data for selected ages.
Next, regression functions for marginal costs were fitted as a function of machine age according to the following procedure: a) Cumulative cost series were established according to the age of each machine. The corresponding incremental quotients ∆y/∆x were calculated, where «x» is the mean age in hours and «y» the total cumulative cost of all the repairs. Different functions were fitted to explain ∆y/∆x = f(x). The potential function was found to best fit the data series. Goodness of fit was measured using the adjusted determination coefficient R 2 . In this first stage, regression coefficients were determined using the ordinary least squares (OLS) estimator ß OLS =[X T X] -1 X T Y, where ß OLS is the regression coeff icient matrix and X and Y are the corresponding transformations of x and ∆y/∆x used to linearise the different functional forms. b) Once the potential function had been selected, the coefficients were recalculated using the generalised least squares (GLS) estimator ß GLS = (X T Ω -1 X) -1 X T Ω -1 Y, where X and Y are the matrices mentioned above and Ω is a diagonal matrix made up of the squared errors U* i 2 of the OLS model, to correct the bias due to heteroscedasticity in estimating the standard deviation of the regression coefficients. Pindyck and Rubinfeld (1981) and Judge et al. (1985), theoretically reviewed the estimator ß GLS , whose use for calculating maintenance and repair costs was subsequently validated by Frank (2002). The variance-covariance matrix of the coefficients of regression ß GLS is Σ 2 (ß GLS ) = (X T Ω -1 X) -1 . Table 5 shows the results obtained.
The functions calculated correspond to the expression Y i = X i ß+U i . If we denote the potential function exponent ß 1 * = λ 1 and the ordinate at the origin ß 0 * = ln(λ 0 ), and X i =ln(x i ) and Y i = ln(∆y i /∆x i ), the differential equation can be resolved as:  where C is a constant equal to zero, since the cost of maintaining a new machine is null. c) Based on the deviations of the regression coefficients and the regression error for an age x i at the end of the machine's useful life 4 , it was considered that σ 2 (Y i ) = X i 2 σ 2 (ß 1 )+ σ 2 (ß 0 )+2 X i σ(ß 1 ;ß 0 )+ σ 2 (U i ). This expression allows us to calculate the variance of Y i to simulate possible M&RCC values using the following equation obtained by resolving the differential equation: where z is a normally distributed random variable and V N is the cost of the new machine. Generating random z values gives a distribution of results that serves to establish a confidence interval for the M&RCC. In our case, we chose to perform 1000 repetitions of z, from which we obtained the conf idence intervals for P{A<M&RCC< B}=0.9 presented in Table 6.
The confidence interval was established from the empirical cumulative probability function derived from simulation. The functional form of the model used in the simulation suggests that the M&RCCs do not show a normal distribution. This presumption can be observed in Figures 1A and 1B, which provide empirical probability distributions of the M&RCCs of both harvesters for wheat/soy and maize platforms. It may be observed that the distribution of the M&RCC is rightasymmetric (positive asymmetry).
In the last stage of the study, we determined whether the M&RCCs of different harvesters showed any longterm trends. To this end, we constructed a X matrix including 26 × 5 independent variables and a Y matrix containing M&RCCs expressed as units of 10 -5 h -1 . The independent variables were 4 binary variables (3 indicative of the type of harvester and a fourth variable indicating the country where the coefficient was calculated) and a discrete variable referring to the year in which the M&RCC was calculated, counted from the year 1960 which was taken as zero. Both matrices are provided in Table 7. The criteria used to assign a year to each M&RCC was that of the oldest bibliographic reference for each case. In addition, if there were appreciable differences in the useful life assigned by North American and Argentinian authors to the different harvesters, costs at 3,000 h were taken as the cost coefficient in an effort to use comparable figures, provided local references contained this information.
Assuming a heteroscedastic structure of the residuals 5 , regression coefficients and their corresponding t statistics* are presented in Table 8.
It may be observed that all the coefficients were significant at a rejection level H 0 ) ß i =0 of 5%. These findings indicate that the M&RCCs calculated for Argenti- Combine repair/maintenance costs 85

Discussion
On simple inspection of the results, it would appear that the coefficients of maintenance and repair for the current transverse cylinder machines are lower than those generally reported for Argentina, given that the latter fall outside the confidence limits estimated by the simulation process. Further, all the values cited in North American references also escape our confidence interval.
The CASE axial harvester showed a higher M&RCC than the traditional Deutz-Fahr harvester. The transverse cylinder harvester was related to higher costs in lubricants and belts, while the axial harvester clearly generates more costs in replacing bearings. Machine operator costs were higher for the traditional harvester, being associated with more lubrication tasks. This does not necessarily indicate the greater technical complexity of one system or another, but may rather be attributed to differences in the particular designs used by each manufacturer. In other words, focusing on one particular type of machine can lead to biased results. The results presented here should therefore be backed up by more extensive studies involving larger sample sizes.
The fall in the M&RCC over time need not necessarily be explained by an increased durability of the different spare parts or by a long-term tendency of the price of spare parts to drop relative to the price of the new machine. It could be that the fall is related to the behaviour of some other factor (e.g., the working width) that varies over time. Unfortunately, the scarce reference made to the technical characteristics of these machines in the past precludes drawing any further conclusions regarding this point.