A joint optimal policy of inspection and age based replacement based on a three-stage failure process

Preventive maintenance (PM) and condition-based maintenance (CBM) are two dominant maintenance policies in industrial applications. Inspection activities are the foundation of PM and CBM policies as to provide the operating information of system through processing the collected vibration data. Age based replacement is one of the most used preventive maintenance policy aiming at avoiding unplanned downtime and higher failure loss. This paper proposes a joint optimal policy of inspection and age based replacement based on a three-stage failure process for a single component system. The three-stage failure process, which is closer to reality, divides the failure process of system into three stages: namely normal, minor defective and severe defective. When the severe defective stage is identified, maintenance action is carried out immediately. The system is replaced once it reaches certain age. However, two potential actions are considered and analyzed in this paper when the minor defective stage is identified: halving the subsequent inspection interval or replacing the item immediately. As inspection may not be perfect because of the complexity of plant items, both perfect and imperfect inspection cases are considered. Finally, a case study is presented to demonstrate the efficiency of the proposed models

Inspection and replacement models for reliability and maintenance: filling in gaps

A thesis submitted in fulfillment of the requirements for the Degree of Doctor of Philosophy, School of Statistics and Actuarial Science, Faculty of Science University of Witwatersrand, Johannesburg. February 2017.The work done in this thesis on finite planning horizon inspection models has demonstrated that with the advent of powerful computers these days it is possible to easily find an optimal inspection schedule when the lifetime distribution is known. For the case of system time to failure following a uniform distribution, a result for the maximum number of inspections for the finite planning models has been derived. If the time to failure follows an exponential distribution, it has been noted that periodically carrying out inspections may not result in maximization of expected profit. For the Weibull distributions family (of which the exponential distribution is a special case), evenly spreading the inspections over a given finite planning horizon may not lead to any serious prejudice in profit. The case of inspection models where inspections are of non-negligible duration has also been explored. The conditions necessary for inspections that are evenly spread over the entire planning horizon to be near-optimal when system time to failure either follows a uniform distribution or exponential distribution have been explored. Finite and infinite planning horizon models where inspections are imperfect have been researched on. Interesting observations on the impact of Type I and Type II errors in inspection have been made. These observations are listed on page 174. A clear and easy to implement road map on how to get an optimal inspection permutation in problems first discussed by Zuckerman (1989) and later reviewed by Qiu (1991) for both the undiscounted and discounted cases has been given. The only challenge envisaged when a system has a large number of components is that of computer memory requirements - which nowadays is fast being overcome. In particular, it has been clearly demonstrated that the impact of repair times and per unit of time repair costs on the optimal inspection permutation cannot be ignored. The ideas and procedures of determining optimal inspection permutations which have been developed in this thesis will no doubt lead to huge cost savings especially for systems where the cost of inspecting components is huge.XL201

Condition-based maintenance policy for systems with a non-homogeneous degradation process

This paper investigates a condition-based maintenance policy for systems subject to a non-homogeneous degradation process. A nonhomogeneous degradation process occurs as a result of deterioration nature and the environmental effect. In the first step, it develops two maintenance models, which consider the constant inspection interval and non-periodic inspection interval. The paper then optimizes a maintenance policy with monotone preventive replacement thresholds. The optimal maintenance decision is shown as a control-limit policy, where the optimal preventive replacement threshold is monotonically decreasing with system age. An illustrative example is presented to show the effectiveness of the proposed maintenance models. The result indicates that preventive replacement can significantly improve the effectiveness of the maintenance policy and sustain system operation

Delay-time modelling of a critical system subject to random inspections

We model the inspection-maintenance of a critical system in which the execution of inspections is random. The models we develop are interesting because they mimic realities in which production is prioritised over maintenance, so that inspections might be impeded or they might be opportunistic. Random maintenance has been modelled by others but there is little in the literature that relates to inspection of a critical system. We suppose that the critical system can be good, defective or failed, and that failure impacts on production, so that a failure is immediately revealed, but a defect does not. A defect, if revealed at inspection, is a trigger for replacement. We compare the cost and reliability of random inspections with scheduled periodic inspections and discuss the implications for practice. Our results indicate that inspections that are performed opportunistically rather than scheduled periodically may offer an economic advantage provided opportunities are sufficiently frequent and convenient. A hybrid inspection and replacement policy, with inspections subject to impediments, is robust to departure from its inspection schedule. Keywords: Maintenance; reliability; random inspection; production; qualit

Determining Optimal Machine Replacement Events with Periodic Inspection Intervals

This research will examine the optimal maintenance and replacement policies for a generic machine with periodic inspection intervals. The considered reliability models consist of a single machine that can fail during operation or else may be found to be inoperative during regularly-scheduled maintenance inspections. A distinction will be made between spontaneously-occurring failures during operation and those that are discovered during inspections. Since the elapsed time between inspections is constant, the resulting stochastic reliability process becomes non-Markovian, and thus a Semi-Markov Decision Process (SMDP) framework must be employed in order to determine the cost-optimal stationary policy consisting of repair and replace decisions and inspection intervals. Using the methodology developed here, a system controller will be able to readily develop an inspection-based strategy to optimize the overall costs of maintaining systems with a variety of failure characteristics over a finite time horizo

