Inspection Policies When Duration of Checkings is Non-Negligible

Inspection policy models deal with stochastically failing systems, in which failure is detected by inspection only. Previous authors assume that the time required for checking is zero, while the current study deals with preparedness models when duration of checking is non-negligible. Costs are introduced for checking, unknown lost time and repairing (or replacing) the failed system. Furthermore, uncertainty probabilities associated with inspections are introduced. Optimal checking policies are calculated for three different objective functions: expected loss per cycle, per time unit and per unit of good time. The models are solved by differentiation and by dynamic programming. Numerical results indicate that the optimal policy for IFR distributions is characterized by decreasing checking time intervals, with a marked difference only between the first and second intervals.     

Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements

This paper proposes two optimization models for the periodic inspection of a system with “hard-type” and “soft-type” components. Given that the failures of hard-type components are self-announcing, the component is instantly repaired or replaced, but the failures of soft-type components can only be detected at inspections. A system can operate with a soft failure, but its performance may be reduced. Although a system may be periodically inspected, a hard failure creates an opportunity for additional inspection (opportunistic inspection) of all soft-type components. Two optimization models are discussed in the paper. In the first, soft-type components undergo both periodic and opportunistic inspections to detect possible failures. In the second, hard-type components undergo periodic inspections and are preventively replaced depending on their condition at inspection. Soft-type and hard-type components are either minimally repaired or replaced when they fail. Minimal repair or replacement depends on the state of a component at failure; this, in turn, depends on its age. The paper formulates objective functions for the two models and derives recursive equations for their required expected values. It develops a simulation algorithm to calculate these expected values for a complex model. Several examples are used to illustrate the models and the calculations. The data used in the examples are adapted from a real case study of a hospital’s maintenance data for a general infusion pump.     

Developments in delay time analysis for modelling plant maintenance

Delay time (DT) analysis is a pragmatic mathematical concept readily embraced by engineers which has been developed as a means to model maintenance decision problems. Attention is focused upon the maintenance engineering decisions of what to do, as opposed to the logistical decisions of how to do it. This paper reviews the cumulative knowledge and experience of delay time modelling. The decision environment within which delay time (DT) models are intended as decision aids is briefly reviewed, and the initial development of simple DT models for a repairable component and a complex plant presented. Variations on the basic model are outlined and discussed including perfect and non-perfect inspection, steady state and non-steady state conditions, and homogeneous and non-homogeneous Poisson arrival rate of defects. Attention is given to the parameter estimation process, and both subjective and objective estimation techniques are outlined. Case sketches present practical experience in using the DT concept to model actual plant, to assess the benefits obtained, and to validate modelling and parameter assessment.     

Availability and maintenance modeling for systems subject to dependent hard and soft failures

This paper develops availability and maintenance models for single‐unit systems subject to dependent hard and soft failures. A hard failure stops the system immediately, whereas a soft failure only reduces the performance capacity of the system. Dependence between these 2 types of failures is reflected in the fact that each soft failure directly increases the hazard rate of the hard failure. On the basis of such interaction, we derive recursive equations for the system reliability and availability functions. To detect both types of failures, inspections are executed periodically. Furthermore, we investigate the optimal inspection policy via the minimization of the expected cost per unit time. The applicability of the developed availability and maintenance models is validated by a case study on an electrical distribution system.     

Delay Time Models of Industrial Inspection Maintenance Problems

The technique of delay time analysis is here extended to problems of industrial plant maintenance. A basic model of inspection maintenance is presented, along with models of some of the variations which have been observed in practice. Numerical examples indicate both the nature and sensitivity of the output from the models.     

考虑非周期检测的视情维修与备件订购联合策略优化

针对单部件系统/关键部件提出视情维修与备件订购联合策略,其中系统退化服从两阶段延迟时间过程且采用非周期检测策略,退化初期以检测间隔T₁检查系统状态,而在第一次识别缺陷状态时,缩短检测周期为T₂、订购备件且进行不完美维修;若系统在随后的退化中被识别处于缺陷状态,执行不完美维修直至超过阈值次数N_max并采取预防性更换,但若在检测周期内发生故障则进行更换。根据系统状态和备件状态分析各种可能更新事件及相应的联合决策,利用更新报酬理论构建最小化单位时间内期望成本的目标函数,优化T₁,T₂, N_max。与对比模型策略相比,算例结果表明所提出的联合策略能有效降低单位时间内的期望成本。     

Condition-Based Inspection Models of Major Civil-Engineering Structures

A method of modelling the task of inspecting major civil-engineering structures is proposed. The objective is to relate measures of both the integrity of the structure and its maintenance cost to the inspection frequency. The option exists within the model to adopt a variety of physical testing techniques. Delay-time analysis is utilized, and the behaviour of the model illustrated with a numerical example. Some possible developments of the model and extension are discussed along with current input requirements.     

