On a two-unit standby redundant system subject to repair and preventive maintenance

This paper derives the mean life and the Laplace-Stieltjes transform of the distribution of the first time to system-down for two dissimilar units standby redundant system with repair and preventive maintenance.Further, special cases of the results obtained here coincide with earlier results for the two-unit standby redundant system. The case when the system is not subject to preventive maintenance is considered as a particular case.     

Profit analysis of a two-unit standby system with two types of repair and preventive maintenance

This paper deals with the profit analysis of a two-unit cold standby system with two types of repairs—cheap and costly. Cheap repair becomes available after a random amount of time while costly is available instantaneously. The preventive maintenance (P.M.) of an operative unit starts at random epochs of time and is done only if the other unit is in standby. The distribution of time to accomplish P.M. is negative exponential while the distributions of failure time, repair times and time to commence P.M. are general. Various economic reliability measures of interest to system designers as well as operation managers have been obtained using regenerative point technique.     

The effect of preventive maintenance to a standby system with two types of failures

A two-unit standby redundant system with two types of failures is considered. Probability of occurrence of each type of failure is known. The Laplace transform (LT) of the survivor function of time up to the first system failure and the mean (TFSF) are derived. Finally, a theorem about the effect of preventive maintenance (PM) is proved.     

Optimal planned maintenance with salvage cost for a two-unit standby redundant system

This paper considers the optimal spare ordering policies for a cold standby redundant system with two dissimilar units. Especially, the planned maintenance schedule with salvage cost is discussed. The failure time distributions for respective units are assumed to be arbitrary. By applying the expected cost per unit time in the steady-state and the stationary availability as criteria of optimality, the optimal ordering policy minimizing or maximizing each criterion is obtained under some economical and/or physical assumptions. Finally, numerical examples are presented, and the effect of the failure time distributions for the optimal ordering policy is examined in detail.     

Optimal maintenance of a two-unit standby redundant system with a generalized cost structure

To maintain a system there are generally several alternatives available to a decision maker. In this paper a usual 2-unit standby system is considered with exponential distribution for life-time of units and arbitrary distribution for repair time. A generalized cost structure with different earning rates in different states, transition rewards and discounting, has been superimposed upon the semi-Markov process generated by the system model. An optimal maintenance policy for the system is the one that maximizes profit rate of the system. A solution algorithm, based on Howard's policy iteration method, is developed. An illustration is presented at the end.     

Stochastic behaviour of a two-unit cold standby redundant system with administrative delay and two types of repairs

In this paper we consider a two-unit cold standby redundant system in which each unit works in three modes—normal, partial failure and total failure with two types of repairs (major and minor) after partial failure mode, with administrative delay to locate expert repair man for major repair. The administrative time distribution is assumed to be exponential, whereas the repair and failure time distributions are exponential and arbitrary. The technique of regenerative processes is applied to obtain various reliability characteristics of interest to system designers.     

On standby redundant system with repair,post repair and preventive maintenance

A two-unit standby system with repair, post repair and preventive maintenance (PM) is considered. The Laplace transform (LT) of survivor function (SF) of time to the first system failure (TFSF) and the mean are derived. Finally one theorem about the effect of (PM) is proved.     

On a two-unit cold standby redundant system with random switching time

This paper, which contains two sections, deals with a two-unit cold standby redundant system with random switching time and imperfect switchover. In Section I, we use the survival functions to find the mean TFSF and the L.S.T. of the distribution to the first system failure. Finally, we find the limiting distribution to the first system failure. In Section II, we find the mean TFSF considering two types of preventive maintenance (PM), type (a) and type (b). Finally we prove that the mean TFSF with type (b) PM is greater than or equal to the mean TFSF with type (a) PM.     

Imbedded semi-Markov process applied to stochastic analysis of a two-unit standby system with two types of failures

A two unit standby redundant system with two types of failures whose system behaviour on [0,∞) can be described by a stochastic process which is not a semi-Markov process (SMP) but possesses an imbedded SMP with the set of up-states as state-space is considered. Failure time distributions are exponential while repair time distributions are general. The closed form results for mean-time-to-system-failure, steady-state availability, expected number of occurrences of a state, etc. are obtained.     

A three-unit standby redundant system with repair and preventive maintenance

This paper deals with the reliability of a renewable three-unit system under preventive maintenance activity. The Laplace transform of the reliability function and the mean lifetime of the system have been obtained under the assumption that the failure times, repair times, inspection times and maintenance times are random variables having different distributions. Some special cases also have been obtained.     

Reliability analysis of a two-unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby redundant system subject to a single repair facility with exponential failure and general repair time distribution. Each unit can work in three different modes — normal, partial failure and total failure. There is a perfect switch to operate the standby unit on total failure of the operative unit. The system has been analysed to determine the reliability parameters e.g. mean time to system failure (MTSF), steady state availability, mean recurrence to a state and expected number of visits to a state, first two moments of time in transient state, by using the theory of Semi-Markov Process. Howard's reward structure has been super-imposed on the Semi-Markov Process to obtained expected profit of the system. A number of results obtained earlier are derived as particular cases.     

Cost-benefit analysis of a one-server two-unit cold standby system with repair and preventive maintenance

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the type where the operating unit is taken up for PM whenever the other unit is available for operation. Initially, one unit is placed in operation and the other unit is kept as a cold standby. When the operating unit fails while the other unit is under service (repair or PM), the system breaks down. The busy period of the server in a time interval (O, t] is divided into time spent for repair and time spent for PM. By identifying regenerative epochs, suitable expressions for the expected values of these times are obtained. The pointwise availability is also derived. With the assumptions that a revenue is earned linearly with up-time, and repair and PM costs are incurred linearly with repair and PM times, respectively, the net expected revenue for a period (O, t] is derived. A particular case where the time to failure of the operating unit is 2-Erlang and the times for repair and PM are exponential has been analysed.     

Switch failure in a two-unit standby redundant system

In this paper we study the effect of imperfect switching on a two-unit standby redundant system, in which each unit works in three different modes (normal, partial failure and total failure) when the failure time distributions are exponential with different means and the repair times are arbitrarily distributed. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and particular cases are shown to corroborate earlier results.     

Probabilistic analysis of a two-unit cold standby system with two-phase repair and preventive maintenance

This paper deals with cost-analysis of a single-server two-unit cold standby system subject to random inspection and k-failure modes. A switch is used to operate the standby unit which works successfully with known probability p(=1 −q). The service facility plays the dual role of inspection and repair of both failed unit and failed switch. Identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in the “up” or “down” state. Laplace transform technique is adopted to solve these equations and various reliability characteristics of interest to system designers and operations managers have been obtained.     

Cost analysis of a two-unit standby system with two types of repairmen

This paper is concerned with a two-unit cold standby system with two types of repairmen. One “regular” repairman is kept for repairing the units as soon as they fail. It is assumed that sometimes he might not be able to do the repairs within some tolerable time (patience time). Another “expert” repairman, assumed to be perfect, is called on to do the repairs on the completion of this patience time or on the failure of the system, whichever is later.Various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the expert repairman should be called after the system failure. Further numerical results for a case, in which repair time and patience time both have non-Markovian property, are also investigated. Then the upper bound of the cost K₃, below which the expert repairman should be called immediately after the system failure and the corresponding increase in profit are calculated.     

Optimal policies in a two-unit standby system with two types of repairmen

This paper is concerned with a two identical unit cold standby system. There is a facility of having two types of repairmen. The “regular” repairman is always kept with the system with the known fact that he might not be able to do some complex repairs within some tolerable “patience” time, while a perfect “expert” repairman is called only in need. On the completion of this tolerable time or on the system failure whichever is earlier, the expert repairman is called on to do the job. We use semi-Markov processes and numerical methods, we discuss optimum policies for calling the expert, maximizing the profit and plot the graphs.     

Stochastic analysis of a two-unit redundant system with two types of failure

The present paper investigates a stochostic model of a two-unit warm standby system with a single repair facility. Before repair, the failed unit is sent for fault detection to decide whether it failed due to machine defect or critical human error. The probability of having machine defect and C.H.E. has been fixed. Using the regenerative point technique in the Markov renewal process various measures of system effectiveness are obtained.     

Stochastic analysis of a two-unit parallel system with partial and catastrophic failures and preventive maintenance

This paper studies a two-unit parallel system with each unit having two types of failure and two modes of operation—normal or partial failure mode. A unit fails either due to change in operating characteristics or due to catastrophe. The system goes for preventive maintenance randomly (in time). Failure rates are constant while repair and (preventive) maintenance rates are general. Using the theory of regenerative and Markov-renewal processes several important measures of reliability are obtained.     

Complex two-unit system with preventive maintenance

A two-unit warm standby redundant system with repair and preventive maintenance is considered. The pdf of the life time of a unit while in standby is assumed to be Erlangian. The pdfs of all the other random variables are arbitrary. Identifying suitable regeneration points, expressions for the Laplace transforms of the availability and reliability of the system are derived.     

Stochastic behavior of a 2-unit standby redundant system with imperfect switchover and preventive maintenance

We discuss a 2-unit standby redundant system with imperfect switchover and preventive maintenance (PM). The switch assumes up and down states repeatedly, independently of the behavior of the main unit. We have the stochastic behavior of the system.