Stochastic analysis of a 2-unit standby system with two failure modes and slow switch

This paper considers the cost-benefit analysis of a one-server two unit system subject to two different failure modes and slow switch. The failure rates of the units are constant. The repair times and the switchover time are assumed to be arbitrarily distributed. The server repairs the units and puts the standby unit into operation. Detailed analysis of the system is done by using regenerating point technique and results are obtained for mean time to system failure, steady state availability, busy period of a repair man, expected number of visits by the repair man and expected profit earned by the system.     

Stochastic analysis of a two-unit warm standby system with slow switch subject to hardware and human error failures

In this paper several important measures of reliability for a two-unit warm standby system with slow switch subject to hardware and human error failures are obtained using regenerative points technique in Markov renewal processes. All times distributions are exponential except the repair times distributions are general.     

Reliability analysis of a repairable system in a changing environment subject to a general alternating renewal process

This paper considers a repairable system in a changing environment subject to a general alternating renewal process. Using Markov renewal theory we obtain the system availability, failure frequency and reliability function.     

Cost analysis of a two unit repairable system subject to on-line preventive maintenance and/or repair

The purpose of this paper is to carry out the cost analysis of a two-unit repairable system subject to on-line preventive maintenance(PM) and repair. The policy adopted here is that the on-line PM work of the operating unit is undertaken followed by repair work of the failed unit(if any). All the random variables that. arise in the analysis are assumed to be independently and arbitrarily distributed. A mathematical model is developed using semi-regenerative phenomena and system of integral equations satisfied by various state probabilities corresponding to various initial conditions are obtained. An iterative numerical method is used to solve the system of integral equations. A cost function is built based on the expected number of various jobs completed by the server in [0, t].     

Cost analysis of a 3-state 2-unit reparable system

This paper presents the cost analysis of a 2-unit system with 3 states: good, degraded and failed. The units suffer from two types of failure: partial and catastrophic. The partial failure brings a unit to degraded state, whereas the catastrophic failure breaks down a unit completely. There is one repair facility, which is availed only when the system is either degraded or failed. The failure and repair times for the system follow exponential and general distributions respectively. Laplace transforms of various probability states have been obtained along with steady-state behaviour of the system. Inversions have also been computed so as to obtain time dependent probabilities, which determine expected profit as well as availability of the system at any time.