Mathematical Models for Reliability and Replacement of Agricultural Tractors

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Sami Atta Elmoula Bakhit Mudawi, Mudawi
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The present study was conducted to build up mathematical model for reliability and replacement of agricultural tractors. The objective of reliability module was to formulate an algorithm to estimate reliability of farm tractors, while the replacement module was used to identify the ideal length of time that a piece of tractor should be kept before replacement. The formulation of the strategy adopted to implement the replacement module was based on economic basis otherwise to develop repair and maintenance plan to keep up the un-replaced tractors. The data for the study were collected from El Guneid Sugar Company (30 tractors) and the Agricultural Bank of Sudan. The models were developed using MS Excel package and Visual Basic package (version 2003). For building reliability module, six forms of probability distribution forms were examined and Gumbel loglog distribution was chosen as the best alternative. Gumbel loglog distribution was used for reliability of farm tractor. The module calculates the Gumbel loglog parameters using the regression analysis of Log probability method. The values =537; and ^6; were 1590.91 and - 3294.72 for Belarus tractor, 194.99 and -2108.27 for John Deere tractor and 223.21 and 1072.43 for Cameco tractor, respectively. One difficulty in the replacement module formulation was to select the proper methods to estimate both depreciation and repair and maintenance costs. Hence, methods of straight line, initial and subsequent, double declining balance and sum of year-digit were examined to predict depreciation, while methods of percentage of original price, power and Exponential were used to predict repair and maintenance costs. On the basis of slope and correlation coefficient the optimum estimation methods selected were double declining balance method for depreciation costs and percentage of original price method for repair and maintenance costs. Verification and validation of the reliability module was made by using Kolmogorov-Smirnov Goodness-of-Fit Test. The implementation of the reliability module was made for Belarus, John Deere and Cameco tractors using actual field data. The results included identification of the time to reach a threshold level of failure of 6399.4, 3002.5 and 1656.7 working hours for Belarus, John Deere and Cameco tractors, respectively. In addition, reliability module was used to develop maintenance schedule for these tractors. The Schedule determines when the tractor is maintained and the spare parts needed, according to the failure type of sub system identified. Also the results indicated that tires followed by the cooling system and the transmission system were the subsystems of frequent and early rate of failure compared to other systems for all tractors. Implementation of replacement module was made for high (140 hp), medium (75 hp) and low cost tractors (Chinese tractor)) using economic data. The results indicated that for both medium and high cost crawler tractors, the optimum age for replacement in Sugar Cane Company of Sudan was 9 and 10 years without and with taxation respectively. The optimum replacement age for Chinese tractor was 14 years without taxation and 13 years with taxation. The results showed that the adjustment of total holding cost to taxation will decrease the replacement time for low cost tractors
Mathematical Models for Reliability and Replacement of Agricultural Tractors