Age replacement policy in the case of no data: the effect of Weibull parameter estimation

Age replacement is a common maintenance policy when wear-out failures occur, and it is characterised by periodic replacement of components. Data on time to failure (TTF), often modelled with the Weibull function, are necessary for estimating optimal replacement intervals to minimise the total maintenance costs. In many cases, such as new components, new machines or new installations, no TTF data are available, so the Weibull parameters and optimal replacement interval cannot be estimated. To overcome this problem, these parameters can be assessed from the experience of the maintenance engineers and technicians. The aim of this study is investigating the relationship between the error in parameter estimation and additional maintenance costs related to this error. Analysis of variance (ANOVA) and multifactorial analysis are carried out for investigating the influence of these estimations on the final costs. Economic decision maps are introduced for supporting maintenance engineering in defining the maintenance policy with minimal additional cost in the case of no data being available. The analysis shows that, when no data are available, the application of the age replacement policy can result in a global saving of more than 50% compared with corrective maintenance.     

Optimal replacement policy and inspection interval for condition-based maintenance

In condition-based maintenance (CBM), replacement policy is often defined as a rule for replacement or leaving an item (or a system) in operation until the next inspection, depending on monitoring results. The criterion for determining the optimal threshold for replacement, also known as optimal control limit, is to minimise the average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. On the one hand, higher frequency of inspections provides more information about the condition of the system and, thus, maintenance actions are performed more effectively, namely, unnecessary preventive replacements are avoided and the number of replacements due to failure is reduced. Consequently, the cost associated to failure and preventive replacements are decreased. On the other hand, in many real cases, inspections require labour, specific test devices, and sometimes suspension of the operations and, thus, as the number of inspections increase, the inspection cost also increases. In this paper, preventive and failure replacement costs as well as inspection cost are taken into account to determine the optimal control limit and the optimal inspection interval simultaneously. The proposed approach is illustrated through a numerical example.     

Optimal age replacement scheduling for a random work system with random lead time

System maintenance and spare parts are two closely related logistics activities since maintenance generates the demand for spare parts. Most studies on integrated models of preventive replacement and inventory of spare parts have focused on age replacement scheduling, while random replacement policy, which is sensible and necessary in practice, is rarely discussed and applied. The purpose of this paper is to present a generalised age replacement policy for a system which works at random time and considers random lead time for replacement delivery. To model an imperfect maintenance action, we consider that the system undergoes minimal repairs at minor failures and corrective replacements at catastrophic failures. Before catastrophic failures, the system is replaced preventively at age T or at the completion of a working time, whichever occurs first. The main objective is to determine an optimal schedule of age replacement that minimises the mean cost rate function of the system in a finite time horizon. The existence and uniqueness of optimal replacement policy are derived analytically and computed numerically. It can be seen that the proposed model is a generalisation of the previous works in maintenance theory.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

On preventive maintenance policy of a critical reliability level for system subject to degradation

Conventional preventive maintenance (PM) policies generally hold same time interval for PM actions and are often applied with known failure modes. The same time interval will give unavoidably decreasing reliabilities at the PM actions for degradation system with imperfect PM effect and the known failure modes may be inaccurate in practice. Therefore, field managers would prefer policy with an acceptable reliability level to keep system often at a good state.A PM policy with the critical reliability level is presented to address the preference of field managers. Through assuming that system after a PM action starts a new failure process, a parameter so-called degradation ratio is introduced to represent the imperfect effect. The policy holds a law that there is same number of failures in the time intervals of various PM cycles, and same degradation ratio for the system reliability or benefit parameters such as the optimal time intervals and the hazard rates between the neighboring PM cycles. This law is valid to any of the failure modes that could be appropriately referred as a ‘general isodegrading model’, and the degradation ratio as a ‘general isodegrading ratio’. In addition, life cycle availability and cost functions are derived for system with the policy. An analysis of the field data of a loading and unloading machine indicates that the reliability, availability and cost in life cycle might be well modeled by the present theory and approach.     

