N. Ravichandran

Stochastic analysis of a dependent parallel system

This article discusses the stochastic behaviour of a two-unit parallel redundant repairable system with statistically dependent units. Important performance measures for the system, namely reliability, mean time to system failure, availability, stationary availability, joint availability and interval reliability are obtained in an explicit form. The transient behaviour of the system is characterised for a wide class of repair time distributions. The lifetimes of the units are modelled as bivariate exponential to capture the statistical dependence of the units. The article concludes with a detailed investigation of the stochastic point process induced by entries to various states, which correspond to the number of failed components in the system.

Interval Reliability of An n-Unit System With Single Repair Facility

This paper derives the interval reliability of an n-unit standby redundant system with warm standbys. The derivation uses renewal theory and regeneration-point techniques. The solution is obtained in the form of Laplace transforms; the transforms can be readily inverted for some special cases.

Availability of a Redundant System

The Laplace transform of the availability of a multicomponent system with spares, is obtained by the regeneration point technique.

Transient Analysis of Multiple Unit Reliability Systems

A general Markovian model representing several multiple unit redundant repairable system is proposed and it’s transient behaviour is studied. Specifically, for multiple unit reliability system the reliability and availability functions are derived in an explicit form for the transient case. The stationary availability and mean time to system failure are deduced from the main results as special cases.

On a two unit standby redundant system with imperfect switchover

Abstract The Laplace transform of the availability of a two unit standby redundant system with imperfect switchover is obtained by identifying suitable regeneration points. The steady state behaviour is also discussed.

Probabilistic analysis of a two-unit parallel redundant system

Abstract Expressions are obtained for the reliability and availability of a two-unit parallel redundant system in which all four distributions involved are arbitrary.

Analysis of (S, s) Inventory System with Decaying Items

This article obtains the stationary distribution of the inventory level of an (S, s) inventory model with decaying items. The demand to this inventory system is governed by a general renewal process. Items decay at a constant rate independently and identically. When the inventory reduces to a level <s, at a demand point an order for replenishment is placed and is received after a random duration whose distribution is arbitrary. The quantity realised is variable and is such that the resulting inventory level is equal to S. Both the cases of complete becklogging and lost sales are treated in the present analysis. The stochastic process L(t) representing the inventory level at any time t is analysed by identifying an embedded MRP. The intensity of decay events and shortages are obtained in an explicit form. Based on the results a total cost expression is derived. Numerical results are presented to illustrate the use of the cost expression in identifying the optimal reorder level.

Probabilistic analysis of a continuous review perishable inventory system with Markovian demand, Erlangian life and non-instantaneous lead time

SummaryThis article obtains an explicit cost expression for a continuous review (S, s) ordering policy inventory system of perishable items, in the stationary case. The cost expression is closely related to the stationary distribution of the stochastic processL(t), representing the inventory at any timet. The stochastic behaviour of the process {L(t),t≳-0} is characterised by identifying an imbedded MRP. The demands of the system are governed by a Poisson process. The items in the inventory have a useful life time characterised by an Erlangian distribution. The lead time is a random variable with specified probability distribution. It is assumed that the demands that arrive when the inventory is zero are lost.ZusammenfassungDer vorliegende Artikel behandelt einen expliziten Kostenausdruck für eine stetige Überprüfung der (S, s) Bestellpolitik eines Lagerhaltungssystems verderblicher Güter im stationären Fall. Der Kostenausdruck ist eng verbunden mit der stationären Verteilung des stochastischen ProzessesL(t), der den Lagerbestand zu jeder beliebigen Zeitt darstellt. Das stochastische Verhalten des Prozesses {L(t),t≳-0} wird characterisiert durch die Identifikation eines eingebetteten MRP. Die Nachfragewerte des Systems werden durch einen Poisson-Prozeß bestimmt. Die gelagerten Güter haben eine nutzbare Lebensdauer, die durch eine Erlang-Verteilung beschrieben wird. Die Durchlaufzeit ist eine Zufallsvariable mit spezifierter Wahrscheinlichkeitsverteilung. Es wird zudem unterstellt, daß nicht befriedigte Nachfrage bei leerem Lager verloren geht.

Analysis of a two-unit parallel redundant system with phase type failure and general repair

Explicit expressions for the Laplace transform of the reliability and availability of a general two-unit parallel redundant system are obtained. The Mean time to system failure and steady state availability are deduced as special cases. Some particular cases of our result are also obtained.

Study of A 2-Unit Priority-Standby System

This paper evaluates the availability of a 2-unit priority-standby repairable system by using the regeneration point technique. The particular hypothesis on the repair policy does not allow the system to be analysed via Markov renewal process.