Reliability analysis of a system with preventive maintenance, inspection and two types of repair

This paper considers a two-unit (identical) parallel system with facilities of preventive maintenance, inspection and two types of repair, type I and type II. These two types of repair facilities have a considerable difference in their costs. Both the units of the system can fail simultaneously due to some common-cause or they can fail one by one. The time of failure of a unit and system, the commencement of maintenance and inspection are assumed to be constant while repair and maintenance times are arbitrarily distributed. Various measures of system effectiveness are evaluated using regenerative point technique.     

Two 1-Server n-Unit Systems with Preventive Maintenance and Repair

This paper deals with the availability and reliability analysis of two different 1-server n-unit systems with preventive maintenance and repair. Initially, one unit operates and the remaining n - 1 units are kept as cold standbys. In the first system the time to failure and the time to preventive maintenance of a unit are arbitrarily distributed. In the second system, each unit consists of 2 components connected in series. When a unit fails, the failed component is taken up for repair while the other waits for preventive maintenance. Explicit expressions for the Laplace transform of the mean down-time of the system in [0, t] and for the mean time to system failure are obtained. Steady-state availability of the system is also discussed. A few special cases have been studied.     

One unit reliability system subject to random shocks and preventive maintenance

In this paper we consider two systems each consisting of one unit. The operating unit is subject to random shocks which occur at random times. Due to the shock the following may happen: (i) The unit is not at all affected by the shock; (ii) the failure rate of the unit increases from λ₀ to λ₁; (iii) the unit fails. The failure time of the unit is exponentially distributed. The repair, shock and preventive maintenance times follow general distributions. In System 2 there is provision of preventive maintenance, whereas in System 1 there is no provision of preventive maintenance. There is one repair man available in each system. In this paper the mean time to system failure, steady state availablities and the impact of shocks on these are studied. In System 2 the effect of the preventive maintenance on MTSF and steady-state availabilities is investigated.     

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.     

Reliability Analysis of a Two-Unit Standby-Redundant System with Preventive Maintenance

We consider a standby-redundant model of two units, where we assume that one unit is operative and the other unit is in standby at time t = 0. If the operative unit fails, a unit in standby is put into preventive maintenance policy of the operative unit to maintain our the preventive maintenance policy of the operative unit to maintain our system with high reliability. Our concern for the system is the time to the first system-down. The Laplace-Stieltjes transform of the time distribution to the first system-down and the mean time to the first system-down are derived by applying the relationship between Markov renewal processes and signal flow graph. Further, the behavior after the system-down is investigated by using the results of Markov renewal processes. Finally, numerical examples are presented for the k-Erlang failure time distributions. The optimal preventive maintenance time is discussed.     

Analysis of a k-out-of-n unit system with two types of failure and preventive maintenance

A k-out-of-n unit system is analysed with two types of failure: (1) failure due to change in operating characteristics and (2) catastrophic failure. Preventive maintenance of the system is allowed at random epochs. All transition rates are taken to be general. Several measures of reliability useful for system designers and operations managers have been obtained by using regenerative point technique with Markov renewal process. Some important results obtained earlier are shown as particular cases.     

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.     

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.     

Cost analysis of a two dissimilar cold standby system with preventive maintenance and replacement of standby

This paper deals with the cost analysis of a two dissimilar unit cold standby redundant system with preventive maintenance, under the assumption that the standby, being substandard, is not repairable and has to be replaced on failure. The failure times have negative exponential distributions while all other distributions involved are general.     

Optimal replacement policy for induced draft fans

This paper derives the optimal block replacement policies for four different operating configurations of induced draft fans. Under the usual assumption of higher cost of repair or replacement on failure compared to preventive replacement, the optimal preventive replacement interval is found by minimising the total relevant cost per unit time. Specifically, this paper finds optimal preventive maintenance strategies for the following two situations.

1. (i)|Both the time to failure and time to carry out minimal repair or replacement are exponentially distributed.

2. (ii)|The time to failure follows the Weibull distribution and there is no possibility of on-line repair or replacement.

For both situations closed form expressions are derived whose solutions give optimum preventive maintenance intervals.     

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.     