Maintenance scheduling of a protection system subject to imperfect inspection and replacement

An inspection and replacement policy for a protection system is described in which the inspection process is subject to error, and false positives (false alarms) and false negatives are possible. We develop two models: one in which a false positive implies renewal of the protection system; the other not. These models are motivated by inspection of a protection system on the production line of a beverage manufacturer. False negatives reduce the efficiency of inspection. Another notion of imperfect maintenance is also modelled: that of poor installation of a component at replacement. These different aspects of maintenance quality interact: false alarms can, in a worst case scenario, lead to the systematic and unnecessary replacement of good components by poor components, thus reducing the availability of the system. The models also allow situations in which maintenance quality differs between alternative maintainers to be investigated.     

O.R. modelling of the deterioration and maintenance of concrete structures

This paper reports on a collaborative venture between operational researchers and civil engineers over 3 years. The main objectives were to collect and publish data on the observed rates of deterioration of particular defect types in a large number of concrete bridges, and to develop predictive mathematical models that relate inspection frequency to maintenance costs. The motivation was in part associated with the prototype modelling paper for inspection practices of major concrete structures, Christer (1988). The paper reports on the analysis of data collected and the estimation of deterioration using the concept of delay time. The two phase delay time model is extended to an extra phase in order to model the process of cracking and spalling in concrete. Maximum likelihood techniques are used to estimate modelling parameters and an appropriate test of fit is carried out. Cost based models are then formulated to predict the cost effects of maintenance and inspection decision options. The cost model is applied first to an element, and then to an aggregate number of component types to produce a cost model for maintenance of a bridge or set of bridges.     

An integrated model for earthquake risk and damage assessment

The primary objective of this paper was to develop an integrated model for earthquake risk and damage assessment. This model consists of three major submodules - the physical damage functions, the economic damage functions, and the institutional aspects related to risk mitigation policies and community preparedness. While the physical damage functions are related to earthquake risk prediction utilizing both probabilistic and deterministic approaches, the economic damage functions refer to the potential vulnerability of various populations at earthquake risk.The feasibility of this model was tested with historical and projected data on earthquake risk and impacted populations for the New Madrid Fault region which includes St. Louis and Memphis Standard Metropolitan Statistical Areas. If the 1811–1812 New Madrid earthquakes would recur between 1980 and 2030, the damage results from the simulations of this model based on the status quo scenario, indicate that the region would experience structural losses in billions of dollars and a death toll of hundreds of persons.     

Optimal maintenance scheduling for a complex manufacturing system subject to deterioration

We address the problem of determining inspection strategy and replacement policy for a deteriorating complex multi-component manufacturing system whose state is partially observable. We develop inspection and replacement scheduling models and other simple maintenance scheduling models via employing an imperfect repair model coupled with a damage process induced by operational conditions. The system state in performance of the imperfectly repaired system is modelled using a proportional intensity model incorporating a damage process and a virtual age process caused by repair. The system is monitored at periodic times and maintenance actions are carried out in response to the observed system state. Decisions to perform imperfect repair and replacement are based on the system state and crossing of a replacement threshold. The model proposed here aims at joint determination of a cost-optimal inspection and replacement policy along with an optimal level of maintenance which result in low maintenance cost and high operational performance and reliability of the system. To demonstrate the use of the model in practical applications a numerical example is provided. Solutions to optimal system parameters are obtained and the response of the model to these parameters is examined. Finally some features of the model are demonstrated. The approach presented provides a framework so that different scenario can be explored.     

Mathematical programming models for piecewise-linear discriminant analysis

Mathematical programming (MP) discriminant analysis models are widely used to generate linear discriminant functions that can be adopted as classification models. Nonlinear classification models may have better classification performance than linear classifiers, but although MP methods can be used to generate nonlinear discriminant functions, functions of specified form must be evaluated separately. Piecewise-linear functions can approximate nonlinear functions, and two new MP methods for generating piecewise-linear discriminant functions are developed in this paper. The first method uses maximization of classification accuracy (MCA) as the objective, while the second uses an approach based on minimization of the sum of deviations (MSD). The use of these new MP models is illustrated in an application to a test problem and the results are compared with those from standard MCA and MSD models.     

