An approximate analytical method of analysis of a threshold maintenance policy for a multiphase multicomponent model

A multicomponent system is investigated that consists of n identical unreliable components whose nonfailure operating time consists of a number of sequential phases with exponential times. A maintenance policy is studied that proposes the instant replacement of all the components as soon as the number of components that are in some doubtful state (before a failure) amounts to a predefined threshold value. A cost function averaged over a large period is studied. For a fixed n, an analytical approach is considered. If n increases, a new approximate analytical approach is proposed, which is based on results of the type of the averaging principle for recurrent semi-Markovian processes. The conditions of existence and properties of the optimal strategy are studied. An example is considered and possibilities of generalizations are discussed. © 2003 Plenum Publishing Corporation

Modified block replacement models in discrete and continuous time

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ., 2000.Thesis (Master's) -- Bilkent University, 2000.Includes bibliographical references leaves 73-75In this study, we present modified multi-component block replacement policies. Units (items) are replaced only at prescribed times j = 1,2,... A failed unit is changed with a good one with probability a. Replacement time is negligible. Three replacement policies for models that are not represented as renewal processes are provided under this setup. Some reliability characteristics are discussed. In the first model, total control is considered. All units are controlled at time jT, j = 1,2,.... In the second model, a partial (group) control is studied in which a sample of size n, (0 < n < A) is taken from all units to inspect. And the last model deals with cyclic control: units are divided into r parties. Part}' k is controlled at time jT , j — 1,2,... where j = k (modulus r), k = l,2 ,...,r — 1 and if k is equal to zero then party r is controlled. A comparison between the partial (group) control and cyclic control is provided. We also introduced cyclic partial control which combines the partial and cyclic control policies. The cyclic partial control and cyclic control is compared as well. Cost type of functionals are considered and optimal replacement interval T* is studied as well.Arun, PelinM.S

Optimal Periodic Inspection of a Stochastically Degrading System

This thesis develops and analyzes a procedure to determine the optimal inspection interval that maximizes the limiting average availability of a stochastically degrading component operating in a randomly evolving environment. The component is inspected periodically, and if the total observed cumulative degradation exceeds a fixed threshold value, the component is instantly replaced with a new, statistically identical component. Degradation is due to a combination of continuous wear caused by the component\u27s random operating environment, as well as damage due to randomly occurring shocks of random magnitude. In order to compute an optimal inspection interval and corresponding limiting average availability, a nonlinear program is formulated and solved using a direct search algorithm in conjunction with numerical Laplace transform inversion. Techniques are developed to significantly decrease the time required to compute the approximate optimal solutions. The mathematical programming formulation and solution techniques are illustrated through a series of increasingly complex example problems

Maintenance and marginal cost analysis of a two-unit cold standby system

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 97-102.The Marginal Cost Analysis (MCA) of maintenance policies is a concept gaining interest in the recent years. This approach, due to Berg, has been categorized as an Economics Oriented Approach, as different from the classical probability centered approach. The MCA has been successfully applied to the Age Replacement and the Block Replacement policies, and was shown to be flexible enough to permit extensions and generalizations. In this thesis, we apply the MCA approach to a more complex model. We consider a two-unit cold standby system. Upon failure of the working unit in the time interval [0,T) the unit is replaced by the standby unit if available. If the standby unit is in repair, the system is down, and a downtime cost is incurred. The item inspected at time T is in one of two states: “good” , or “critical” . The good unit continues operation, whereas a unit in critical state is sent to repair. The switchover is immediate. We derive and compare the marginal cost function as well as the long-run cost per unit time function.Hamdaoui, ChokriM.S

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

Una aplicación multi-criterio para la decisión de reemplazar un equipo

AbstractOne of the main problems, in the operations management, is the adequate planning of equipment replacement, not only because of its impact in the operations cost, but also, because of its effects on the service level. For such reason, the present article shows the construction of a procedure for equipment replacement, based on the use of multicriteria techniques and expert methods. The results of this application, in the replacement decision of two equipments for a sugar factory, are presented.ResumenUno de los principales problemas, en la dirección de operaciones es laadecuada planificación para el reemplazo de los equipos, no solamente por su impacto sobre el costo de las operaciones, sino también por sus efectos sobre el nivel de servicios. Por esta razón, el presente artículo muestra la construcción de un procedimiento para el reemplazo de equipos, basado en el uso de técnicas multicriteriales y métodos expertos; los resultados de esta aplicación en la decisión de reemplazar dos equipos para una fábrica de azúcar se muestran a continuación

