Reliability analysis of a system with a mixture of warm and cold standby

A single-server two-unit standby system with two modes of each unit—normal and total failure—is considered. The standby units are repeatedly interconverted after a random time from warm to cold and cold to warm. Upon failure of the operative unit, the standby unit, if it is warm, starts to operate instantaneously; otherwise, the system goes down until the cold standby starts to operate. System failure occurs when both units fail totally. Identifying the system at suitable regenerative epochs, the integral equations are set up and the expressions for reliability and mean time to system failure (MTSF) are obtained. The graphical behaviour of MTSF is also studied in a particular case.     

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.     

Cost-benefit analysis of a single server three-unit redundant system with inspection, delayed replacement and two types of repair

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. The type of the failure of operative or warm standby unit is detected by inspection only. The service facility plays the triple role of replacement, inspection and repair of a unit. Failure time distributions of operative and warm standby units are negative exponential whereas the distributions of replacement time, inspection time and repair times are arbitrary. The system has been studied by using regenerative points.     

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 analysis of a two-unit standby system with delayed replacement and better utilization of units

This paper develops the model for a system, having two identical units—one operative and the other cold standby. Each unit of the system has three modes—normal, partial failure and total failure. The replacement time of a failed unit by a standby unit is not negligible but is a random variable. System fails when both the units fail totally. Failure time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers and operations managers have been evaluated using the theory of regeneration point technique.     

The effect of preventive maintenance on a two-dissimilar unit standby system

A system which consists of two dissimilar units, one as a main unit the other as a standby, is considered, taking account of repair and preventive maintenance (PM). The standby unit cannot fail and the switch is perfect. The Laplace transform (LT) of the survivor function of the time to the first system failure (TFSF) and the mean are derived. Finally, a theorem about the effect of maintenance is proved.     

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.     

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 repairable redundant system with delayed replacement

The paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. Failure time distributions of operative and standby units are exponential whereas all repair times follow arbitrary distributions. The system has been studied in detail by applying the results from the theory of semi-Markov process and mean-time-to-system-failure, steady-state availability, expected number of visits to a state, second moment of time in an up-state and expected profit of the system have been obtained.     

Probabilistic analysis of a two-unit system with a warm standby subject to preventive maintenance and a single service facility

The object of this paper is to carry out the availability and the reliability analysis of a two-unit system with a warm standby having a single service facility for the performance of preventive maintenance and repair. The failure times, the repair times, the inspection times and the preventive maintenance times of the main unit and of the standby one are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. Explicit expressions for the mean down time of the system and for the mean time to system failure are obtained. Some previous results are derived from this work as special cases.     

Reliability and availability analysis of a system with warm standby and common cause failures

This paper presents reliability and availability analyses of a two unit parallel system with warm standby and common-cause failures. The standby and switching mechanisms are subject to failure. The failed system repair times are assumed to be arbitrarily distributed. Expressions for Laplace transforms of system state probabilities, steady state system availability, system reliability, and mean time to failure are developed.     

A note on a multi-unit system with r repair facility

This paper deals with a system consisting of (n + m) identical units; n units are needed for the system to function and the remaining m units are warm standby supported by r repair facility. The online and standby units have different but constant failure rates; the repair time distribution for the standby unit is taken to be a constant and the distribution for the online unit is arbitrary. Functions describing the behaviour of all the other units when one unit is undergoing online repair are studied and an earlier result is recovered as a special case.     

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.     

CHE failure in a two-unit standby system with slow switch, repair and post repair

A mathematical model of a two-unit cold standby system with critical human errors (CHE) and slow switch is investigated. The CHE leads to complete system failure, and repair and post-repair are needed before the system can be put back into operation. Slow switch means that on failure of the operative unit the switch puts the standby unit into operation after a random time. Failure time and switchover time distributions are negative exponential whereas all the repair and post repair time distributions are general. Using a regenerative point technique, we obtain various reliability characteristics which can be used to carry out the cost-benefit analysis. In a particular case, the behaviour of the cost function is also studied graphically.     

Analysis of a two-unit warm standby system subject to degradation

This paper deals with the reliability analysis and the mean time to system recovery of a single server, two-unit (priority and ordinary) warm standby subject to degradation. Initially the priority unit is operative and the ordinary unit is kept as a warm standby. The priority unit passes through three different operative stages (excellent, good and satisfactory) before it fails. The priority unit enters into the total failure mode only from the satisfactory stage, and after repair it enters into the normal mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with different probabilities. The failure, repair and degradation time distributions are assumed to be general and arbitrary. The system is observed at suitable regenerative epochs in order to carry out the expected first passage time analysis. Moreover, three special cases have been considered. The results of Gupta [Int. J. Systems Sci.22 (11) 2329–2338 (1991)] are derived from the present results as a special case. A computer program for calculating the mean time to system failure and the mean time to system recovery is made.     

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.     

Reliability and Profit Evaluation of a PLC Hot Standby System Based on a Master-Slave Concept and Two Types of Repair Facilities

Programmable Logic Controllers (PLC) are frequently used by a good number of companies like steel plants, biscuit manufacturing companies, etc. Various plants/companies use two PLC at a time: one operative, and the other as a hot standby to avoid big losses. Analysis of the reliability, and profit of a hot standby PLC system is of great importance; and hence the present paper examines such a system wherein two PLC are working in master-slave fashion. Initially, the master unit is operative, and the slave unit is in hot standby. The slave unit can also fail, but with a lower failure rate than the master unit. The master unit has the priority of operation ∓mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp;mp; repair over the slave unit. While operating, the latest information from the master unit keeps on transferring to the slave unit. There are three types of failure: minor, major-repairable, and major-irreparable. The ordinary repairman who stays with the system repairs the minor failures. The expert repairman who is available upon demand repairs the major failures. Various measures of the system effectiveness, such as the mean time to system failure, steady-state availability, busy period of the ordinary as well as expert repairmen, expected number of replacements, etc. are obtained by using semi-Markov processes, and regenerative point Techniques. Profit incurred to the system is evaluated, and a graphical study is also made. Real data from an industrial application is used in this study.     

Analysis of a two-unit cold standby system with three modes

This paper analyses a two-unit cold standby system under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units are exponential, whereas repair time distributions are arbitrary. Breakdown of the system occurs when both the units are in total failure mode. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

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.     

Common-cause failure analysis of a redundant system with non-repairable units

This paper presents a newly developed generalized expression for mean time to failure, MTTF, of a non-repairable identical unit parallel system with warm standby and common-cause failures. Also presented is a modified version of this formula that takes into account the repairability of the warm standby and/or switching mechanism. Generalized expressions for system reliability and variance of time to failure are presented along with some tables and plots of system reliability and MTTF.