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.     

Analysis of a two unit deteriorating standby system with repair

This paper deals with the reliability analysis of a two unit standby system with repairs for common cause failure and critical human error. The deteriorating effect of the standby unit on the system is studied. Various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

A multi-component standby system subject to inspection and truncated normal failure time distribution

This paper investigates a stochastic model of a single server, two identical unit cold standby system. Each unit consists of n separately maintained independent components arranged in series. After each failure, an inspection is required to detect which component of the unit has failed. The failure time distribution of a unit is truncated normal while all the other time distributions are negative exponential. Using the regenerative point technique, we obtained various measures of system effectiveness to carry out the profit function analysis.     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

Cost analysis of a two-unit warm standby reliability system with two types of repair facilities

This paper deals with a two-unit warm standby system. These units are identical, but have different failure rates and repair time distributions, when failed in operating or standby state. If the unit fails in operating state, we wait for the repairman for some maximum time or until the other unit fails, and if the unit fails in standby state we wait for the repairman until the other unit fails. On the failure of the second unit or on the completion of the maximum time, we call the repairman immediately at the higher cost.The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results pertaining to some particular cases are also added.     

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.     

Analysis of a two-dissimilar unit cold standby redundant system subject to inspection and random change in units

This paper deals with the stochastic behaviour of a two-dissimilar unit cold standby redundant system with random change in units. In this system each unit works in two different modes—normal and total failure. It is assumed that the failure, repair, post repair, interchange of units and inspection times are stochastically independent random variables, each having an arbitrary distribution. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure are obtained. Certain important results have been derived as particular cases.     

Cost analysis of a two-dissimilar unit cold standby redundant system with administrative delay and no priority in repair

This paper deals with the cost analysis of a two-dissimilar unit cold standby redundant system with three modes for each unit under the assumption that there is administrative delay and no priority in repair. The failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers have been obtained. Moreover some previous results are derived from the present results as special cases.     

Two models for two-dissimilar-unit cold standby redundant system with partial failure and two types of repairs

This paper deals with the availability function and the mean time to the first failure for two models of a cold standby redundant system with two different types of repair. Each model consists of two dissimilar units. In the first model, the operative unit has two modes of operation, normal mode and partial failure mode. The standby unit has one mode of operation, normal mode. In the second model, each unit has three modes of operation, normal mode, failure mode and total failure mode. Both models are analyzed by the semi-Markov process technique, assuming that the failure time and repair time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Moreover, we give computer programs for calculating the MTSF for each model (see Appendix).     

Stochastic analysis of a man-machine system with critical human error

This paper studies various economic reliability measures of a repairable man-machine system. The physical condition (good/poor) of the operator may affect the performance of the system. Repair time distributions of the system are general while all other transition time distributions are negative exponential. The system can be in one of the three modes—normal, partial failure and total failure. Regenerative technique in MRP is applied to obtain several reliability characteristics of interest to system designers.     

Stochastic behaviour of a two-unit standby system with better utilization of units

This paper obtains various measures of reliability of a two-unit redundant system with three modes. Upon partial failure of an operative unit the cold standby starts operation only when it becomes active. A single service facility is available (1) for repairing a partially or totally failed unit and (2) to activate the cold standby unit whenever required. Failure time distributions are negative exponential while repair and activating time distributions are general.     

Some characteristics of a two-dissimilar-unit cold standby redundant system with three modes

This paper deals with the stochastic behaviour of a two-dissimilar-unit cold standby redundant system in which each unit works in three different modes—normal, partial failure and total failure. It is assumed that the failure and repair times are stochastically independent random variables each having an arbitrary distribution. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Explicit expressions for the Laplace-Stiektjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady state availability of the system are obtained. Certain important results have been derived as particular cases.     

Analysis of a system having super-priority, priority and ordinary units with arbitrary distributions

This paper deals with the analysis of a three non-identical unit cold standby system model. A single repairman is available to repair a failed unit. The priority in respect of operation and repair is being given to the units in order. All failure and repair time distributions are assumed to be general having different p.d.f.'s. Several measures of system effectiveness are obtained by using a regenerative point technique.     

Cost-benefit analysis of a 2-unit priority-standby system withpatience-time for repair

The cost of a one-server two-unit (one priority and the other ordinary) cold-standby system with two modes-normal and total failure-is analysed. Whenever the repair time of a failed priority unit exceeds some given maximum time, it is rejected and an order is placed for a new unit. Failure and delivery time distributions are negative exponentials, whereas repair and replacement time distributions are arbitrary. An analysis of the system is made to determine the reliability measures (MTSF (meantime to system failure), steady-state availability, busy period analysis of repairman, etc.) by using the regenerative point technique     

Stochastic analysis of a parallel system with common cause failure,preventive maintenance and two types of repair

This paper studies a two-unit (identical) parallel system with facilities of preventive maintenance and two types of repair, i.e. regular and occasional. When the regular repairman is unable to repair the unit/system, the occasional (expert) repairman is called for. The system can also fail due to common cause. The time of the failure of a unit and the system, the commencement of maintenance and to call the occasional repairman are assumed to be constant while the repair and maintenance times are arbitrarily distributed. The system is analysed by using regenerative point technique to obtain various economics related measures, such as mean time to system failure, steady state availability, probability that the repairman is busy, expected number of visits by the occasional repairman and the expected profit earned by the system.     

Some characteristics of a man-machine system operating subject to different weather conditions

This paper deals with some characteristics of a single unit of a man-machine system operating under different weather conditions. It is assumed that the failure, repair and change of weather conditions (normal-stormy) are stochastically independent random variables, each having an arbitrary distribution. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady-state availability of the system are obtained. Several important results have been derived as particular cases.     

Reliability Considerations for a 2-Unit Redundant System with Erlang-Failure and General Repair Distributions

This paper considers the case of a 2-identical-unit redundant system with Erlang-failure and general repair distributions. Two cases are considered: 1) the failure of each unit is independent of the other; 2) when one unit fails, the failure distribution in the other unit changes. The Laplace transforms of the distribution of time to system failure and the explicit formula for the mean time to system failure are derived.     

Cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair

This paper deals with the cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair where each unit of the system has two modes, normal and failed. It is assumed that the failure, repair, replacement and inspection times are stochastically independent random variables each having an arbitrary distribution. The cold standby unit replaces the failed operative unit after a random amount of time. An inspection is required to decide whether it needs type I (minor repair) or type 2 (major repair). In this system the repairman is not always available with the system, but is called whenever the operative unit fails. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Pointwise availability, steady-state availability, busy period by a server and the expected cost per unit time of the system are obtained. Certain important results have been derived as particular cases.     

Analysis of a two unit standby redundant fail-safe system

This paper evaluates reliability and fail-safety of a two unit cold standby fail-safe redundant system. Three modes of failure—(1) failure due to human error, (2) failure due to unit faults and (3) failure due to switchover faults—are considered. The complete failure states of the system are divided into two categories, fail-safe state and fail-dangerous state. Several fail-safety measures of interest to a fail-safe system designer are defined and evaluated, such as safety function, safety ratio and danger ratio.     

On a two-dissimilar-unit standby system with three modes and administrative delay in repair

This paper considers a two-dissimilar-unit cold standby redundant system with three modes of each unit under the assumption that there is an administrative delay in getting the repair man at the system location. The system is analyzed by the semi-Markov process technique, assuming that the failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Further, special cases of the results of this paper coincide with earlier results obtained by Pandey and by Gupta.