214 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Repair and Maintenance Cost Analysis of John Deere 5403 Tractor in the Gambia Tchotang Théodorea, Lucien MEVA’Ab, Bienvenu Kenmeugnec, Pa Tamba Jammehd* a,b,cNational Advanced School of Engineering, Department of Industrial and Mechanical Engineering, University of Yaoundé I, BP 8390, Yaoundé, Cameroon dAgricultural Engineering Service, Department of Agriculture, Yundum Agriculture Station, The Gambia aEmail: theodore.tchotang@polytechnique.cm, bEmail: jrl67_meva’a@yahoo.com cEmail: bienvenu.kenmeugne@polytechnique.cm, dEmail: ptjammeh85@gmail.com Abstract The paper presents an approach for deriving a mathematical model that predict repair and maintenance (R&M) cost of farm tractors in The Gambia. As John Deere (JD) tractors are widely used by Gambian farmers, a study was conducted to predict accumulated repair & maintenance costs (Y) of the two-wheel drive (2WD) JD-5403 tractor based on accumulated working hours (X). In order to determine the mathematical model for the studied tractor, regression analysis using knowledge based analytical software (SPSS STATISTICS 21 and Excel 2016 version) was performed on the calculated data generating five regression models: linear, logarithmic, polynomial, power and exponential. The statistical results showed that the polynomial model gave better cost prediction with higher confidence and less variation than other models. Finally, it was established that repair and maintenance cost increased with an increase in working hours of JD-5403 tractor. Keywords: Statistical analysis; R&M cost; 2WD-Tractor; JD-5403; The Gambia. 1. Introduction Machinery and equipment are major cost items in farm businesses. Larger machines, new technology, higher prices for parts and new machinery, and higher energy prices have all caused machinery and power costs to rise in recent years. However, good machinery managers can control machinery and power costs per acre. ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 215 Making smart decisions about how to acquire machinery, when to trade, and how much capacity to invest in can reduce machinery costs as much as $50 per acre. All these decisions require accurate estimates of the costs of owning and operating farm machinery [1]. Gambia’s agricultural mechanization technology has continued to be import-oriented. Over the years, the government in response to the national plight of farmers to alleviate their labor shortage, has brought into the country agricultural machines and equipment. The maintenance of these machines is paramount in order to get the expected results of increasing the productivity of the Gambian farmer leading to increase in food production. Accurate prediction of repair & maintenance cost trends is critical in determining the optimum economical life of agricultural machines as well as making appropriate decisions for machinery replacements and general farm management purposes [2]. One of the difficulties in analyzing R&M costs is that they change over time. Depreciation tends to be great at first, especially for a machine purchased new, but declines over time. Likewise, interest expense is high initially but gradually diminishes. This is true whether the interest cost is cash interest paid on a loan, or an opportunity cost based on revenue foregone by continuing to own a machine year after year. On the other hand, repair costs may amount to little or nothing when a machine is still under warranty, but eventually increase as parts wear out and maintenance requirements rise. Fuel and lubrication costs usually do not change much over time, although an older engine may eventually lose some degree of fuel efficiency [3]. In order to specify the repair and maintenance factor, a regression analysis explaining the accumulated repair and maintenance costs as a function of accumulated work units is typically performed. Introducing the estimated service life as accumulated work units in the estimated function yields the repair and maintenance factor. Although widely applied, this approach suffers from two limitations. Firstly, only one independent variable is used, which reduces the explanatory power. As an important reason for this, a couple of analyses compare several functional forms, including quadratic form. Secondly, data requirements are substantial, with accumulated repair and maintenance costs as well as accumulated work units being necessary for each machine. To follow the trend of costs for each machine, the accumulated repair and maintenance costs for each service interval, say every 1,000 hours for tractors, is required. Bearing in mind that agricultural machinery can easily be used for 10 years or more, detailed records kept by the farm manager over decades are essential [1]. Limitations: This study will not address every aspect of the repair and maintenance cost analysis problem. It will only investigate the relationship between accumulated repair and maintenance costs (ARM) and accumulated working hours (AWH) of the machine. As such only two variables will be part of the regression equations: machine age in hours and R&M costs expressed as percentage of the initial cost price. 