Cost analysis of a two-unit cold standby system with two types of operation and repair

This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.     

Cost-benefit analysis of a system with inspection, replacement and two types of repair

This paper investigates a mathematical model of a system composed of two units—one operative and the other in cold standby. There is a single repair facility which serves the triple role of inspection, repair and replacement of a failed unit. After inspection, the unit goes to minor (major) repair with probability p(q = 1 − p). Whenever the failed unit goes to major repair, an order is immediately placed for a new unit to replace the unit under major repair. Failure, inspection and delivery time distributions are negative exponential, whereas repair time distribution is arbitrary. The system is analysed in detail using the regenerative point technique and several reliability characteristics of interest to system designers and operation managers are obtained. Earlier results are verified in particular cases.     

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.     

Two-unit redundant system with inspection and adjustable rates

A two-unit redundant system is studied, in which one unit is operative and the other is a warm standby which replaces the operative failed unit instantaneously. To increase system availability, the failure rate of the operative unit and the repair rate of the failed unit adjust automatically according to the state of the standby unit. Also, after repair of the operative failed unit it is sent for inspection to decide whether the repaired unit is perfect or not. If the repaired unit is found to be imperfect, it is sent for post repair. Using a regenerative point technique in the Markov renewal process, several reliability characteristics of interest to system designers and operation managers are obtained.     

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.     

On the transient analysis of a maintained system subject to random stresses

This paper deals with the probablistic analysis of a system subject to stresses. The system consists of a basic unit and a standby and is provided with a service facility to carry out maintenance, inspection prior to repair and repair of the units in the system. The operating unit is sent for maintenance as soon as its strength, after being hit by a stress, falls below a specified critical value, the strength being assumed to be deterministic. The operating unit may also fail on any stress by virtue of the stress exceeding the strength. The failed unit is subject to inspection prior to repair to ascertain the type of repair the unit has to undergo. The stress experienced by a unit is assumed to be a random variable governed by a probability law. The time between successive stresses and the time for maintenance, inspection and repair are random variables governed by probability laws. Explicit expressions for various system characteristics have been obtained using the state-space method and the regeneration point technique.     

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 an intermittently used system

We consider a one unit system backed by a repair facility, the system itself being used intermittently with the use (need) and non-use (no need) period alternating in a Markov manner while the repair and life time of the unit are assumed to be independent random variables distributed quite generally. If a need arises in the time interval in which the unit is under repair or if the unit fails while it is in need, the need waits for a random period. If however the repair time is longer than the waiting time, a disappointment results and the need is taken care of by other means. The probabilistic analysis of the system is provided and suitable measures characteristic of the system are obtained. In particular explicit expressions are provided for the probability distribution of the time to the first disappointment as well as the expected value of the number of disappointments in an arbitrary time interval.Reliability Analysis of an Intermittently used System     

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-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.     

Stochastic analysis of a two-unit cold standby system subject to maximum operation and repair time

A two-unit standby system is considered under excess time stochastic behaviour, i.e. the failure and repair time of the on line (off line) unit is exceeding some prespecified value. Whenever an operating unit crosses a prespecified operation time, it is sent to preventive maintenance and when repair of a failed unit crosses a prespecified time, the unit is rejected and replaced by a new unit. Using the regeneration point technique, certain characteristics of the system are derived and the cost of the system is calculated. Particular cases of the system are also considered.     

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

1 Model and Assumption In reliability analysis of repairable systems, it is usually assumed that the repair facility neither fails nor deteriorates as well as the repairman is instantaneously available. So that the repair is started immediately upon the failure of a unit provided that he is not busily repairing another unit. However, in actual practice, the repair facility in a repairable system is subject to failure and can be replaced (or can be repaired) after it fails, and certain delay ac…     

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

The paper deals with the cost-benefit analysis of a one-server two-nonidentical-unit cold standby system with repair and preventive maintenance (PM). The system consists of two units, one main unit and one secondary unit. If both units are up, the main unit is always in operation and the secondary unit is in cold standby. The secondary unit operates only when the main unit is taken off for repair or PM. There is no PM on the secondary unit. On the main unit, PM is of the age replacement type. Using regenerative point technique, the point-wise availability of both main and secondary units is obtained. The busy period of the server is broken up into the time spent for repair of the main unit, time spent for repair of the secondary unit and time spent for PM of the main unit. It is assumed that all revenues are earned and costs are incurred at a linear rate with time. The s-expected net revenue (revenue minus costs) in [0, t) is obtained.     

