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Forecasted Inflation Based Block Replacement Model Using Stochastic Process

The replacement problems are concerned with the situation that arises on decrease in the efficiency of the item, failure or breakdown. The problem of replacement is to identify the best policy to determine the ideal replacement time which is most economical. Group replacement model is applicable to the items that fail completely on usage and the result is group replacement age for the entire group of items in the system irrespective of whether they are functioning or not. The present paper proposes intermediate states i.e., minor repair and major repair states in between functioning and irreparable breakdown states. In addition, higher order Markov chains are used in generating the probabilities of items which are falling in different states. In order to consider money value, macro-economic variable, inflation is considered in this model. In the present model, real interest rates are calculated using forecasted inflation for future periods. Future period values of inflation are predicted by using the forecasting technique and a regression model with trigonometric function. These methods are used to accommodate cyclical fluctuation in the prices of items/inflation. The optimal replacement age is the time bucket in which the average cost of the individual replacement, repair and the cost of the items is minimum.