Reliability and Condition-Based Maintenance Analysis of Deteriorating Systems Subject to Generalized Mixed Shock Model

For successful commercialization of evolving devices (e.g., micro-electro-mechanical systems, and biomedical devices), there must be new research focusing on reliability models and analysis tools that can assist manufacturing and maintenance of these devices. These advanced systems may experience multiple failure processes that compete against each other. Two major failure processes are identified to be deteriorating or degradation processes (e.g., wear, fatigue, erosion, corrosion) and random shocks. When these failure processes are dependent, it is a challenging problem to predict reliability of complex systems. This research aims to develop reliability models by exploring new aspects of dependency between competing risks of degradation-based and shock-based failure considering a generalized mixed shock model, and to develop new and effective condition-based maintenance policies based on the developed reliability models. In this research, different aspects of dependency are explored to accurately estimate the reliability of complex systems. When the degradation rate is accelerated as a result of withstanding a particular shock pattern, we develop reliability models with a changing degradation rate for four different shock patterns. When the hard failure threshold reduces due to changes in degradation, we investigate reliability models considering the dependence of the hard failure threshold on the degradation level for two different scenarios. More generally, when the degradation rate and the hard failure threshold can simultaneously transition multiple times, we propose a rich reliability model for a new generalized mixed shock model that is a combination of extreme shock model, δ-shock model and run shock model. This general assumption reflects complex behaviors associated with modern systems and structures that experience multiple sources of external shocks. Based on the developed reliability models, we introduce new condition-based maintenance strategies by including various maintenance actions (e.g., corrective replacement, preventive replacement, and imperfect repair) to minimize the expected long-run average maintenance cost rate. The decisions for maintenance actions are made based on the health condition of systems that can be observed through periodic inspection. The reliability and maintenance models developed in this research can provide timely and effective tools for decision-makers in manufacturing to economically optimize operational decisions for improving reliability, quality and productivity.Industrial Engineering, Department o

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005

Interval reliability inference for multi-component systems

This thesis is a collection of investigations on applications of imprecise probability theory to system reliability engineering with emphasis on using survival signatures for modelling complex systems. Survival signatures provide efficient representation of system structure and facilitate several reliability assessments by separating the computationally expensive combinatorial part from the subsequent evaluations submitted to only polynomial complexity. This proves useful for situations which also account for the statistical inference on system component lifetime distributions where Bayesian methods require repeated numerical propagation for the samples from the posterior distribution. Similarly, statistical methods involving imprecise probabilistic models composed of sets of precise probability distributions also benefit from the simplification by the signature representation. We will argue the pragmatic benefits of using statistical models based on imprecise probability models in reliability engineering from the perspective of inferential validity and provision of objective guarantees for the statistical procedures. Imprecise probability methods generally require solving an optimization problem to obtain bounds on the assessments of interest, but monotone system structures simplify them without much additional complexity. This simplification extends to survival signature models, therefore many reliability assessments with imprecise (interval) component lifetime models tend to be tractable as will be demonstrated on several examples

A generalised semi-Markov reliability model.

The thesis reviews the history and literature of reliability theory. The implicit assumptions of the basic reliability model are identified and their potential for generalisation investigated. A generalised model of reliability is constructed, in which components and systems can take any values in an ordered discrete or continuous state-space representing various levels of partial operation. For the discrete state-space case, the enumeration of suitable system structure functions is discussed, and related to the problem posed by Dedekind in 1897 on the cardinality of the free distributive lattice. Some numerical enumerations are evaluated, and several recursive bounds are derived. In the special case of the usual dichotomic reliability model, a new upper bound is shown to be superior to the best explicit and non-asymptotic upper bound previously derived. The relationship of structure functions to event networks is also examined. Some specific results for the state probabilities of components with small numbers of states are derived. Discrete and continuous examples of the generalised model of reliability are investigated, and properties of the model are derived. Various forms of independence between components are shown to be equivalent, but this equivalence does not completely generalise to the property of zero-covariance. Alternative forms of series and parallel connections are compared, together with the effects of replacement. Multiple time scales are incorporated into the formulation. The above generalised reliability model is subsequently specialised and extended so as to study the optimal tuning of partially operating components. Simple drift and catastrophic failure mechanisms are considered. Explicit and graphical solutions are derived, together with several bounds. The optimal retuning of such units is also studied and bounds are again obtained, together with some explicit solutions