Optimal Selection Methods for Failure & Repair Rates Using Nomographs

This paper explains the optimal selection methods using nomographs to solve two essentially different problems. The one is the problem of unit level, and the other is the one of system level. The unit level assumes that the cost information as a function of failure rate ? and repair rate ? are empirically known. The paper presents a method, by which a nomograph is used to select easily the optimum pair from the infinitely many pairs (?, ?) of feasible solutions, to gain the required unit availability at minimum cost of this assumption. At the system level, the system is composed of n serial i-units which are selectable from a group provided for each i-unit (i = 1, 2, ..., n), several different repair plans are available for the unit. Each unit has a specific failure rate and associated cost, and each repair plan has a specific repair rate and associated cost. There are service personnel for each unit. The failure and repair rates are constant. The paper presents: 1) A method using nomographs to select the optimum pairs from the many pairs (?i, ?i) (i = 1, 2, ..., n) of feasible solutions, to gain the required system availability at the minimum system cost, 2) A method to select the optimum pairs, from the many pairs (?i, ?i (i = 1, 2, .     

Comparison of two stochastic models for two-unit series system with cold standbys

Reliability characteristics are compared for two stochastic models of a system that has two non-identical units, arranged in series, each unit with its identical cold standby. The same set of assumptions is used for both models, except that in model 2 both of the standby units replace the failed operative unit instantaneously whereas in model 1 an operative failed unit is replaced by its corresponding standby unit (i.e. only one unit is replaced in this case). A single repair facility is available to repair the failed unit. Failure and repair time distributions are assumed to be negative exponential.     

Reliability of a 2-Unit Standby Redundant System with Constrained Repair Time

This paper considers a 2-unit warm-standby redundant system with repair. The repair of a failed unit is constrained as follows: Associated with each failure of a unit is a random variable termed the Maximum-Repair-Time (MRT) of the failure. If the repair of a failed unit is not completed within the MRT, the unit is rejected for further use. Two types of failure stituations for the system are considered: 1) No allowed down time, and 2) Some allowed down time. Expressions for the Cdf of the Time to System Failure (TSF) and the mean TSF are derived by using Markov renewal processes.     

Cost-benefit analysis of one-server two-unit imperfect switch system subject to multistage repairs

This paper deals with the cost-benefit analysis of 1-server 2-unit system with imperfect switch where repairs take place in stages. The repair times of the unit and of the switch are assumed to be arbitrarily distributed while the failure rates of units and of the switch are constants. Initally, one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. The repair of the switch is given preference after completion of current repair of a unit. The analysis is carried out by regeneration point technique. Explicit expressions for the expected durations the server is busy in (0, t) with particular stages of repair of the unit and of the switch are obtained to carry out the cost-benefit analysis of the system.     

Using system reliability to determine supportability turnaroundtime at a repair depot

This paper uses an expression for system reliability at a repair depot to construct a nonlinear, nonpolynomial function which is amenable to numerical analysis and has a zero equal to the supportability turnaround time (STAT) for a failed unit. System reliability is in terms of the constant failure rate for all units, number of spares on-hand at the time a unit fails, and projected repair completion dates for up to four unrepaired units. In this context, STAT represents the longest repair time (for a failed unit) which assures a given reliability level; system reliability is the probability that spares are ready to replace failed units during the STAT period. The ability to calculate STAT-values is important for two reasons: (1) subtraction of the repair time for a failed unit from its STAT-value yields the latest repair start-time (for this unit) which assures a desired reliability, and (2) the earlier the latest repair start-time, the higher the priority for starting the repair of this unit. Theorems show the location of STAT with respect to the list of repair completion dates, and form the foundation of the root-finding-based algorithm for computing STAT-values. Numerical examples illustrate the algorithm     

Availability of Priority Standby Redundant Systems

A priority standby system consisting of two repairable units is considered. One unit, the priority unit, is always in service except when it is failed. The standby unit is in service only for the duration of repair of the priority unit. Expressions are derived for the availability of such a system for both preemptive and nonpreemptive repair. The results assume reasonably general failure-time and repair-time distributions of the priority and standby units. The preemptive priority results are relatively insensitive to the form of the distributions.