2. Material and Methods The study was conducted in Yundum agricultural station, The Gambia. Data on twenty active 2WD tractors were collected using structured questionnaires, direct survey and oral interview during the nationwide maintenance activities carried by the Agricultural Engineering Service (AES) .The AES is the service unit of the Department of Agriculture (DOA), responsible for designing and introducing to farmers appropriate and low- cost machinery for crop production and processing. For each tractor, information was sought on, tractor model, American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 216 age initial purchase price, annual hours of use, annual repairs and maintenance of costs (fuel consumption cost, lubrication cost, oil and filter cost, spare parts costs and workmanship cost). After stratifying samples, the tractors were then classified according to their age (years) into 10 groups (i.e. 1 to 10). 2.1. Characterization of the JD-5403 model The JD-5403 model selected for this study is 65 hp, 2-wheel drive (2-WD) tractor (figure 1). They are mainly used for yard work on livestock farms, orchards, vineyards and specialist production of some field-scale vegetable and salad crops. One advantage of two-wheel drive is better maneuverability and cheaper purchase price as compare to a 4-WD tractor. Figure 1: The John Deere JD-5403 model tractor 2.2. Determination of mathematical model to predict R&M costs of the JD-5403 tractor To determine regression model(s) for predicting R&M costs of these tractors at any point of service life, accumulated working hours for each year were added up to previous usage hours and the sum was considered to be independent variable (X) of the model (s) as shown in equation (1) and reported by [4]. 𝑋𝑋𝑛𝑛 = �𝑥𝑥𝑖𝑖 𝑛𝑛 𝑖𝑖=1 (1) where Xn is the accumulated working hours for the group in hour (h), n is the tractor age group in year (y), x is the mean annual operating hours per group in hour per year (h/y) for the group i. The Repair & Maintenance costs as percentage of initial purchase price which was considered to be dependent American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 217 variable (Y) obtained through dividing the total accumulated R&M costs by initial purchase price of tractor using equation (2) below as reported by [5]. 𝑌𝑌𝑛𝑛 = �𝑦𝑦𝑖𝑖 𝑛𝑛 𝑖𝑖=1 (2) Where Yn is the accumulated repair and maintenance costs based on percent of list price, y is the mean annual repair and maintenance costs each tractor in per class based on percent of list price. In order to determine mathematical model for the studied tractor, regression analysis using SPSS 21 was performed on the data. Five models as shown in equation (3-7) were used to carry out regression analysis, which included the following: 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑥𝑥 Linear mode (3) 𝑌𝑌 = 𝑎𝑎 + 𝑏𝑏𝑥𝑥 Polynomial model (4) 𝑌𝑌 = 𝑎𝑎𝑒𝑒𝑏𝑏𝑏𝑏 Exponential model (5) 𝑌𝑌 = 𝑎𝑎 + 𝑙𝑙𝑙𝑙 𝑏𝑏𝑥𝑥 Logarithmic model (6) 𝑌𝑌 = 𝑎𝑎𝑥𝑥𝑏𝑏 Power model (7) Where Y and x are dependent and independent variables; a, b, c, z: are regression coefficients. The regression model (s) having the highest coefficient of determination (R2) was selected as the best model(s) for predicting actual R&M costs trend. In addition, in the most published studies in this field power and polynomial models gave better cost prediction with higher confidence and less variation than that of linear exponential and logarithmic models. Because of, its easiness in calculations, high correlation coefficients and using of this model by many researchers, the polynomial model as given in equation (4) was suggested as final form of the repair and maintenance cost model in the present study. The following repair and maintenance cost components of the JD-5403 tractor were determined. Average fuel consumption and cost Average annual fuel consumption and fuel cost for the studied tractors were estimated using equation (8-9) and as reported by [6]. 