Computing Limiting Average Availability of a Repairable System through Discretization

Formulas for limiting average availability of a repairable system exist only for some special cases: (1) either the lifetime or the repair time is exponential; or (2) there is one spare unit and one repair facility. We consider a more general setting involving several spare units and several repair facilities; and we allow arbitrary life- and repair time distributions. Under periodic monitoring, which essentially discretizes the time variable, we compute the limiting average availability. The discretization approach closely approximates the existing results in the special cases; and increases the limiting average availability as we include additional spare unit or additional repair facility

A review on maintenance optimization

To this day, continuous developments of technical systems and increasing reliance on equipment have resulted in a growing importance of effective maintenance activities. During the last couple of decades, a substantial amount of research has been carried out on this topic. In this study we review more than two hundred papers on maintenance modeling and optimization that have appeared in the period 2001 to 2018. We begin by describing terms commonly used in the modeling process. Then, in our classification, we first distinguish single-unit and multi-unit systems. Further sub-classification follows, based on the state space of the deterioration process modeled. Other features that we discuss in this review are discrete and continuous condition monitoring, inspection, replacement, repair, and the various types of dependencies that may exist between units within systems. We end with the main developments during the review period and with potential future research directions

A two-phase inspection policy with imperfect testing

This paper presents an inspection policy to detect failures of a single component system that remain hidden otherwise. Inspection reveals whether the unit is in good or failed state. The possibility of non perfect testing is assumed, thus, successive inspections may fail detecting a failure or result in a false alarm. The occurrence of false alarms is reported in optical fire detectors and inspection of printing circuit boards which are on the basis of electronic systems. A two-phase inspection schedule takes into account the changes in component’s aging. The system may undergo different inspection frequencies to detect both early failures or those due to the natural deterioration in the system as time goes by. The examples reveal the advantages of a two-phase inspection when comparing with the unique interval inspection

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

A Multi-Objective Approach to Optimize a Periodic Maintenance Policy

The present paper proposes a multi-objective approach to find out an optimal periodic maintenance policy for a repairable and stochastically deteriorating multi-component system over a finite time horizon. The tackled problem concerns the determination of the system elements to replace at each scheduled and periodical system inspection by ensuring the simultaneous minimization of both the expected total maintenance cost and the expected global system unavailability time. It is assumed that in the case of system elements failure they are instantaneously detected and repaired by means of minimal repair actions in order to rapidly restore the system. A non-linear integer mathematical programming model is developed to solve the treated multi-objective problem whereas the Pareto optimal frontier is described by the Lexicographic Goal Programming and the \u3b5-constraint methods. To explain the whole procedure a case study is solved and the related considerations are given

System Maintenance Using Several Imperfect Repairs Before a Perfect Repair

Allowing several imperfect repairs before a perfect repair can lead to a highly reliable and efficient system by reducing repair time and repair cost. Assuming exponential lifetime and exponential repair time, we determine the optimal probability $p$ of choosing a perfect repair over an imperfect repair after each failure. Based on either the limiting availability or the limiting average repair cost per unit time, we determine the optimal number of imperfect repairs before conducting a perfect repair

A study on group maintenance policies

Master'sMASTER OF ENGINEERIN

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach

Modelling inspection and replacement quality for a protection system

An inspection and replacement policy for a protection system is described by a mathematical model that incorporates multiple aspects of maintenance quality. A three-state component failure model is assumed, with a defective state preceding failure. The quality of maintenance intervention is modelled by supposing that inspections may misclassify defects (false positives and false negatives) and further that an inspection may induce a defect. The quality of replacement is modelled by supposing that a component arises from a heterogeneous population, composed of weak and strong items and with the mixing parameter determining quality. Isolation valves used in water distribution systems motivate the model development, and a case study is considered in this context. We evaluate the impact of these aspects of the quality of maintenance upon cost and production losses. Defect induction is found to be a key determinant of the cost-optimal policy. The proposed model allows us to verify conditions that justify investment in higher quality maintenance, and thus to provide guidance for prioritization of this investment

Study on New Sampling Plans and Optimal Integration with Proactive Maintenance in Production Systems

Sampling plans are statistical process control (SPC) tools used mainly in production processes. They are employed to control processes by monitoring the quality of produced products and alerting for necessary adjustments or maintenance. Sampling is used when an undesirable change (shift) in a process is unobservable and needs time to discover. Basically, the shift occurs when an assignable cause affects the process. Wrong setups, defective raw materials, degraded components are examples of assignable causes. The assignable cause causes a variable (or attribute) quality characteristic to shift from the desired state to an undesired state. The main concern of sampling is to observe a process shift quickly by signaling a true alarm, at which, maintenance is performed to restore the process to its normal operating conditions. While responsive maintenance is performed if a shift is detected, proactive maintenance such as age-replacement is integrated with the design of sampling. A sampling plan is designed economically or economically-statistically. An economical design does not assess the system performance, whereas the economic-statistical design includes constraints on system performance such as the average outgoing quality and the effective production rate. The objective of this dissertation is to study sampling plans by attributes. Two studies are conducted in this dissertation. In the first study, a sampling model is developed for attribute inspection in a multistage system with multiple assignable causes that could propagate downstream. In the second study, an integrated model of sampling and maintenance with maintenance at the time of the false alarm is proposed. Most of the sampling plans are designed based on the occurrence of one assignable cause. Therefore, a sampling plan that allows two assignable causes to occur is developed in the first study. A multistage serial system of two unreliable machines with one assignable cause that could occur on each machine is assumed where the joint occurrence of assignable causes propagates the process\u27s shift to a higher value. As a result, the system state at any time is described by one in-control and three out-of-control states where the evolution from a state to another depends on the competencies between shifts. A stochastic methodology to model all competing scenarios is developed. This methodology forms a base that could be used if the number of machines and/or states increase. In the second study, an integrated model of sampling and scheduled maintenance is proposed. In addition to the two opportunities for maintenance at the true alarm and scheduled maintenance, an additional opportunity for preventive maintenance at the time of a false alarm is suggested. Since a false alarm could occur at any sampling time, preventive maintenance is assumed to increase with time. The effectiveness of the proposed model is compared to the effectiveness of separate models of scheduled maintenance and sampling. Inspired by the conducted studies, different topics of sampling and maintenance are proposed for future research. Two topics are suggested for integrating sampling with selective maintenance. The third topic is an extension of the first study where more than two shifts can occur simultaneously