Stochastic analysis of six wheeler automobile system model with a spare wheel

The present paper deals with a stochastic model of a transport bus/truck running with six identical tyres and one spare wheel considered as standby. Out of six tyres, two tyres are in working position arranged one in each side of front end. Whereas remaining four are arranged in rear end with two of each side in parallel. The bus/truck will fail due to the tyre failure if in addition of spare unit any side of front-end tyre fails or both the tyres working in parallel in either of the rear-end side fail completely. The repair is carried out only when the transport bus/truck fails completely due to the tyre failure. The replacement of a failed tyre with standby spare wheel is carried out with constant rate and during this replacement process the system remains down. For the successfully running of the bus/truck each side of front end tyres and at least one of each side of rear-end tyre must be in good condition. The continous parametric markov process and supplementary variable technique is used to obtain various economic related measure of system effectiveness. Maximum likelihood approach is used to derive the estimates of unknown parameters for MTSF.