Effect of intermittent repair in a two unit redundant system with standby failure

A two-unit standby redundant system with exponential failure time distribution of the operative unit is considered. It is assumed that failure of the standby unit is detected only at the time of use and is available with a known probability. Repair facility is also available at the time of need with a known probability. Repair and preoccupation times are general. Stochastic behaviour of the system has been studied by Semi-Markov process and parameters of interest eg. MTSF, steady state availability, expected profit have been obtained. Expected profit of this model is compared with that of an earlier model and a condition on extra incurred cost is obtained.     

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.     

Stochastic analysis of a two unit cold standby system with preparation time for repair

This paper deals with the cost-benefit analysis of a two unit cold standby system in which the cold standby unit replaces the failed operative unit after a random amount of time. Inspection is required to decide whether it needs type I or type II repair. Failure, repair, replacement and inspection time distributions are arbitrarily distributed. A repair man is not always available with the system, but is called for repair whenever the operative unit fails.     

Cost analysis of a two unit cold standby system with preparation time for repair

This paper deals with a model of a two unit cold standby system with imperfect switch in which the repair man appears and disappears from the system randomly. The standby unit takes random switchover time for operation when the operative unit fails. Failure time of a unit, appearance and disappearance time of the repair man and switchover time of the standby unit are negative exponential, whereas repair time is arbitrary. The system is analysed by using regenerative point technique and several parameters of interest are obtained.     

Analysis of a two unit standby system with partial failure and two types of repairs

A two dissimiliar unit standby system is analysed. The priority unit can either be in normal or partial operative mode. When the unit fails from the partial mode, it undergoes minor repair and the unit becomes operative with different failure rate. If this unit fails again, it goes to major repair after which it works as good as new. The standby unit while in use is either operative or failed. This non priority unit fails without passing through the partial failure mode and undergoes only one type of repair with different repair time distribution. Failure and repair time distributions are negative exponential and general respectively. Regenerative technique in MRP is applied to obtain several reliability characteristics of interest to system designers.     

A two-unit deteriorating standby system with inspection

This paper studies a single server two-unit standby system in which the standby can fail when offline and its repair starts only after knowing about its failure from its time to time inspection. The inter-inspection time is assumed to be arbitrarily distributed. Various measures of reliability useful to system designers and operations managers are obtained.     

Analysis of a two server-two unit cold standby system with correlated failures and repairs

This paper studies a two (non-identical) unit cold standby system with correlated failures and repairs. The system has two types of server—regular (not perfect) and expert. The regular repairman is always available with the system while the expert repairman is called when it is needed. The joint distributions of failure and repair times are taken to be bivariate exponential (B.V.e.). Important reliability characteristics useful to system managers are obtained.     

Switch failure in a two duplex unit standby system

A two duplex unit standby system with an imperfect switch and subject to preventive maintenance is discussed. It is assumed that switch is available at the time of need with probability p(= 1−q). The failure time of a duplex unit is taken to be negative exponential whereas the repair time distributions of duplex unit and switch and the time taken for preventive maintenance action, respectively, are assumed to be arbitrarily distributed. The analysis is carried out by using the regenerative point technique, and some particular cases are discussed.     

Profit analysis of a cold standby system with two repair distributions

A single server two-identical unit cold standby system is analysed. Each unit has two operative modes—normal and quasi-normal. When a normal unit fails, it undergoes minor repair with probability p₁ and p₂ respectively. Upon minor repair unit works with reduced efficiency and is known as quasi-normal unit while upon major repair unit works as good as new (normal unit). When a quasi-normal unit fails, it undergoes minor or major repair with probability q₁ and q₂ respectively. Failure rates of normal and quasi-normal units are different. Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique in MRP the system characteristics of interest to system designers and operations managers have been obtained.     

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.     

Profit evaluation of a two unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby system subject to a single repair facility with exponential failure time and arbitrary repair time distribution. Each unit has three modes—normal (N), partial (P) and total failure (F). By using the regenerative point technique the system has been analysed to determine mean time to system failure and profit earned by the system. A numerical example is used to highlight the important results.     

Cost analysis of a two unit, three state standby redundant complex system with two types of repair facilities under waiting

This paper deals with the cost analysis of a two unit, three state standby redundant complex system, incorporating the concept of two types of repair facilities, viz. minor and major repair. The concept of waiting time for the major repair of the failed system has also been introduced. The system can suffer from two types of failures, namely catastrophic and partial. Failure and waiting times of units follow exponential time distribution, whereas repair of units follows general time distribution. Using the supplementary variable technique, Laplace transforms of probabilities of the complex system being in various states have been computed. In addition, using Abel's lemma, steady state behaviour has also been examined. Some important graphs have been sketched at the end to highlight the important results.     

Stochastic analysis of a deteriorating standby system with three modes and inspection

A two-unit (identical) deteriorating standby system is analysed. Each unit can be in one of the three modes—normal, partial failure and total failure. A unit can fail totally but not partially during its standby state. Standby is inspected at random epochs. Using regenerative point technique in Markovrenewal process theory, several reliability characteristics of interest to system designers and operation managers are obtained.     

System characteristic and cost analysis of a two unit standby system with spare units

This paper deals with the stochastic analysis of a standby system having two main units and two spare units.A spare unit is only used for operation when both main units fail and if it fails,it is replaced by the new one until the repair of the failed main unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. Using renewal theoretical arguments, certain characteristics of the system are derived and using them the cost of the system is calculated. Particular cases of the model are also considered.     

Comparison of two unit cold standby reliability models with three types of repair facilities

This paper develops three models for cold standby redundant systems, consisting of two identical units. These models are different in the sense that different types of repairmen are employed. In model 1, the repairman is always with the system. In model 2, he comes immediately at the failure of a unit, while in model 3, he takes some random time in reaching the system.Profit is evaluated in each case. Comparison of these profits is done in two parts. Part 1 considers the comparison of different models. In part 2 comparison is done by taking different criteria for evaluating the profit for the same model. Computer programs for these comparisons are also given (in the Appendix).     

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.     

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 ? q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.     

On the effect of weather condition in a two unit cold standby system

This paper investigates a two unit cold standby system in which operation is affected by the weather conditions. Weather conditions are subject to a Markov process with two states—normal and abnormal. These are independent of the system state. Using the regeneration point technique we obtain several characteristics of the system.     

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.     

Analysis of a standby system with dependent repair time and slow switching device

This paper analyses a two-unit cold standby system with a slow switch. The failure and repair times of each unit are assumed to be correlated by taking their joint densities as bivariate exponential. Using the regenerative point technique, various reliability characteristics of interest are obtained. The behaviour of steady state availability is also studied graphically.