Profit analysis of the machine repair problem with cold standbys and two modes of failure

In this paper we deal with the cold-standby machine repair problem where machines have two failure modes under steady-state conditions. The two failure modes have equal probability of repair. Failure time of the machines and repair time of the repairmen are assumed to follow a negative exponential distribution. The failed machines are served by R repairment according to first-come, first served discipline. Profit model is developed in order to determine the optimal values of the number of cold standbys and the number of repairmen simultaneously, while maintaining a minimum specified level of system availability. Numerical results are presented in which several system characteristics are calculated under optimal operating conditions.     

Reliability and profit analysis of two single-unit models with three modes and different repair policies of repairmen who appear and disappear randomly

Cost-benefit analysis of a single-unit system with three possible modes of the unit—normal (N), partial failure (P) and complete failure (F)—is carried out. The paper consists of two models: in model 1, the unit goes under repair (if a repairman is available) the moment it fails partially, whereas in model 2 the unit goes under repair at complete failure. The repairman appears in, and disappears from, the system randomly. A comparison between these two models after calculating MTSF and profit has also been made.     

Cost analysis of a two-unit standby system with two types of repairmen

This paper is concerned with a two-unit cold standby system with two types of repairmen. One “regular” repairman is kept for repairing the units as soon as they fail. It is assumed that sometimes he might not be able to do the repairs within some tolerable time (patience time). Another “expert” repairman, assumed to be perfect, is called on to do the repairs on the completion of this patience time or on the failure of the system, whichever is later.Various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the expert repairman should be called after the system failure. Further numerical results for a case, in which repair time and patience time both have non-Markovian property, are also investigated. Then the upper bound of the cost K₃, below which the expert repairman should be called immediately after the system failure and the corresponding increase in profit are calculated.     

Cost-benefit analysis of a system with intermittent repair and inspection under abnormal weather

This paper studies a repairable system with intermittent repair. Weather under which the system works changes randomly (in time) from normal to abnormal weather and vice-versa. By intermittent repair, we mean that the repair facility is not available instantaneously but takes random time to be available. The system operating under abnormal weather is sent for inspection randomly with Poisson process. Failure rates of the system and rates of change of weather are constant while repair times, inspection time and inter-inspection time are arbitrarily distributed. The system is analysed by using regenerative point technique to obtain various economic measures such as mean time to system failure, steady state availability, probability that the repairman is busy, expected number of visits by repairman and expected profit earned by the system.     

Stochastic behaviour and profit function of a system with precautionary measures under abnormal weather

A repairable system under normal and abnormal weather conditions is analysed. The system can be in one of the three modes—normal, partial and total failure. Failure rates of system and rates of change of weather conditions are constant while the repair rates are arbitrary functions of time. The repair time distributions depend upon the state from which the repair starts and are invariant with the change of weather. Using regenerative point technique various reliability characteristics such as mean time to system failure, steady state availability, the probability that the repairman is busy, expected number of visits by repairman and expected profit earned by the system are obtained.     

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.     

Cost analysis in a two-unit standby system with a regular repairman and patience time

This paper develops a model for standby redundant system consisting of two identical units and a regular repairman. In an effort to increase the working time of the system, we put some “patience time” as the upper limit to repair time of the regular repairman. If the regular repairman is not able to do the repair within this patience time, we call an “expert” repairman for doing the repairs. Then the various measures of system effectiveness are calculated using semi-Markov processes and regenerative processes. Based on these measures, a rule is developed whether the services of the expert repairman should be utilized profitably or not. Further using numerical methods, we discuss the optimum patience time for various costs, maximizing the profit.     

A two dissimilar unit multi-component system with correlated failures and repairs

This paper investigates a two non-identical unit cold standby system model. Each unit is composed of n independent components arranged in a series configuration. A single repairman is available to repair a failed unit. The priority in operation is being given to the first unit, while in repair the priority is given to the second unit. The failure and repair times of the ith and jth component for the first and second unit, respectively, are jointly distributed as bivariate exponentials (B.V.E.) with different parameters. Using a regenerative point technique, various reliability characteristics have been analysed.     

The effect of minimal repairs on economic lot-sizing

This paper examines the problem of lot-sizing in a production facility in the face of machine breakdowns. Failures are dealt with by minimal repairs, until the required lot has been produced, at which point a new cycle is set-up and the machine restored to “as-new” condition. Given the expected duration of a repair, and the duration of a set-up, optimal lot sizes are obtained for Weibull distributed times to failure. Empirical evidence suggests that for an exponential time to failure, the failure process can usually be safely ignored, whereas for machines with a sharply increasingly failure rate, this is not the case.     

An Application of Optimal Control Theory to Repairman Problem with Machine Interference

Optimal preventive maintenance policy for a system of machines subject to random breakdowns and repairs is derived using optimal control theory. The optimal policy is shown to be `bang-bang'. The model accounts for the waiting line at the repair facility and establishes a link between machine maintenance and classical repairman problem involving machine interference. An example illustrates the procedure to obtain the optimal preventive maintenance policy. An important feature of this work is that the usual assumption of the steady-state behaviour of the queue is relaxed (by directly considering the Kolmogorov differential equations as state equations of the system) and its transient behaviour is explicitly taken into account.     

A maintenance inspection model for a single machine with general failure distribution

In this paper we develop a mathematical model for determining a periodic inspection schedule in a preventive maintenance program for a single machine subject to random failure. We formulate the problem as a profit maximization model with general failure time distribution. We show that under certain conditions on the probability density function of failure, a unique optimal inspection interval can be obtained. When the failure times are exponentially distributed, we propose alternative optimal and heuristic procedures to find exact and approximate inspection intervals. Our heuristic solution method is shown numerically to be more efficient than an earlier published heuristic procedure. We also investigated the sensitivity of the optimal inspection interval and expected profit per unit of time with respect to the changes in the two parameters of the Weibull time to failure distribution.     

Comparative study of the profit of a two server system including patience time and instruction time

The paper is concerned with two unit cold standby systems having one regular repairman and one expert repairman. The expert is called only if the regular repairman is not able to complete the repair within some toletable (patience) time. In model 1, it is assumed that an expert, on his arrival, gives instructions to the regular repairman for completing the repair, in model 2, it is assumed that the expert himselg takes over the system and the regular repairman leaves the repair in the presence of the expert. In model 3, there is no provision of calling the expert. Techniques of the semi-Markov processes and regenerative processes are used to obtain various measures of system effectiveness and profit incurred. A pairwise comparison of model 1 is made with model 2 and model 3 through graphs.     

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.     

Probabilistic analysis of a two-unit cold standby system with instructions at need

A two-unit cold standby system with an expert repairman and his assistant is examined. If the expert repairman is busy in repairing a failed unit and at that time the second unit fails, the assistant repairman repairs the latter unit. The assistant repairman needs or does not need instructions for doing repair with probability p and q, respectively. Using a regenerative point technique, various measures of system effectiveness are obtained.     

On the characteristics of a system having master and helping unit

A system having one master and one helping unit with two failure modes-partial and total-is analysed. The helping unit is used to support the master unit in operation. Whenever the helping unit fails it is either repaired or replaced with probability p(q). Failure time distributions are taken to be negative exponential whereas repair time distributions are taken to be arbitrary. Using the regeneration point technique, several system characteristics such as mean time to system failure, availability, busy period of the repairman, etc. are obtained. Finally, some graphs are drawn in order to highlight the important results in particular cases.     

Diffusion equation for GI/G/r machine interference problem with spare machines

A diffusion approximation technique is developed for an (m, M) machine repair system containing M identical machines under the care of r repairmen provided N spare machines. The machines may fail in groups of random size. As soon as machines fail, they are replaced by spare machines, provided spare machines are available. By approximating the discrete flow of failed machines by a continuous one, the analysis is carried out by using the diffusion approximation technique. We have obtained expressions for various measures of performance in terms of means and variances of inter-failure, repair and group size distributions. We have also discussed the modified boundary conditions required to improve the approximation.     

A generalized multi-standby multi-failure mode system with various repair facilities

We consider a system of (m + 1) non-identical units—one functioning and m standby. Each unit of the system has the following states: normal, N types of partial failures and corresponding to them N types of total failures. There are k distinct major repair facilities and one on the spot repairman. One unit can pass from one state to another with known probability and then the time of staying in this state has a general distribution. The system starts to work at t = 0 and fails when the (m + 1)th unit after a total failure is finally rejected. Using semi-Markov techniques we obtain Laplace transforms of transition probabilities. Considering particular cases we derive known results for systems which have been defined in the past.     

Stochastic analysis of a 2-unit standby system with two failure modes and slow switch

This paper considers the cost-benefit analysis of a one-server two unit system subject to two different failure modes and slow switch. The failure rates of the units are constant. The repair times and the switchover time are assumed to be arbitrarily distributed. The server repairs the units and puts the standby unit into operation. Detailed analysis of the system is done by using regenerating point technique and results are obtained for mean time to system failure, steady state availability, busy period of a repair man, expected number of visits by the repair man and expected profit earned by the system.     

Redundancies and don't cares in sequential logic synthesis

The relationships between redundant logic and don't care conditions in combinational circuits are well known. Redundancies in a combinational circuit can be explicitly identified using test generation algorithms or implicitly eliminated by specifying don't cares for each gate in the combinational network and minimizing the gates, subject to the don't care conditions.In this article, we explore the relationships between redundant logic and don't care conditions in sequential circuits. Stuck-at faults in a sequential circuit may be testable in the combinational sense, but may be redundant because they do not alter the terminal behavior of a nonscan sequential machine. These sequential redundancies result in a faulty State Transition Graph (STG) that is equivalent to the STG of the true machine.We present a classification of redundant faults in sequential circuits composed of single or interacting finite state machines. For each of the different classes of redundancies, we define don't care sets which if optimally exploited will result in the implicit elimination of any such redundancies in a given circuit. We present systematic methods for the exploitation of sequential don't cares that correspond to sequences of vectors that never appear in cascaded or interacting sequential circuits. Using these don't care sets in an optimal sequential synthesis procedure of state minimization, state assignment, and combinational logic optimization results in fully testable lumped or interacting finite state machines. We present experimental results which indicate that medium-sized irredundant sequential circuits can be synthesized with no area overhead and within reasonable CPU times by exploiting these don't cares.     

Markovian analysis of the M/Ek/1 machine repair problem with spares

This paper considers the M^X/E_k/1 spare machine repair problem under steady state conditions. A Markovian approach is used as a solution technique to the machine repair problem with spares. The approach followed in this paper provides expressions for state probabilities and machine availability simultaneously. The results are of both practical and theoretical interest as an extension of the standard Poisson batch failure case.