Extended block replacement policy of a system subject to shocks

A generalization of the block replacement (BR) policy is proposed and analyzed for a system subject to shocks. Under such a policy, an operating system is preventively replaced by new ones at times i·T (i=1,2,3,...) independently of its failure history. If the system fails in: (a) ((i-1)·T, (i-1)·T+T₀), it is either replaced by a new one or minimally repaired; or (b) ((i-1)·T+T₀, i·T), it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two actions is based on some mechanism (modeled as random) which depends on the number of shocks since the latest replacement. The average cost rate is obtained using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed. Various special cases are considered. The results extend many of the well-known results for BR policies     

A two-unit priority standby system subject to random shocks and Releigh failure-time distribution

This paper deals with the cost-benifit analysis of a two-unit priority standby system subject to random shocks. The priority unit gets preference both for repair and operation over the ordinary unit and has three modes- Normal, Quasi-normal and Total-failure. The ordinary unit has only two-modes- Normal and Total-failure. The distributions of shock-time, repair-time of the ordinary unit and failure time of the priority unit are negative exponential. The distribution of the repair-time of the priority unit is taken to be general while the time to failure of ordinary unit follows Releigh distribution. Various characteristics related to system effectiveness have been obtained by using the regenerative point technique.     

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.     

Two-unit standby reliability system subject to effective and non-effective random shocks

This paper considers a system consisting of two units. The system experiences shocks after certain random intervals. These random intervals are independently and identically distributed each with a general probability density function. Further, the shocks are classified into three types according to the effect of the shocks on the system: Type I, the shock that has no effects on the system, Type II, the shock increases the failure rate and Type III, the shock that fails the system. The system can fail either due to a shock of Type III or due to the internal stress and strain of the operation of the unit or due to two successive shocks, the first shock being of Type II. The repair times of the units are assumed to be exponentially distributed. The mean time to system failure (MTSF), steady state availability of the system and expected number of times the repairman is required are investigated. Finally, MTSF-shock rate and steady state availability-shock rate figures are drawn for special cases and certain interesting results are observed therefrom.     

The availability of inspected systems subject to shocks andgraceful degradation

This paper studies maintained systems with nonself-announcing ("hidden") failures that deteriorate due to both shocks and graceful degradation. Shocks occur according to a Poisson process, shock magnitudes are i.d.d. random variables, and between shocks, deterioration occurs at a constant rate. Inspections are performed periodically. Using regenerative arguments, an expression is derived for limiting average availability. This expression provides insight into the effect of system life distribution on availability, and suggests opportunities for more effective inspection strategies     

Reliability analysis of a repairable system in a changing environment subject to a general alternating renewal process

This paper considers a repairable system in a changing environment subject to a general alternating renewal process. Using Markov renewal theory we obtain the system availability, failure frequency and reliability function.     

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.     

A single unit multicomponent system subject to various types of failures

This paper investigates the mathematical model of a reparable system with several possible states of operation, failure and repair. There is also an inspection facility for deciding whether on failure, the system needs minor repair or overhaul. Repair rates are arbitrary functions of the time spent. All other transition rates are constant. Several reliability characteristics of interest to system designers as well as operations managers have been computed and results obtained earlier are verified as particular cases.     

Two-unit cold-standby redundant system subject to random checking, corrective maintenance and system replacement with repairable and non-repairable types of failure

We consider a system comprising two identical units. Initially one unit operates and the other remains as a cold standby. At random intervals, checking is done to ascertain the need of Corrective Maintenance (CM). In case CM has to be carried out, the standby unit starts operating. While the unit is operative, it may fail. Failures are of two types, repairable and non-repairable. When the system fails with non-repairable failure of both the units, it is replaced. Several reliability characteristics of interest to system designers as well as to operations managers have been evaluated.     

Optimal replacement of an item subject to cumulative damage under periodic inspections

An item undergoes cumulative damage through use. The item fails randomly but the failure rate depends on the accumulated damage. The item is preventively replaced if it survives a certain damage limit at periodic inspections; on failure, it is replaced immediately. The optimal damage limit for preventive replacement which minimizes the long-run expected cost rate is derived. It is unique if an item has increasing damage-dependent failure rate. Numerical example for a stationary gamma process with Weibull distributed failure is given.     

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.     

Some characteristics of a man-machine system operating subject to different weather conditions

This paper deals with some characteristics of a single unit of a man-machine system operating under different weather conditions. It is assumed that the failure, repair and change of weather conditions (normal-stormy) are stochastically independent random variables, each having an arbitrary distribution. 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. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady-state availability of the system are obtained. Several important results have been derived as particular cases.     

Cost-benefit analysis of a one-server two-unit system subject to shock and degradation

This paper deals with the cost-benefit analysis of 1-server 2-unit system subject to two modes of failure, namely, shock and degradation. Initially, one unit starts operating and the other is kept as cold-standby. The type of repair a unit undergoes depends upon the nature of its failure. The various essential characteristics of the system have been found out to carry out the cost-benefit analysis.     

Periodic replacement with minimal repair at failure and general random repair cost for a multi-unit system

A policy of periodic replacement with minimal repair at failure is considered for the multi-unit system which have the specific multivariate distribution. Under such a policy an operating system is completely replaced whenever it reaches age T (T > 0) at a cost c₀ while minimal repair is performed at any intervening component failures. The cost of the j-th minimal repair to the component which fails at age y is g(C(y),c_j(y)), where C(y) is the age-dependent random part, c_j(y) is the deterministic part which depends on the age and the number of the minimal repair to the component, and g is an positive nondecreasing continuous function. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the component. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited.