05733915

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05733915 Fu, Yonghong Yu, Miaomiao Tang, Yinghui Li, Cailiang Steady-state probability algorithm and performance evaluation for $M/ (M_r,G_s)/1/N/N$ machine repair model under bi-level repair policy. J. Shandong Univ., Nat. Sci. 44, No. 4, 72-78 (2009). 2009 Editorial Board of Journal of Shandong University, Jinan, Shandong ZH machine repairable model finite source queuing system supplementary variable technique Summary: Applying the supplementary variable technique, we study a machine repair model with bi-level $ (r, s)$ repair policy and two types of repairmen. Using the recursive method of the Laplace transform and the recursive method for the derivative at zero of the Laplace transform, we obtain the steady-state probability distribution of the number of machines down in an arbitrary time period. Furthermore, we investigate various system performance measures, such as the average number of machines down in the system and machines waiting for repair, the average number of operating machines, the number of machine failures per unit time, the steady-state machine availability, the average waiting time for repair of a machine down, and the average shutdown time of a machine down. Finally, we present some numerical examples for some special cases and compare the difference between a single threshold $r$ repair policy and a bi-level $ (r,s)$ repair policy.