Model for Optimal Block Replacement Decision of Air Conditioners Using First Order Markov Chains with & without Considering Inflation

In this paper, a mathematical model has been developed for group replacement of a block of Air Conditioners using discrete-time First Order Markov Chains. To make the model more realistic, three intermediate states viz., Minor Repair State, Semi-Major Repair State and Major Repair States have been introduced between Functioning State & Complete Failure States of the system. The Transition Probabilities for future periods for First Order Markov Chain (FOMC) are estimated by Spectral Decomposition Method. Using these probabilities, the number of systems in each state and accordingly the corresponding average maintenance cost is computed. The forecasted inflation for Air Conditioners and the real value of money using Fisherman’s relation are employed to study and develop the real time mathematical model for block replacement decision making.