Short communication optimal replacement scheduling in multi‐state series–parallel systems

The paper generalizes a replacement schedule optimization problem to multi‐state systems, where the system and its components have a range of performance levels—from perfect functioning to complete failure. The multi‐state system reliability is defined as the ability to satisfy a demand which is represented as a required system performance level. The reliability of system elements is characterized by their lifetime distributions with hazard rates increasing in time and is specified as expected number of failures during different time intervals. The optimal number of element replacements during the study period is defined as that which provides the desired level of the system reliability by minimum sum of maintenance cost and cost of unsupplied demand caused by failures. To evaluate multi‐state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Examples of the optimal replacement schedule determination are demonstrated. Copyright © 2000 John Wiley & Sons, Ltd.     

Application of RCM to a medium scale industry

The factors which are assuming considerable importance in cost effective decision making of operation of any industrial enterprise are in the order of significance liability, safety and environmental conditions. Hence, preventive maintenance (PM) optimisation is providing wide opportunities and challenges to everyone involved in all aspects of operation of industrial enterprise. Reliability centred maintenance (RCM) methodology offers the best available strategy for PM optimisation. It incorporates a new understanding of the ways in which equipment fails.In this paper, the concept of RCM has been applied to steel melting shop of a medium scale steel industry. By systematically applying the RCM methodology, failures, failure causes and effects on the system are analysed. To preserve the system function, PM categories are suggested for various failure modes in the components such as (1) time directed (2) condition directed (3) failure finding (4) run to failure. Features of predictive maintenance of a medium scale steel industry are deduced through this paper in a rather generalised form.     

Condition based maintenance in the context of opportunistic maintenance

Condition based maintenance (CBM) uses the operating condition of a component to predict a failure event. Compared to age based replacement (ABR), CBM usually results in higher availability and lower maintenance costs, since it tries to prevent unplanned downtime and avoid unnecessary preventive maintenance activities for a component. However, the superiority of CBM remains unclear in multi‐component systems, in which opportunistic maintenance strategies can be applied. Opportunistic maintenance aims to group maintenance activities of two or more components in order to reduce maintenance costs. In a serial system, this may also result in less downtime of the production line. The aim of this paper is to examine the impact of opportunistic maintenance on the effectiveness of CBM. We simulate a small system consisting of three components in series and vary the number of components under a CBM policy, the length of the opportunistic maintenance zone, the cost benefits of grouping maintenance activities, and the chance of a failure occurrence within a preventive maintenance (PM) interval. The results show that within the current experimental settings, CBM remains cost effective in the multi‐component serial system, but is less effective than ABR in grouping maintenance activities. When the chance of failure is small and the length of the opportunistic maintenance zone is large, ABR may even be a better option if line productivity is important.     

Optimal burn-in strategy for two-dimensional warranted products considering preventive maintenance

Burn-in and preventive maintenance (PM) are effective approaches to reduce the number of warranty claims and warranty cost during post-sale support. With harsher burn-in settings, early product defects can be removed, but at the same time product degradation is accelerated and more wear-out failures may be introduced. PM actions within warranty alleviate these negative effects. This paper proposes an optimal burn-in strategy for repairable products sold with a two-dimensional base warranty (BW) and an optional extended warranty (EW). Both performance-based and cost-based models incorporating PMs are developed to obtain optimal burn-in settings, including the burn-in duration and the burn-in usage rate, so as to minimise the expected number of warranty claims and total cost respectively. The impacts of different accelerated coefficients and PM degrees on the optimal burn-in strategy are analysed. In view of the performance and cost structures, we conduct numerical examples to illustrate the applicability of the proposed models. Practical implications from a sensitivity analysis for key parameters are also elaborated.     

Optimal age-based inspection scheme for condition-based maintenance using A* search algorithm

In condition-based maintenance (CBM) with periodic inspection, the system is preventively replaced if failure risk, which is calculated based on the information obtained from inspection, exceeds a pre-determined threshold. The determination of optimal replacement threshold is often based on the minimisation of average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. It is often assumed that inspections are performed at equal time intervals with no cost. However, in practice, inspections require labour, specific test devices, and sometimes suspension of operations and, thus, it is reasonable to inspect less frequently during the time the system is in its early age and/or in a healthier state and to perform inspections more frequently as time passes and/or as the system degrades. In other words, an age-based inspection scheme.