Studies on Optimal Maintenance Policies for Extended Inspection Models

The thesis studies optimal inspection and maintenance policies for high reliable systems. Some modified and extended inspection models from the viewpoint of actual models are considered. Using the reliability theory, such models are mathematically analyzed and useful inspection schedules are determined. Reasonable costs of inspections and failures for each model are introduced, and the expected costs until the detection of failures are obtained. Optimal inspection policies which minimize these expccted costs are derived analytically and numerically. In particular, these results would be practically applied to determine inspection schedules for systems such as digital control devices. Further, optimal maintenance and inspection policies for a finite interval are similarly considered and are analytically discussed. This thesis is divided into 7 chapters. An initial chapter gives the introduction which is constructed by the review of literatures and the organization of this thesis. Chapters 2 to 4 consider the modified inspection models and discuss these optimal policies: Chapter 2 studies optimal inspection policies for a two-unit system. First, the system operates as a two-unit system, and when one unit fails, it operates as a single-unit system. The system is checked continuously or periodically while it operates as a two-unit system, and is checked periodically by self-diagnosis after a failed unit is detached from the system. Chapter 3 studies optimal inspection policies for a system with self-testing which can detect some failures without performing external inspection. However, the failure might not be detected rapidly by self-testing, and so, it would be necessary to check the system periodically by inspection. This chapter considers the model where a failure is detected by either self-testing or periodic inspection. Then, optimal inspection policies which minimize the expected costs are analytically derived. Chapter 4 studies optimal maintenance and inspection policies for a finite interval. Optimal policies which minimize the expected costs of periodic replacement with minimal repair, block replacement, simple replacement and inspection policy are derived for a finite interval. Chapter 5 studies optimal inspection policies for a system with two types of inspection: There might exist some failures which can not be detected by type-1 inspection and can be detected only by type-2 inspection, however, type-1 inspection has a lower cost than that of type-2 inspection. An optimal number to perform type-1 inspection until the next type-2 inspection is analytically derived. Chapter 6 considers an extended model in Chapter 5, where the system is replaced at the specified N-th type-2 inspection. The expected cost per unit of time is analytically obtained, and an optimal number to perform type-1 inspection until the next type-2 inspection is numerically derived. Finally, in Chapter 7, the results are summarized

Maintenance of systems with critical components. Prevention of early failures and wear-out

We present a model for inspection and maintenance of a system under two types of failures. Early failures (type I), affecting only a proportion p of systems, are due to a weak critical component detected by inspection. Type II failures are the result of the system ageing and preventive maintenance is used against them. The two novelties of this model are: (1) the use of a defective distribution to model strong components free of defects and thus immune to early failures. (2) the removal of the weak critical part once it is detected with no other type of rejuvenation of the system which constitutes an alternative to the minimal repair. We study the conditions under which this model outperforms, from a cost viewpoint, other two classical age-replacement models. The analysis reveals that inspection is advantageous if the system can function with the critical component in the defective state for a long enough time. The proportion of weak units and the quality of inspections also determine the optimum policy. The results about the range of application of the model are useful for decision making in actual maintenance. A case study concerning the timing belt of a four-stroke engine illustrates the model

Network-Level Reliability-Based Bridge Inspection, Maintenance and Replacement Optimization Model

This paper presents a reliability-based optimization model of inspection, maintenance and replacement for a system of several highway bridges. The objective in the formulation is to minimize the total expected social cost, including the expected cost of failure. The frequency of inspections is included as a decision variable. The probability of failure is explicitly taken into account in the constraints. A bottom-up approach is used, which allows for bridge-specific details to be taken into account. Most existing system level models assume that component deterioration is memoryless; however, this assumption is relaxed in this paper, and history-dependent deterioration models are used. The formulation is flexible enough to accommodate different types of facilities, deterioration processes and failure modes. A parametric study is conducted to demonstrate the model’s response to different assumptions on the deterioration rates, maintenance costs and efficiency

Maintenance Models for Systems subject to Measurable Deterioration

Complex engineering systems such as bridges, roads, flood defence structures, and power pylons play an important role in our society. Unfortunately such systems are subject to deterioration, meaning that in course of time their condition falls from higher to lower, and possibly even to unacceptable, levels. Maintenance actions such as inspection, local repair and replacement should be done to retain such systems in or restore them to acceptable operating conditions. After all, the economic consequences of malfunctioning infrastructure systems can be huge. In the life-cycle management of engineering systems, the decisions regarding the timing and the type of maintenance depend on the temporal uncertainty associated with the deterioration. Hence it is of importance to model this uncertainty. In the literature, deterioration models based on Brownian motion and gamma process have had much attention, but a thorough comparison of these models lacks. In this thesis both models are compared on several aspects, both in a theoretical as well as in an empirical setting. Moreover, they are compared with physical process models, which can capture structural insights into the underlying process. For the latter a new framework is developed to draw inference. Next, models for imperfect maintenance are investigated. Finally, a review is given for systems consisting of multiple components

Maintenance Models for Systems subject to Measurable Deterioration

Complex engineering systems such as bridges, roads, flood defence structures, and power pylons play an important role in our society. Unfortunately such systems are subject to deterioration, meaning that in course of time their condition falls from higher to lower, and possibly even to unacceptable, levels. Maintenance actions such as inspection, local repair and replacement should be done to retain such systems in or restore them to acceptable operating conditions. After all, the economic consequences of malfunctioning infrastructure systems can be huge. In the life-cycle management of engineering systems, the decisions regarding the timing and the type of maintenance depend on the temporal uncertainty associated with the deterioration. Hence it is of importance to model this uncertainty. In the literature, deterioration models based on Brownian motion and gamma process have had much attention, but a thorough comparison of these models lacks. In this thesis both models are compared on several aspects, both in a theoretical as well as in an empirical setting. Moreover, they are compared with physical process models, which can capture structural insights into the underlying process. For the latter a new framework is developed to draw inference. Next, models for imperfect maintenance are investigated. Finally, a review is given for systems consisting of multiple components