Modified periodic preventive maintenance policies

This paper proposes four preventive maintenance policies where the unit is scheduled to be maintained preventively or to be repaired only at periodic times kT (k = 1, 2, …): If a failure occurs during ((k?1)T, kT), then A) the unit remains failed, B) the failed unit undergoes only minimal repair, C) the failed unit is replaced by a spare unit, and D) the failed unit is repaired instantaneously. The expected cost rates for each model are obtained and the optimal policies are discussed.     

Optimal policies with decreasing probability of imperfect maintenance

This study applies periodic preventive maintenance to three repair models: major repaired, minimal repaired, or fixed until perfect preventive maintenance upon failure. Two types of preventive maintenance are performed, namely imperfect preventive maintenance, and perfect preventive maintenance. The probability that preventive maintenance is perfect depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas for the expected cost per unit time are obtained. For each model, the optimum preventive maintenance time T/sup */, which would minimize the cost rate, is discussed. Various special cases are considered. A numerical example is presented.     

Analysis of a two-engine aeroplane model with two types of failure and preventive maintenance

This paper deals with an aeroplane model; namely, a two-unit (non-identical) parallel system with dual mode of failures—(1) failure due to change in operating characteristics and (2) failure due to common cause. The system goes for preventive maintenance at random epochs. We assume that the failure, repair and maintenance times are stochastically independent random variates each having an arbitrary distribution. Using the regenerative point technique several measures of reliability are obtained. Certain important results have been derived as particular cases.     

A Technique for Optimal Sequential Maintenance Scheduling

This paper presents the mathematical development of, and a simple solution technique for, an optimal sequential maintenance scheduling problem. The model is shown to satisfy the Kuhn-Tucker conditions, the necessary and sufficient conditions for the existence of an optimal solution. Real-world systems consisting of mixtures of constant and increasing failure rate devices are considered in the model. Sequential preventive maintenance schedules are developed for groups of identical items with increasing failure rates. Provision is made for the corrective maintenance of these groups if failures occur in between the preventive maintenance schedules. Also, constant failure rate devices are accorded corrective maintenance when failures occur. Optimality is achieved by minimizing the total annual maintenance cost, subject to constraints on the system availability, number of maintenance personnel and intervals of preventive maintenance. The model is applied to a coal mine power system example.     

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 duplicating standby system with correlated failure-repair/vbreplacement times

This paper considers the stochastic analysis of a two-unit (original and duplicate) cold standby system model with preventive maintenance and replacement of the failed duplicate unit. The failed duplicate unit is non-repairable but its replacement is considered with an identical duplicate unit which is available instantaneously. Joint distributions of failure and repair/replacement times of original/duplicate units are bivariate exponential with different parameters. Various reliability characteristics of the system model under study are obtained by using regenerative point technique. Mean time to system failure and steady state availability have also been studied through graphs.     

Cost-optimal condition-monitoring for predictive maintenance of2-phase systems

The deterioration processes of many industrial systems can be modeled in 2-phases. A 2-phase system begins its life in a new condition where it resides for a random amount of time before progressing to a worn condition where it resides for a random amount of time preceding system failure. If monitoring takes place while the system is in the worn condition, preventive maintenance is performed. This paper analyzes predictive maintenance policies for systems exhibiting 2-phase behavior, and presents cost-minimizing policies, as well as satisfying policies, to determine when monitoring should take place, and for allocating monitoring resources to multiple systems. The solution approach is based on decomposing the expected cost (per unit time) into 2 components: the expected cost due to maintenance actions, and the expected cost due to monitoring actions. This decomposition facilitates the construction of operating-characteristic curves that represent policy performance, and allows evaluation of the policy tradeoffs in many situations including those with constrained or unconstrained monitoring resources, multiple or single systems, and fixed or nonfixed monitoring intervals     

Cost analysis of a system with common cause failure and two types of repair facilities

A mathematical model to predict the cost involved to run an n-component single unit system which can fail in n-mutually exclusive ways of total failure or due to common cause, has been developed. Each component has two modes (normal and failure) with two types of repair facilities. Repair rates are arbitrary functions of the time spent. All other transition rates are constant. Laplace transform of the state probabilities are developed along with steady-state behaviour of the system. Inversions are computed to determine the expected profit and availability of the system at any time.     

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.