𝑄𝑄𝑎𝑎𝑎𝑎𝑎𝑎 = 0.060 × 𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝 (8) 𝐹𝐹𝐹𝐹 = 𝑄𝑄𝑎𝑎𝑎𝑎𝑎𝑎 × 𝑓𝑓𝑓𝑓𝑒𝑒𝑙𝑙 𝑝𝑝𝑝𝑝𝑝𝑝𝐹𝐹𝑒𝑒 (9) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 218 where: 𝑄𝑄𝑎𝑎𝑎𝑎𝑎𝑎 is average gasoline consumption (l/h) 𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝 is maximum PTO power (kW) 𝐹𝐹𝐹𝐹 is fuel cost Lubrication cost The lubricating cost was calculated using 15% of the fuel cost in line with the approach employed by [7] using equation (10). 𝐿𝐿𝐹𝐹 = 0.15𝐹𝐹𝐹𝐹 (10) Where, 𝐿𝐿𝐹𝐹 is the lubricating cost 𝐹𝐹𝐹𝐹 is the fuel cost Workmanship cost The labor costs were determined by multiplying the labor wage rate times by 1.1 or 1.2 as reported by [6] using equation (11). 𝑊𝑊𝑊𝑊𝑝𝑝𝑊𝑊𝑊𝑊𝑎𝑎𝑙𝑙𝑊𝑊ℎ𝑝𝑝𝑝𝑝 𝐹𝐹𝑊𝑊𝑊𝑊𝑐𝑐 = 𝑤𝑤𝑎𝑎𝑤𝑤𝑒𝑒 𝑝𝑝𝑎𝑎𝑐𝑐𝑒𝑒 × 1.1 𝑊𝑊𝑝𝑝 1.2 (11) Other cost parameters such as the cost of spare parts and filters (oil and fuel) were determined from the records presented at the AES 3. Result and Discussions 3.1. Determination of mean annual R&M cost of the studied tractor Repair and maintenance costs of the JD-5403 tractor were sought from the following: fuel consumption cost, lubrication oil cost, oil and filter replacement cost, spare parts cost and workmanship cost. Figure (2) presents the result of the calculated mean annual repair and maintenance costs of the studied tractor with the cost of each parameter and percentage share of the total using equations (8-11). It was observed that the cost of tractor spare parts replacement had the highest percentage share compared to other cost parameters. The resulted values of spare parts cost for JD-5403 was 52%. The large share of tractor spare parts cost can be due to numerous factors such as making use of substandard tractor spare parts and unsuitable use of tractor by inexperience operators. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 219 Figure 2: The mean annual R&M costs for JD-5403 The next R&M cost parameter with high cost of the percentage total was the workmanship cost with 29%. While the least cost was obtained from oil and fuel filters parameter valuing 3% for JD-5403. The large share of workmanship cost can be mainly due to high interest rate and subsequent rapid wage increase. The results reported in this study was similar to the one obtained by [4] and [8]. Table (1) presents the results of the calculated accumulated repair and maintenance cost (dependent variable) and accumulated working hours (independent variable), determined for the JD-5403 tractor using Eq (1-2) for their different ages. These results were used as data base for the trend function analysis, regression analysis and development of our mathematical model. Table 1: Accumulated Working Hours and Accumulated Repair and Maintenance cost percentage for the studied tractor Age (Years) JD-5403 Accumulated working hours (h) Accumulated R&M cost as a Percentage of list purchase price (%) 1 1020 0.38 2 2150 1.19 3 3380 2.45 4 4318 3.98 5 5461 6.65 6 6506 7.89 7 7381 11.03 8 8406 14.33 9 9318 18.86 10 10284 24.43 Spare parts 52% Workmanship 29% Oil and fuel filters 3% Fuel consumption 12% Lubrication oil 4% Spare parts Workmanship Oil and fuel filters Fuel consumption Lubrication oil American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 220 3.2. Results of the trend function analysis using Excel In order to establish the equations for predicting future R&M cost of the studied tractors, a trend function analysis was carried out using Excel 2016. This permits us to create scatterplots and overlay trend line on the chart. The results of the trend analysis outlining the equations and R2 value of the five models (linear, logarithmic, polynomial, power and exponential) are presented in figure (3). These results allow us to select the relationship that seems to “fit” (best describe) our data base on the R2 value. The closer to 1, the better the line fits the data. The R2 also permits us to select the best model for our predictions. Notice the shape of the graphs. The slope of the curve increases as the number of hours of use increases. This indicates that repair costs are low early in the life of a machine, but increase rapidly as the machine accumulates more hours of operation. Figure 3: Comparison of accumulated R&M costs as percent of list price based on accumulated working hours of the JD-5503 tractor using Excel y = 3E-07x2 - 0.0007x + 1.2898 R² = 0.9945 y = 0.0025x - 5.2655 R² = 0.9148 y = 0.4818e0.0004x R² = 0.9427 y = 9.1463ln(x) - 68.445 R² = 0.6959 y = 1E-06x1.7916 R² = 0.9931 -10.