Inspection policy with failure due to inspection

In this paper, we discuss the inspection policy for the modified inspection model taking account of the system failure due to any inspection. We obtain the nearly optimal inspection policy which minimizes the nearly total expected cost up to the detection of the system failure. We also present the numerical examples of the nearly optimal inspection policy by assuming a Weibull distribution for illustration.     

An inspection policy for one-unit system subject to revealed and unrevealed failures

This paper deals with a single-server one-unit system subject to both revealed and unrevealed failures. We shall assume that a revealed failure is detected as soon as it occures but an unrevealed failure is detected by an inspection only. Under an inspection policy, the Laplace transform of the pointwise availability of the system and the stationary availability of the system are derived by using the supplementary variable method. Further, we discuss the optimum inspection schedule maximizing the stationary availability. Finally, some numerical examples are presented.     

Comparison of two wafer inspection methods for particle monitoringon semiconductor manufacturing

The two methods examined differ in the procedure used to select wafers for inspection. In the first, or fixed-policy, method, the same number of wafers is inspected regardless of defect density. In the second method a variable policy is used. It is found that in a superclean production environment these inspection methods are not equivalent in defect density estimation: estimates obtained by the variable policy may be biased, while those obtained with the fixed policy are always unbiased. Fundamental reasons for such a phenomenon are discussed and recommendations are made     

Significance of Equipment Reliability in a Telephone Network

A reliability concept is considered in which telephone traffic is taken into account for a telephone network. An analytic model of a simple network with parallel paths shows how telephone traffic is included in the telephone network reliability analysis. Examples are given to demonstrate the usefulness of this concept in the investigation of an optimum inspection policy for each path, and the effects of path age and failure rate on telephone network service.     

Human Error Considerations in Determining the Optimum Test Interval for Periodically Inspected Standby Systems

This paper incorporates the effects of two types of human error in a model for determining the optimal time between inspections for a safety system. The possibility that a bad safety system is undetected upon inspection (Type B human error), as well as the possibility that a good safety system is inadvertently left in a bad state after the inspection (Type A human error), are considered. We develop a Markov model for the steady-state availability of the safety system which is then used to determine the optimum time between inspections which either maximizes the availability or minimizes the combined inspection and unavailability costs. The safety system failure (hazard) rate need not be constant. The optimum time between inspections increases as the probability of a Type A error increases and a Type B error decreases. The optimum availability decreases and the optimum total cost increases as the error probabilities increase.     

Optimal inspection policy for a parallel redundant system

This paper considers an inspection policy for an n-unit parallel redundant system which is checked at successive times x (k=1, 2,…). The preventive maintenance is made if j units (1<j<n−1) fail at each inspection. The expected cost is derived and the optimum policy to minimize it is discussed. Two modified models are introduced. A numerical example is given when the failure times of each unit have a Weibull distribution.     

An inspection-maintenance model for systems with multiple competing processes

In some applications, the failure rate of the system depends not only on the time, but also upon the status of the system, such as vibration level, efficiency, number of random shocks on the system, etc., which causes degradation. In this paper, we develop a generalized condition-based maintenance model subject to multiple competing failure processes including two degradation processes, and random shocks. An average long-run maintenance cost rate function is derived based on the expressions for the degradation paths & cumulative shock damage, which are measurable. A geometric sequence is employed to develop the inter-inspection sequence. Upon inspection, one needs to decide whether to perform a maintenance, such as preventive or corrective, or to do nothing. The preventive maintenance thresholds for degradation processes & inspection sequences are the decision variables of the proposed model. We also present an algorithm based on the Nelder-Mead downhill simplex method to calculate the optimum policy that minimizes the average long-run maintenance cost rate. Numerical examples are given to illustrate the results using the optimization algorithm.     

Inspection policy for two-unit parallel redundant system

This paper deals with a single-server two-unit parallel redundant system with non-negligible inspection time. We shall assume that a failure of a unit or the system failure is detected by inspection only. We consider two inspection policies and under each inspection policy the stationary availability is derived by applying Piecewise Markov Process. Optimum inspection schedule is discussed to maximize the stationary availability of the system. A numerical example is presented.     

Continuous-time predictive-maintenance scheduling for adeteriorating system

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system     

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.     

Profit analysis of a one-server one-unit system with partial failure subject to random inspection

This paper deals with the cost-benefit analysis of a single-server one-unit system with partial failure, which is subject to random inspection. An inspection policy model is considered in which the partial failure of the unit is detected only by inspection, but complete failure of the unit is detected instantaneously without inspection. The system is observed at suitable regenerative epochs in order to obtain several economics-related system characteristics. Explicit results are obtained in a few particular cases. Graphs are also given.     

A Basic Dynamic Routing Problem and Diffusion

Diffusion theory has sometimes been successful in providing excellent approximate solutions to difficult queueing problems. Here we explore whether such methods can be used to analyze a basic dynamic routing strategy associated with a single idealized node in a data network. We analyze a dynamic routing policy where messages, or packets, that arrive at a certain node are routed to leave the node on the link having the shorter queue. In the model, message or packet arrivals are Poisson and the service time is exponentially distributed. We explore a heavy traffic diffusion method and we also discuss the limitations of an ad hoc approach to applying diffusion. For a node withKoutgoing queues we find, under the assumption of heavy traffic, the optimum dynamic strategy, in the sense of minimizing the average delay. When this optimum dynamic strategy is compared to a static strategy where the outgoing traffic is split among theKqueues, we find that the average delay for the dynamic system is better by a factor ofK.     

