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On the Relative Mix Transition Probabilities of three Machine Each of two Different Types in Repairman Problem with Batch Deterministic Repairs

  • Sunday Olanrewaju Agboola
  • Titilola Obilade
The relative mix in the distribution of each machine type and the link between the durability and maintenance of each type of machine is presented. Compared to existing machine The relative mix in the distribution of each machine type and the link between the durability and maintenance of each type of machine is presented. Compared to existing machine repair problem, this study considered the repairman problem with multiple batch deterministic repairs of two different machine types A_1 and A_2. There are integer k_1=3 of type A_1 machines and integer k_2=3 of type A_2 machines in the system such that k_1+k_2=k. Each type A_1 (A_2 ) machine occasionally breaks down and moves into repair queue Q_1 (Q_2 ) at Poisson rate λ_1 (λ_2). The Repair station has a capacity to repair at most two machines in a session. Flow balance equations were obtained for each state of the system as defined by observing the system at repair time points. The resulting equations were solved for stationary probabilities for repair point and occupancy mode conditions using Gaussian elimination. Steady state repair completion probabilities (p1,p2,...,p49) and steady state occupancy probabilities (qj∶ j = 1,2,••• ,13) were obtained. Subsequently, the work are evaluated with adopted arrival rates λ_1 = 0.25,0.50,0.75,1.00,••• ,2.50, λ_2 = 2.00, and specific deterministic repair times D_st for s and t units of type A_1 and A_2 machines respectively, using Minkwoski distance of the various runs and system configuration as a guide, it was established that the closer the system is to a balanced situation the less is the discrepancy in the relative mix of the state probability distribution. We concluded that the relative mix can be rather different from each other depending on the appropriate parameters for the model.repair problem, this study considered the repairman problem with multiple batch deterministic repairs of two different machine types A_1 and A_2. There are integer k_1=3 of type A_1 machines and integer k_2=3 of type A_2 machines in the system such that k_1+k_2=k. Each type A_1 (A_2 ) machine occasionally breaks down and moves into repair queue Q_1 (Q_2 ) at Poisson rate λ_1 (λ_2). The Repair station has a capacity to repair at most two machines in a session. Flow balance equations were obtained for each state of the system as defined by observing the system at repair time points. The resulting equations were solved for stationary probabilities for repair point and occupancy mode conditions using Gaussian elimination. Steady state repair completion probabilities (p1,p2,...,p49) and steady state occupancy probabilities (qj∶ j = 1,2,••• ,13) were obtained. Subsequently, the work are evaluated with adopted arrival rates λ_1 = 0.25,0.50,0.75,1.00,••• ,2.50, λ_2 = 2.00, and specific deterministic repair times D_st for s and t units of type A_1 and A_2 machines respectively, using Minkwoski distance of the various runs and system configuration as a guide, it was established that the closer the system is to a balanced situation the less is the discrepancy in the relative mix of the state probability distribution. We concluded that the relative mix can be rather different from each other depending on the appropriate parameters for the model.
Select Volume / Issue:
Year:
2022
Type of Publication:
Article
Keywords:
Machine Repair Problem; Flow Balance Equations; Occupancy Mode Condition; Relative Mix
Journal:
IJASM
Volume:
9
Number:
1
Pages:
1-15
Month:
January
ISSN:
2394-2894
Hits: 1720
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