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 0 2000 4000 6000 8000 10000 12000 Ac cu m ul at ed R & M c os ts a s p er ce nt ag e of li st p ur ch as e pr ic e (% ) Accumulated working (h) Accumulated R&M costs as percentage of list purchase price (%) Poly. (Accumulated R&M costs as percentage of list purchase price (%)) Linear (Accumulated R&M costs as percentage of list purchase price (%)) Linear (Accumulated R&M costs as percentage of list purchase price (%)) Expon. (Accumulated R&M costs as percentage of list purchase price (%)) Log. (Accumulated R&M costs as percentage of list purchase price (%)) Power (Accumulated R&M costs as percentage of list purchase price (%)) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 221 3.3. Results of the regression analysis using SPSS The relationship between the accumulated repair and maintenance cost and the accumulated working hours on the mathematical models is shown in Table (2). It illustrates the description, coefficient of determination (R2) and Fisher (F) test results of the analysis obtained for the studied tractors. It was observed that the highest value of coefficient of correlation (R2) amongst the models were found on polynomial model (R2 = 0.9945), which indicate its higher conformity with the actual data trend in comparison with the other models (linear, polynomial logarithmic and exponential). These findings are in agreement with results obtain by [9] and [10] with R2 values of (0.996) & (0.998) respectively. Table 2: Model summary and parameter estimates for JD-5403 Model Model summary Parameter estimate R2 F value a B c Linear 0.9148 4346.622 -5.2655 0.0025 Logarithmic 0.6959 45.646 -68.445 9.1463 Polynomial 0.9945 3980.293 1.2898 -0.0007 3E-07 Power 0.9931 2100.673 1E-06 1.7916 Exponential 0.9427 71.898 0.4818 0.0004 3.4. Determination of the final model for prediction of R&M cost for JD-5403 tractor For prediction of accumulated R&M costs in the present study, the polynomial model as in equation (12) was selected as the final model for tractor JD-5403 for having the highest correlation coefficients and conforming well to actual data trend particularly at later life time of tractor. 𝑌𝑌 = 0.003 � 𝑋𝑋 100 � 2 − 0.07 � 𝑋𝑋 100 � + 1.2898 (12) 3.5. Comparison of Actual data and Modelled data obtained by the predictive Model Figure (4) illustrate the comparison between the actual and modelled data obtained by the final predictive model (Polynomial) for JD-5403 model tractor. The figures show that the actual data and modelled data have very little differences in their curve. It can be seen that the rate of accumulated R&M costs for the tractors at earlier life time of them was low and fairly similar. However, trend of R&M costs was rapidly increasing thereafter. Differences in increasing rate of R&M costs may be attributed to the facts like quality in design and manufacturing, inherent deficiencies, and also incompatible field operations to their power and efficiencies. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 222 Figure 4: Comparison of Actual Data and Modelled Data using polynomial model 3.6. Percentage error determination The magnitude of the errors in terms of percentage was determined as the difference between the actual and modelled data as shown in figure (5). It’s worthy of note that graphs produced from these developed models, are seen as depicting the more accurate accumulated repair and maintenance cost (ARM) and accumulated working hours (AWH) for the tractor models studied, when compared with that obtained from the data collected. The little difference as noticed among the two is likely to be as a result of errors inherent in the documentation of the data ranging from input error, biased information, etc. Figure 5: Percentage error determination of the actual and modelled data 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 0 2000 4000 6000 8000 10000 12000 Ac cu m ul at ed R & M c os ts a s p er ce nt ag e of li st pu rc ha se p ric e (% ) Accumulated working hours (h) Graph of actual and estimated data for JD-5403 Polynomial Model Actual R&M Cost Estimated R&M Cost 0.00 2.00 4.00 6.00 8.00 10.00 12.00 -5.