Modelling Inspection Policies for Building Maintenance

A method of assessing the potential of an inspection maintenance policy as opposed to an existing breakdown maintenance policy for a building complex is developed. The method is based upon information likely to be available and specific subjective assessments which could be made available. Estimates of the expected number of defects identified at an inspection and the consequential cost saving are presented as functions of the inspection frequency.     

Inspection and maintenance optimization methods

Three methods of the optimal planning of the inspection and maintenance of offshore structures are described. The models are based on respectively: the maximization of the effect of inspections, measured by the total importance value of the errors detected, subject to a given total economical budget; the minimization of the total costs of obtaining respectively: a given importance value of errors detected or given numbers of inspections of various types. Special selections of the importance values of structural elements give problems of the maximization of the reliability of the structural system, or the minimization of the economical consequences of failures, or the minimization of the sum of the costs of inspections and failure-consequences, subject to a given total failure probability of the system.Different failure types of elements and time schedules of inspections can be included in the model.An extension of the incremental method of Fox is applied, and an evaluation measure is given for the calculation of bounds of the optimal objective value, or given numbers of inspections are planned by application of continuous linear programming with integral solutions.     

两层多人多目标决策模型及其凸性

本文提出了四种一般性两层多人多目标决策模型及其最优解概念，它们适应于下层以不同已知信息提供给上层并涉及多个决策者不同偏好的两层多目标决策问题，研究了与这些模型相关的几种集值函数（包括下层有效前沿面，下层目标空间构成的集值函数和上层的两种复合目标集值函数）在各种意义下的凸性。     

An integrated systems approach to process control and maintenance

Organizational leaders increasingly recognize process management as an essential element in organizational performance. Two key tools for process management––Statistical Process Control and Maintenance Management––can create profound economic benefits, particularly when they are coordinated. This paper demonstrates the value of integrating Statistical Process Control and maintenance by jointly optimizing their policies to minimize the total costs associated with quality, maintenance, and inspection. While maintenance is often scheduled periodically, this analysis encourages “adaptive” maintenance where the maintenance schedule accelerates when the process becomes unstable. This paper presents a number of models to demonstrate the economic behavior and value of coordinating process control and maintenance. Finally, a sensitivity analysis is conducted to develop insights into the economic and process variables that influence the integration efforts.     

The impact of inspection errors,imperfect maintenance and minimal repairs on an imperfect production system

This paper develops an integrated model of production lot-sizing, maintenance and quality for considering the possibilities of inspection errors, preventive maintenance (PM) errors and minimal repairs for an imperfect production system with increasing hazard rates. In this study, a PM activity is imperfect in that a production system cannot be recovered as good as new and might cause the production system to shift to the out-of-control state with a certain probability. Numerical analyses are used to simulate the effect of changes in various parameters on the optimal solution for which the time that the process remains in the in-control state is assumed to follow a Weibull distribution. In addition, we investigate the effects of inspection errors and PM errors on the minimum total cost of the optimal inspection interval, inspection frequency and production quantity.     

On economically based quality control decisions

A new approach to the problem of quality control is investigated. It is based on the theories and models developed for optimal maintenance policies for equipment subject to stochastic failure. Four alternative sampling/inspection procedures are examined. They are easy to implement, do not require the process operator to compute his own operating decisions, and are capable of finding optimal intervals between successive samplings/inspections. Both fixed and variable costs are included in the models. Relatively efficient algorithms have been developed for finding the optimal quality control procedures; this is due, partially, to the simple form of the objective function.     

Accelerating the DC algorithm for smooth functions

We introduce two new algorithms to minimise smooth difference of convex (DC) functions that accelerate the convergence of the classical DC algorithm (DCA). We prove that the point computed by DCA can be used to define a descent direction for the objective function evaluated at this point. Our algorithms are based on a combination of DCA together with a line search step that uses this descent direction. Convergence of the algorithms is proved and the rate of convergence is analysed under the ?ojasiewicz property of the objective function. We apply our algorithms to a class of smooth DC programs arising in the study of biochemical reaction networks, where the objective function is real analytic and thus satisfies the ?ojasiewicz property. Numerical tests on various biochemical models clearly show that our algorithms outperform DCA, being on average more than four times faster in both computational time and the number of iterations. Numerical experiments show that the algorithms are globally convergent to a non-equilibrium steady state of various biochemical networks, with only chemically consistent restrictions on the network topology.     

A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multiple objectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p − 1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known ε-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved.