All opportunity-triggered replacement policy for multiple-unitsystems

A model is presented for a system which consists of n i.i.d units. Hazard rates of these units are increasing in time. A unit is replaced at failure or when the age of a unit exceeds T, whichever occurs first. When a unit is replaced, all the operating units with their age in the interval (T-w,T) are replaced. Both failure replacement and active replacement create the opportunities to replace other units preventively. This policy allows joint replacements and avoids the disadvantages resulting from replacement of new units, down time, and unrealistic assumptions for distributions of unit life. An algorithm is developed to compute the steady-state cost rate. Optimal T&W are obtained to minimize the mean total replacement cost rate. Application and analysis of results are illustrated through a numerical example     

Hazard-rate tolerance method for an opportunistic-replacementpolicy

A model for a system with several types of units is presented. A unit is replaced at failure or when its hazard (failure) rate exceeds limit L, whichever occurs first. When a unit is replaced because its hazard rates reaches L, all the operating units with their hazard rate falling in the interval (L-u, L) are replaced. This policy allows joint replacements and avoids the disadvantages resulting from the replacement of new units, down time, and unrealistic assumptions for distributions of unit life. The long-run cost rate is derived. Optimal L and u are obtained to minimize the average total replacement cost rate. Application and analysis of results are demonstrated through a numerical example     

Optimal operation of a markovian queueing system with a removable and non-reliable server

This paper deals with the optimal operation of a single removable and non-reliable server in a Markovian queueing system under steady-state conditions. The server can be turned on at arrival epochs or off at departure epochs. We assume that the server may break down only if working and requires repair at a repair facility. Interarrival and service time distributions of the customers are assumed to be exponentially distributed. Breakdown and repair time distributions of the server are assumed to be exponentially distributed. The following cost structure is incurred to the system: a holding cost for each customer in the system per unit time, costs per unit time for keeping the server on or off, a breakdown cost per unit time when a server fails, and fixed costs for turning the server on or off. The total expected cost function per unit time is developed to obtain the optimal operating policy at minimum cost.     

A geometric-process repair-model with good-as-new preventive repair

This paper studies a deteriorating simple repairable system. In order to improve the availability or economize the operating costs of the system, the preventive repair is adopted before the system fails. Assume that the preventive repair of the system is as good as new, while the failure repair of the system is not, so that the successive working times form a stochastic decreasing geometric process while the consecutive failure repair times form a stochastic increasing geometric process. Under this assumption and others, by using geometric process we consider a replacement policy N based on the failure number of the system. Our problem is to determine an optimal replacement policy N such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal replacement policy can be determined analytically or numerically. And the fixed-length interval time of the preventive repair in the system is also discussed. Finally, an appropriate numerical example is given. It is seen from that both the optimal policies N** and N* are unique. However, the optimal policy N** with preventive repair is better than the optimal policy N* without preventive repair     

(τ, k) block replacement policy with idle count

The authors propose a new block replacement policy for a group of nominally identical units. Each unit is individually replaced on failure during a specified time interval. Beyond the failure replacement interval, failed units are left idle until a specified number of failures occur, then a block replacement is performed. The average cost rate for this two-phase block replacement policy is derived and analyzed. The policy yields lower cost rate than two block replacement policies published previously. Numerical examples demonstrate the results     

Optimum ordering policies with random lead times and salvage cost

This paper deals with the optimum ordering policy for a one unit system with general lifetime, where the failed unit is not repairable. A spare can only be provided after a lead time. Two kinds of orders (regular and emergency) are possible, each having a different lead time. A sensing device is attached to the unit by which the operational status of the unit is monitored continuously. The device is repairable and its lifetime and repair time are assumed to be exponentially distributed, random variables. The costs considered include salvage, penalty, downtime, ordering and repair costs. The optimal policy discussed is the one which maximizes the cost effectiveness.     

Defect-oriented test scheduling

As tester complexity and cost increase, reducing test time is an important manufacturing priority. Test time can be reduced by ordering tests so as to fail defective units early in the test process. Algorithms to order tests that guarantee optimality require execution time that is exponential in the number of tests applied. We develop a simple polynomial-time heuristic to order tests. The heuristic, based on criteria that offer local optimality, offers globally optimal solutions in many cases. An ordering algorithm requires information on the ability of tests to detect defective units. One way to obtain this information is by simulation. We obtain it by applying all possible tests to a small subset of manufactured units and assuming the information obtained from this subset is representative. The ordering heuristic was applied to manufactured digital and analog integrated circuits (ICs) tested with commercial testers. When both approaches work, the orders generated by the heuristic are optimal. More importantly, the heuristic is able to generate an improved order for large problem sizes when the optimal algorithm is not able to do so. The new test orders result in a significant reduction, as high as a factor of four, in the time needed to identify defective units. We also assess the validity of using such sampling techniques to order tests     

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.     

An optimal inspection policy for a storage system with high reliability

A system such as missiles and spare parts of aircrafts has to perform a normal operation at any time when it is used. However, a system is in storage for a long time from the transportation to the usage and its reliability goes down with time. Such a system should be inspected and maintained at periodic times to hold a higher reliability than a prespecified value q. This paper suggests a periodic inspection of a storage system with two kinds of units where unit 1 is inspected and maintained at each inspection, however, unit 2 is not done. The system is replaced at detection of failure or at time when the reliability is below q. The total expected cost until replacement is derived and an optimal inspection time which minimizes it is discussed. Numerical examples are given when failure time distributions are exponential and Weibull ones.     

Cost limit replacement policy under minimal repair

This paper presents a policy for either repairing or replacing a system that has failed. When a system requires repair, it is first inspected and the repair cost is estimated. Repair is only then undertaken if the estimated cost is less than the “repair cost limit”. However, the repair cannot return the system to “as new” condition but instead returns it to the average condition for a working system of its age. Examples include complex systems where the repair or replacement of one component does not materially affect the condition of the whole system. A Weibull distribution of time to failure and a negative exponential distribution of estimated repair cost are assumed for analytic amenability. An optimal “repair cost limit” policy is developed that minimizes the average cost per unit time for repairs and replacement. It is shown that the optimal policy is finite and unique.     

An Optimal Decision Rule for Repair vs Replacement

This paper presents a policy for either repairing or replacing a system that has failed. The policy applies to systems whose mean residual life function is decreasing. An optimal policy is developed that minimizes the cost per unit time for repair and replacement. Results are shown graphically for a particular distribution of time to failure and are motivated in terms of an automobile replacement problem.     

Optimal ordering policies and optimal number of minimal repairs before replacement

Many maintenance policies in the literature have assumed that whenever a unit is to be replaced, a new unit is immediately available. However, if the procurement lead time is not negligible an odering policy should determine when to order a spare and when to replace the operating unit. This paper presents a model for determining the optimal ordering point and the optimal number of minimal repairs before replacement which include the optimal number of minimal repairs before replacement of Park as a special case. We derive the expected cost per unit time in the steady-state as a criterion of optimality and seek the optimum policy by minimizing that cost. Finally, we present the numerical examples for illustration.     

Structured Threshold Policies for Dynamic Sensor Scheduling—A Partially Observed Markov Decision Process Approach

We consider the optimal sensor scheduling problem formulated as a partially observed Markov decision process (POMDP). Due to operational constraints, at each time instant, the scheduler can dynamically select one out of a finite number of sensors and record a noisy measurement of an underlying Markov chain. The aim is to compute the optimal measurement scheduling policy, so as to minimize a cost function comprising of estimation errors and measurement costs. The formulation results in a nonstandard POMDP that is nonlinear in the information state. We give sufficient conditions on the cost function, dynamics of the Markov chain and observation probabilities so that the optimal scheduling policy has a threshold structure with respect to a monotone likelihood ratio (MLR) ordering. As a result, the computational complexity of implementing the optimal scheduling policy is inexpensive. We then present stochastic approximation algorithms for estimating the best linear MLR order threshold policy.     

Availability analysis of a repairable system with common-cause failure and one standby unit

This paper investigates the mathematical model of a system consisting of two non-identical parallel redundant active units, with common-cause failure, and a cold standby unit. The failed units are repaired one at a time or are repaired together, if they fail due to common cause failure. All repair time distributions are arbitrary and different. The analysis is carried out under the assumption of having a single service facility for repair and replacement.Applying the supplementary variable technique, Laplace transforms of the various state probabilities are developed. Explicit expressions for the steady state probabilities and the steady state availability are derived.Some well known results are obtained as special cases. A numerical example is given to illustrate the effect of the repair policy on the steady state probabilities and the availability of the system.     

A simple ordering policy with linear lifetime for a unit

In this paper optimum ordering policies of a one-unit system where each failed unit is scrapped and each space is only provided after a lead time by an order with a deterministic linear lifetime for the unit is considered. The optimum ordering policy minimizing the expected cost per unit time in the steady state is discussed by introducing the two types of constant lead times along with ordering costs and downtime cost. The problem concludes with a numerical example minimizing the expected cost function.     

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.     

A maintenance policy for repairable systems based on opportunisticfailure-rate tolerance

An opportunistic hazard rate replacement policy for a repairable system with several types of units is presented. A unit is repaired at failure when the hazard rate falls in (0, L-u). A unit is replaced at failure when the hazard rate falls in (L-u , L). An operating unit is replaced when its hazard rate reaches L. When a unit is replaced because its hazard rate reaches L, all operating units with their hazard rates falling in (L-u, L) are replaced. The long-run mean cost rate as a function of L and u is derived. Optimal L and u are obtained to minimize the total maintenance cost rate. Application and analysis of results are demonstrated through a numerical example. The maintenance model is designed for a system with multitype units. Each type has its own increasing hazard rate. Units are repaired or replaced depending on their hazard rate at a failure or active replacement of another unit. The repair interval, replacement limit, and replacement tolerance are determined to yield the optimal total maintenance cost rate     

Cost analysis of a two-unit warm standby reliability system with two types of repair facilities

This paper deals with a two-unit warm standby system. These units are identical, but have different failure rates and repair time distributions, when failed in operating or standby state. If the unit fails in operating state, we wait for the repairman for some maximum time or until the other unit fails, and if the unit fails in standby state we wait for the repairman until the other unit fails. On the failure of the second unit or on the completion of the maximum time, we call the repairman immediately at the higher cost.The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results pertaining to some particular cases are also added.     

Optimum Ordering Policies with Lead Time for an Operating Unit in Preventive Maintenance

An ordering policy allows a spare, delivered after a constant lead time, to be put into inventory. Under certain conditions there exists a finite and unique ordering policy maximizing the cost effectiveness, which balances the system effectiveness and the cost and is defined as [s-availability]/[s-expected cost rate].     

Optimal Ordering and Replacement for a 1-Unit System

A problem of ordering and replacement for a unit which degrades is discussed. The optimal age for ordering and for preventive replacement, which minimizes the total s-expected cost per unit time in an infinite time span, is obtained. Some numerical examples are presented.