An ordering policy with age-dependent minimal repair and age-dependent random repair costs

In this paper we consider an ordering policy for a one-unit system with age-dependent minimal repair and age-dependent random repair costs. 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. We show that, under certain conditions, there exists a finite and unique optimum policy. Various special cases are discussed.     

An inspection model with minimal and major maintenance for a systemwith deterioration and Poisson failures

A new condition-based maintenance model for a system, subject to deterioration-failures and to Poisson-failures, is presented. After an inspection, based on the degree of deterioration, a minimal maintenance or a major maintenance is performed, or no action is taken. Deterioration failures are restored by major repair; Poisson failures are restored by minimal repair. Major maintenance or major repair restores the system to “good as new” while minimal maintenance restores the system one stage. Generalized stochastic Petri Nets are used to represent and analyze the model, which represents a condition-based maintenance strategy. Based on maximization of the system throughput, an optimal inspection policy within this strategy and optimal inter-inspection time are obtained. The effects of inspection, maintenance and repair parameters are investigated. For a given inspection parameter, a 3-region diagram identifies the effectiveness of an inspection policy based on minimal maintenance, major maintenance, and major repair parameters     

Analysis of a 2-phase model for optimization ofcondition-monitoring intervals

Condition monitoring is a maintenance strategy where decisions are made depending on either continuously or regularly measured equipment states. It reduces uncertainty with respect to actual states of equipment, and can thus avoid unnecessary repair or replacement. However, it involves capital expenditure and/or operational costs to perform measurements. This paper presents a basic model for the economic evaluation and optimization of the interval between successive condition measurements (also called inspections), where measurements are expensive and cannot be made continuously. It assumes that the technique can detect an intermediate state to failure for a failure mode of interest. The influence of competing risks is analyzed, leading to the conclusion that once the cost-effectiveness of the condition-monitoring has been established, competing risks need not be considered in determining the optimum condition monitoring interval. Inspection is cost-effective if the intermediate state has a: (1) nondecreasing hazard rate, and (2) shorter mean residence time than the good state (good-as-new condition), while costs of failure are high enough compared with inspection and repair costs in the intermediate state. Assuming that the distribution of the residence time in the second state is unimodal, estimation of the mean (or scale parameter) and standard deviation of this state, in many cases, provides enough information to make a good decision on the inspection interval. The most important model parameters are identified by sensitivity analyses; it is shown that the model can be simplified without seriously affecting optimal decision making     

A semi-regenerative process of two-unit warm standby system

This paper deals with two identical units warm standby system; a failure of operating unit can be detected at any time but a failure of standby unit can not be done until a system is inspected. We are able to look upon the stochastic behavior of our model as that of semi-regenerative process. The pointwise unavailability and the steady state unavailability of the system are derived by using the limit theorem of semi-regenerativeprocess. Further, we shall discuss the optimum inspection period minimizing the steady state unavailability. A numerical example is presented.     

A note on optimum checkpointing policies

In this paper, we treat checkpointing policies. We derive the total expected loss time and obtain the optimum checkpointing policy which minimizes that expected loss time. We further present the numerical examples using the exponential and the Weibull distributions. First, we discuss the model in which the intervals between checkpointing completion times may vary, and secondly the model with constant intervals.     

Optimum stochastic inspection policies for a system with safety device

In this paper we discuss an optimal stochastic inspection policy for systems that consist of a safefy related module which is supervised by a second module. The life time distributions of the modules are arbitrary. A failure of the safety relevant module is determined by the supervising module provided the latter is functioning. Function of the supervising module can be determined only upon inspection. An inspection returns the system into a state as good as new. The system fails if the safety relevant module fails undetected. The optimal inspection policy is searched among stochastic strategies, i.e. strategies that are able to consider different inspection times with various probabilities.     

Distortion Control for Delay-Sensitive Sources

We investigate the problem of finding minimum-distortion policies for streaming delay-sensitive but distortion-tolerant data. We consider cross-layer approaches which exploit the coupling between presentation and transport layers. We make the natural assumption that the distortion function is convex and decreasing. We focus on a single source-destination pair and analytically find the optimum transmission policy when the transmission is done over an error-free channel. This optimum policy turns out to be independent of the exact form of the convex and decreasing distortion function. Then, for a packet-erasure channel, we analytically find the optimum open-loop transmission policy, which is also independent of the form of the convex distortion function. We then find computationally efficient closed-loop heuristic policies and show, through numerical evaluation, that they outperform the open-loop policy and have near optimal performance.     

Periodic-replacement models with threshold levels

The authors suggest five replacement policies where a unit is replaced at periodic times, jT(j=1,2, . . .), and the replacement cost is expensive when some number of events occurring in (0,t) is greater than a threshold level. The usual models for inspection, periodic replacement, block replacement, parallel systems, and cumulative damage can be transformed into replacement models with threshold levels. The mean cost-rate of each model is obtained, using well-known results of reliability theory. The optimum replacement time which minimizes the cost-rate of an inspection model is discussed and shown to exist uniquely