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 Er ro r (E M ) Predicted R&M cost as a Percentage of list purchase price (%) Percentage Error determination JD-5403 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 223 3.7. Comparison of models developed by different researchers in predicting R&M costs The comparison of models developed by different researchers in predicting the accumulated repair and maintenance costs are presented in table (3). It was observed that most of these models developed gave a similar R2 values when compared with the model developed in the present study. And in terms of the model developed, it was observed that the model developed in this study has similar structure and characteristics as the model obtained by [9]. Table 3: Models developed by different researchers and for present study Models developed by different researchers R2 Source 𝑌𝑌 = 1.2 � 𝑋𝑋 1000 � 2 0.890 ASAE (1983) 𝑌𝑌 = 0.042 � 𝑋𝑋 100 � 1.796 0.986 R. Majid (2010) 𝑌𝑌 = 0.002 ( 𝑋𝑋 100 )2 − 0.109 � 𝑋𝑋 100 � + 2.877 0.996 𝑌𝑌 = 0.072 � 𝑋𝑋 120 � 1.6 0.920 Bowers and Hunt (1970) 𝑌𝑌 = 0.005𝑋𝑋1.2 0.977 Abubakar and his colleagues (2013) [11] 𝑌𝑌 = 0.003 � 𝑋𝑋 100 � 2 − 0.07 � 𝑋𝑋 100 � + 1.2898 0.995 For the present work (JD-5403 Tractor) 3.8. Discussion The R&M costs prediction models and agricultural machinery repair coefficients values are generally dependent on factors such as research method performance and time spans, number and type of samples under study, type of operation and working conditions, repair and maintenance management, quality of materials used, weather conditions and skill of operator. Results of this study indicated that average R&M costs per hour increased with machine age. This resulted in a marginally increased total repair cost curve. These results also confirmed that the model developed for the studied tractors (JD-5403) has the tractor accumulated operating hours as the major determining factor of the repair and maintenance costs. In summary, the results of this finding will be very useful in farm machinery management with regards to prediction of R&M costs of agricultural tractors in The Gambia. It would provide policy makers, farm managers and other agencies for future planning in the provision of tractor services to the farmers at relatively lower repair and maintenance cost. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 224 4. Conclusions The following conclusions were drawn from this study: It was established that repair and maintenance cost increased with an increase in working hours of JD-5403 tractor. The model developed has the tractor accumulated operating hours as the major determining factor of the repair and maintenance costs. Repair and maintenance cost of the JD-5403 tractor as a percentage of initial purchase price (%) in The Gambia can be accurately predicted using the following mathematical model: 𝑌𝑌 = 0.003 � 𝑋𝑋 100 � 2 − 0.07 � 𝑋𝑋 100 � + 1.2898 5. Recommendations It is recommended to carry out a comparative study of the John Deere tractor and other models of tractors (Massey Ferguson, New Holland, Mahindra) present in The Gambia in order to develop a standard cost model to predict the repair & maintenance cost. References [1] E. William, "Estimating Farm Machinery Costs," Iowa State University Extension and Outreach, Iowa, 2015. [2] A. Nyockeh, "Training for 50 farmers on tractor operating underway," The Point Newspaper, The Gambia, Thursday August 2012. [3] P. T. Jammeh and M. Minteh, "Reports of the 3rd Nation-wide maintenance activity," Agric Engineering Service Unit, Yundum, 2015. [4] G. Khoub bakht, H. Ahmadi, A. Akram and M. Karimi, "Repair and maintenance cost models for MF285 tractor: A case study in central region of Iran," American Eurasian Journal of Agricultural and Environmental Science, vol. I, no. 4, p. 76 80, 2008. [5] S. Ward, M. PB and C. MB, "Repair costs of 2 and 4 WD tractors," Transactions of the ASAE, vol. 28, no. 4, pp. 1074-1076, 1985. [6] M. Hanna, "Machinery Management: Fuel Required for Field Operations," AgDM information File A3-27, Iowa State University Extension, 2001. [7] K. C. Oni, "Reliability of agricultural machinery in Kwara State," in Paper presented at the 11th Annual Conference of Nigerian Society of Agricultural Engineers, University of Nigeria., 1987. [8] S. Oluka, "costs of tractor ownership under different management systems in Nigeria, Nigerian journal of American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 38, No 2, pp 214-225 225 technology," vol. 19 (1), pp. 15-28, 2000. [9] M. Rashidi and I. Ranjbar, "Modeling of Repair and Maintenance Costs of," American-Eurasian J. Agric. & Environ. Sci, vol. 9 , no. 6, pp. 605-609, 2010. [10] R. Khodabakhshian and M. Shakeri, "Prediction of repair and maintenance costs of farm tractors by using of preventive maintenance," International Journal of Agriculture Sciences, vol. 3, no. 1, pp. 39-44, 2011. [11] M. Abubakar, "Determination of repair and maintenance cost for MF375 tractor: a case study in kano metropolis, Nigeria," Zone Journal of Engineering, Technology and Environment, vol. 9, pp. 27-35, 2013.