An Optimal Replacement Problem of A Semi-Markovian Deteriorating System

This paper discusses an optimal replacement problem of a multi-state system when the deterioration of the system state is described by a semi-Markov process. It is assumed that the system has operating costs and replacement costs depending on its states. The problem is to derive a replacement policy which minimizes the expected average cost per unit time over the infinite horizon. Moreover, under some reasonable conditions reflecting the physical and economical meaning of the deterioration, we show that an optimal replacement policy has a monotone structure

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

Semi-Markov and delay time models of maintenance

This thesis is concerned with modelling inspection policies of facilities which Qraduallv deteriorate in time. The context of inspection policies lends itself readily to probabilistic modelling. Indeed, many of the published theoretical models to be found in the literature adopt a Markov approach, where states are usually 'operating', 'operating but fault present', and 'failed'. However, most of these models fail to discuss the 'fit' of the model to data,a nd virtually no exampleso f actual applications or case-studiesa re to be found. hi a series of recent papers dating from 1984, a robust approach to solve these problems has been introduced and developed as the Delay Time Model (DTM). The central concept for this model is the delay time, h, of a fault which is the time lapse from when a fault could first be noticed until the time when its repair can be delayed no longer because of unacceptable consequences. The bottle neck in delay time modelling is how to estimate the delay time distribution parameters. Two methods for estimating these parameters have been developed. namely the subjective method and the objective method. Markov models have the advantage of an extensive body of theory. 'fliere are, however. difficulties of definition, measurement, and calculation when applying Markov models to real-world situations within a maintenance context. Indeed. this problem has motivated the current research which ainis to explore the two modelling methodologies in cases where comparison is valid, and also to gain an insight as to how robust Markov inspection models can be as decision-aids where Markovian properties are not strictly satisfied. It Nvill be seen that a class of inspection problems could be solved by a serni- Markov model using the delay time concept. In this thesis, a typical senii-i%Ia, rkov inspection model based upon the delay time concept is presented for a complex repairable systein that may fail during the course of its service lifetime and the results are compared. Finally, a case study of the senii-Markov inspection model and the delay time model is discussed

Optimisation of Maintenance Policies Based on Right-Censored Failure Data Using a Semi-Markovian Approach

This paper exposes the existing problems for optimal industrial preventive maintenance intervals when decisions are made with right-censored data obtained from a network of sensors or other sources. A methodology based on the use of the z transform and a semi-Markovian approach is presented to solve these problems and obtain a much more consistent mathematical solution. This methodology is applied to a real case study of the maintenance of large marine engines of vessels dedicated to coastal surveillance in Spain to illustrate its usefulness. It is shown that the use of right-censored failure data significantly decreases the value of the optimal preventive interval calculated by the model. In addition, that optimal preventive interval increases as we consider older failure data. In sum, applying the proposed methodology, the maintenance manager can modify the preventive maintenance interval, obtaining a noticeable economic improvement. The results obtained are relevant, regardless of the number of data considered, provided that data are available with a duration of at least 75% of the value of the preventive interval.Proyecto RTI2018-094614-B-I00 (SMASHING), and the “Programa Estatal de I+D+i Orientada a los Retos de la Sociedad

Optimisation of Maintenance Policies Based on Right-Censored Failure Data Using a Semi-Markovian Approach

This paper exposes the existing problems for optimal industrial preventive maintenance intervals when decisions are made with right-censored data obtained from a network of sensors or other sources. A methodology based on the use of the z transform and a semi-Markovian approach is presented to solve these problems and obtain a much more consistent mathematical solution. This methodology is applied to a real case study of the maintenance of large marine engines of vessels dedicated to coastal surveillance in Spain to illustrate its usefulness. It is shown that the use of right-censored failure data significantly decreases the value of the optimal preventive interval calculated by the model. In addition, that optimal preventive interval increases as we consider older failure data. In sum, applying the proposed methodology, the maintenance manager can modify the preventive maintenance interval, obtaining a noticeable economic improvement. The results obtained are relevant, regardless of the number of data considered, provided that data are available with a duration of at least 75% of the value of the preventive interval.Ministerio de Ciencia, Innovación y Universidades (MICINN). España RTI2018-094614-B-I00 (SMASHING

Maintenance optimization for a Markovian deteriorating system with population heterogeneity

We develop a partially observable Markov decision process model to incorporate population heterogeneity when scheduling replacements for a deteriorating system. The single-component system deteriorates over a finite set of condition states according to a Markov chain. The population of spare components that is available for replacements is composed of multiple component types that cannot be distinguished by their exterior appearance but deteriorate according to different transition probability matrices. This situation may arise, for example, because of variations in the production process of components. We provide a set of conditions for which we characterize the structure of the optimal policy that minimizes the total expected discounted operating and replacement cost over an infinite horizon. In a numerical experiment, we benchmark the optimal policy against a heuristic policy that neglects population heterogeneity

DECISION SUPPORT MODEL IN FAILURE-BASED COMPUTERIZED MAINTENANCE MANAGEMENT SYSTEM FOR SMALL AND MEDIUM INDUSTRIES

Maintenance decision support system is crucial to ensure maintainability and reliability of equipments in production lines. This thesis investigates a few decision support models to aid maintenance management activities in small and medium industries. In order to improve the reliability of resources in production lines, this study introduces a conceptual framework to be used in failure-based maintenance. Maintenance strategies are identified using the Decision-Making Grid model, based on two important factors, including the machines’ downtimes and their frequency of failures. The machines are categorized into three downtime criterions and frequency of failures, which are high, medium and low. This research derived a formula based on maintenance cost, to re-position the machines prior to Decision-Making Grid analysis. Subsequently, the formula on clustering analysis in the Decision-Making Grid model is improved to solve multiple-criteria problem. This research work also introduced a formula to estimate contractor’s response and repair time. The estimates are used as input parameters in the Analytical Hierarchy Process model. The decisions were synthesized using models based on the contractors’ technical skills such as experience in maintenance, skill to diagnose machines and ability to take prompt action during troubleshooting activities. Another important criteria considered in the Analytical Hierarchy Process is the business principles of the contractors, which includes the maintenance quality, tools, equipments and enthusiasm in problem-solving. The raw data collected through observation, interviews and surveys in the case studies to understand some risk factors in small and medium food processing industries. The risk factors are analysed with the Ishikawa Fishbone diagram to reveal delay time in machinery maintenance. The experimental studies are conducted using maintenance records in food processing industries. The Decision Making Grid model can detect the top ten worst production machines on the production lines. The Analytical Hierarchy Process model is used to rank the contractors and their best maintenance practice. This research recommends displaying the results on the production’s indicator boards and implements the strategies on the production shop floor. The proposed models can be used by decision makers to identify maintenance strategies and enhance competitiveness among contractors in failure-based maintenance. The models can be programmed as decision support sub-procedures in computerized maintenance management systems