R. Subramanyam Naidu

Cost—benefit analysis of a one-server two-unit cold standby system subject to inspection

Abstract This paper deals with the cost—benefit analysis of a single-server two-unit cold standby redundant repairable system subject to inspection. An inspection policy model is considered in which the failure of a unit is detected by inspection only but system failure is detected instantaneously without inspection. The failure time of a unit is assumed to be exponentially distributed with parameter λ. Initially, a unit is switched on and the other one is kept as cold standby. The system breaks down if a unit fails while the other is still under repair. In this paper, the system is characterised by the probabilities of its being in the up or the down state. Integral equations are set up for these probabilities by identifying suitable regenerative epochs. Laplace transform technique is employed to solve these equations. System characteristics, namely: 1. pointwise availability of the system during (0, t 2. s -expected up-time of the system in (0, t 3. s -expected busy-period of the service facility in (0, t 4. steady-state availability of the system; are obtained to carry out the cost—benefit analysis. Numerical results pertaining to three particular cases are also presented.

Stochastic behaviour of a two-unit repairable system subject to inspection

Abstract This paper deals with the stochastic behaviour of a one-server two-unit repairable system subject to inspection. An inspection strategy is proposed in which the failure of a unit as well as the system failure is detected by inspection only. The present paper investigates the stochastic behaviour of such a system when inspection is of instantaneous duration. It is assumed that the time to failure of a unit is exponentially distributed with parameter λ. At time t = 0, a unit is switched on and the other one is kept as a cold standby. System breakdown occurs when no unit is in operable condition. Here, the system is characterized by the probabilities of its being in the up or the down state. Integral equations are formed for these probabilities by identifying suitable regenerative epochs. The Laplace transform technique is adopted to solve these equations. The economics-related measures of system effectiveness, namely: o 1. point-wise availability of the system in (0, t; 2. s-expected up-time of the system in (0, t 3. s-expected busy-period of the service facility in (0, t 4. s-expected net gain per unit time in (0, t 5. steady-state availability of the system; are obtained to carry out the cost—benefit analysis. Numerical results pertaining to three particular cases are obtained.

Cost-benefit analysis of a one-server two-unit warm standby system subject to different inspection strategies

Abstract This paper deals with the cost-benefit analysis of a single-server two-unit repairable system with a warm (partially energised) standby subject to inspection. Two inspection strategies are proposed, namely: (i) failure of the operating unit as well as the standby unit are detected by inspection only, but system failure is detected instantaneously without inspection; (ii) failure of the operating unit and the standby unit as well as system failure are detected by inspection only. It assumes that the failure times of the units are exponentially distributed with parameters λ and λ1, respectively. Initially, a unit is switched on and the other one is kept as a warm standby. The system breaks down if a unit fails while the other is still under repair. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes and employs the Laplace transform technique to solve these equations. System characteristics, namely: 1. 1. point-wise availability of the system in (0, t]; 2. 2. s-expected up-time of the system in (0, t]; 3. 3. s-expected busy-period of the service facility in (0, t]; 4. 4. s-expected net gain per unit time in (0, t]; 5. 5. steady-state availability of the system, are obtained to carry out the cost-benefit analysis. Numerical results pertaining to two particular cases are presented.

Cost-benefit analysis of a one-server two-unit system subject to arbitrary failure, inspection and repair

The main intention of this paper is to develop a cost-benefit analysis for a single-server two-unit system subject to arbitrary failure, inspection and repair. The service facility is called for whenever (i) a unit fails, (ii) the system fails and is retained until no unit is waiting for service. Various system parameters or vital significance, such as point-wise availability of the system at any instant t, s-expected up-time of the system, s-expected inspection time of the server, s-expected type i (i = 1, 2) repair time of the server and s-expected net gain per unit time in a specified time span, say (0,t] have been obtained. Regeneration point technique is adopted to carry out the analysis. Numerical results pertaining to the case when failure and inspection times are exponentially distributed while repair times are distributed as two-stage Erlangian have been obtained.

Analysis of a two-unit repairable system with random inspection subject to two types of failure

Abstract This paper deals with a two-unit cold standby repairable system with two types of failure subject to random inspection. There is a single service facility which plays the dual role of inspection as well as repair. The analysis is carried out by identifying the system at suitable regenerative epochs. Explicit expressions pertaining to 1. 1. s -expected up-time of the system in (0, t ], 2. 2. s -expected inspection time in (0, t ], 3. 3. s -expected repair time of type i ( i = 1,2) in (0, t ], 4. 4. s -expected net gain per unit time in (0, t ] have been obtained.

Cost-benefit analysis of a one-server two-unit system subject to two types of failure

Abstract The main intent of the present paper is to develop a cost-benefit analysis of a two-unit repairable system when the operating unit is subject to two types of failure. The service facility is summoned whenever the operating unit fails. Upon inspection, the service facility resorts to the appropriate type of repair. The analysis is carried out under the supposition that the failure rate of the on-line unit is constant while all other distributions are arbitrary. Explicit expressions pertaining to 1. 1. point-wise availability of the system in (0, t ], 2. 2. s -expected up-time of the system in (0, t ], 3. 3. s -expected inspection time of the server in (0, t ], 4. 4. s -expected type i ( i = 1,2) repair time of the server in (0, t ], 5. 5. s -expected idle-time of the server in (0, t ], have been obtained to carry out the cost-benefit analysis.

Busy-period analysis of a one-server two-unit system subject to non-negligible inspection time

Abstract This paper deals with the busy-period analysis of a single-server two-unit cold standby redundant repairable system subject to inspection. Inspection policy models deal with stochastically failing systems in which failure is detected by inspection only. Previous authors assume that the time required for inspection is zero, while the current study deals with preparedness models when duration of inspection is non-negligible. A preparedness model is considered in which the failure of a unit is detected by actual inspection but a system break-down can be detected instantaneously without inspection. The failure time of a unit is assumed to be exponentially distributed with parameter γ. Initially, a unit is switched on and the other one is kept as a cold standby. The system breaks down if a unit fails while the other is still under repair. This paper characterizes the system by the probabilities of its being in the up or the down state, sets up integral equations for these probabilities by identifying suitable regenerative stochastic processes and employs the Laplace-transform technique to solve these equations. Measures of system effectiveness, namely: 1. 1. Point-wise availability of the system in (0, t ], 2. 2. s -expected up-time of the system in (0, t ], 3. 3. s -expected busy-period of the service facility in (0, t ], 4. 4. Steady-state availability of the system, have been derived to obtain the s -expected net gain per unit time. Finally, numerical results pertaining to four particular cases are presented.

Stochastic behavior of a two-unit repairable system subject to two types of failure and inspection

Abstract The stochastic behavior of a single-server two-unit system subject to two types of failure is investigated under the service policy, namely summon the service facility whenever the system fails and retain it until no unit is left for service. Explicit expressions pertaining to 1. 1. s -expected up-time of the system in (0, t ], 2. 2. s -expected inspection time in (0, t ], 3. 3. s -expected type i ( i = 1,2) repair time in (0, t ], 4. 4. s -expected net gain per unit time in (0, t ], have been obtained.

Busy-period analysis of a two-unit warm standby system with inspection time

Abstract This paper deals with the busy-period analysis of a single-server two-unit warm standby system subject to inspection. Two inspection policies are proposed, namely: (i) failure of the operating unit as well as the standby unit are detected by inspection only but system failure is detected instantaneously without inspection; (ii) failure of the operating unit and the standby unit as well as the system failure are detected by inspection only. The current study deals with the above suggested inspection policies when duration of inspection is non-negligible. The failure times of the operating unit and the standby are assumed to be exponentially distributed with parameters λ and λ 1 , respectively. Regeneration point technique is adopted to carry out the analysis. System parameters, such as 1. 1. point-wise availability of the system in (0, t ] 2. 2. s -expected up-time of the system in (0, t ] 3. 3. s -expected busy-period of the service facility in (0, t ] 4. 4. s -expected net gain per unit time in (0, t ] 5. 5. steady-state availability of the system are obtained.

Stochastic behavior of a 1-server n-unit system subject to arbitrary failure, exponential inspection and repair

Abstract The stochastic behavior of a single-server n -unit cold standby system has been investigated extensively under the supposition that the life-time of a unit is arbitrarily distributed while inspection and repair times are distributed exponentially. Service facility is called for whenever k (1 ≤ k ≤ n ) units are in failed condition and is retained until no unit is waiting for service. Regeneration point technique is adopted to carry out the analysis. Explicit results pertaining to various system parameters of vital significance, such as 1. 1. point-wise availability of the system at any instant t 2. 2. s -expected up-time of the system in (0, t ] 3. 3. s -expected inspection-time of the server in (0, t ] 4. 4. s -expected repair-time of type i ( i = 1,2,…, r ) in (0, t ] and 5. 5. s -expected net gain per unit time in (0, t ] have been obtained.