This paper proposes a novel two-phase approach for the determination of an optimal replacement threshold and an optimal age-based inspection scheme for CBM such that the total long-run average costs of replacements and inspections are minimised. First, it takes into account failure and preventive replacement costs to determine the optimal replacement threshold assuming that inspections are performed at equal time intervals with no cost. This assumption is, subsequently, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure based on A* search algorithm to obtain the optimal age-based inspection scheme. The proposed approach is illustrated through a numerical example.     

Preventive maintenance and replacement policies for deteriorating production systems subject to imperfect repairs

This paper presents a special case of integration of the preventive maintenance into the repair/replacement policy of a failure-prone system. The machine of the considered system exhibits increasing failure intensity and increasing repair times. To reduce the failure rate and subsequent repair times following a failure, there is an incentive to perform preventive maintenance on the machine before failure. When a failure occurs, the machine can be repaired or replaced by a new one. Thus the machine's mode at any time can be classified as either operating, in repair, in replacement or in preventive maintenance. The decision variables of the system are the repair/replacement switching age or number of failures at the time of the machine's failure and the preventive maintenance rate. The problem of determining the repair/replacement and preventive maintenance policies is formulated as a semi-Markov decision process and numerical methods are given in order to compute optimal policies which minimise the average cost incurred by preventive maintenance, repair and replacement over an infinite planning horizon. As expected, the decisions to repair or to replace the machine upon a failure are modified by performing preventive maintenance. A numerical example is given and a sensitivity analysis is performed to illustrate the proposed approach and to show the impact of various parameters on the control policies thus obtained.     

Optimal inspection policies with predictive and preventive maintenance

A model is proposed to study the inspection and maintenance policy of systems whose failures can be detected only by periodic tests or inspections. Using predictive techniques, the time of the system failure can be predicted for some failure modes. If the system is found failed in an inspection, a corrective maintenance action is carried out. If the system is in a good condition but the predictive test diagnoses a failure in the period until the next inspection, then the system is replaced. The cost rate function is obtained for general distribution function of the signal time of a future failure and for one specific distribution function recently proposed. An algorithm is presented to find the optimal time between inspections and predictive tests and the optimal system replacement times for an age replacement policy. Numerical experiments illustrate the model.     

Availability and cost functions for periodically inspected preventively maintained units

Unavailability and cost rate functions are developed for components whose failures can occur randomly but they are detected only by periodic testing or inspections. If a failure occurs between consecutive inspections, the unit remains failed until the next inspection. Components are renewed by preventive maintenance periodically, or by repair or replacement after a failure, whichever occurs first (age-replacement). The model takes into account finite repair and maintenance durations as well as costs due to testing, repair, maintenance and lost production or accidents. For normally operating units the time-related penalty is loss of production. For standby safety equipment it is the expected cost of an accident that can happen when the component is down due to a dormant failure, repair or maintenance. The objective of maintenance optimization is to minimize the total cost rate by proper selection of two intervals, one for inspections and one for replacements. General conditions and techniques are developed for solving optimal test and maintenance intervals, with and without constraints on the production loss or accident rate. Insights are gained into how the optimal intervals depend on various cost parameters and reliability characteristics.     

Multi-phase preventive maintenance policy for leased equipment

This paper proposes a multi-phase preventive maintenance (PM) policy for leased equipment by combining the advantages of both periodic PM and sequential PM. The lease period of the equipment is divided into multiple PM phases. The PM activities within each phase are performed periodically with the convenience of implementation, while the frequency of PM for each phase is different and it gives a gradual increase because of the imperfect effect of PM. A multi-phase PM model is built up based on the age reduction method for imperfect PM with the penalty for equipment failures and overtime of repair involved. The optimal PM intervals for every PM phases are achieved by minimising the cumulative maintenance cost throughout the lease period from the perspective of the lessor. Numerical example shows that the cumulative maintenance cost under the proposed multi-phase PM policy is lower than that under periodic PM policy.     

On reliability criteria and the implied cost of failure for a maintained component

This paper considers age-based replacement and block replacement when reliability is also a decision criterion. We describe how specification of the operational reliability of component function determines the replacement policy, and that setting a value for the cost of failure and specifying an operational reliability requirement are equivalent. This duality then implies a simple method for checking the consistency of the cost of failure and operational reliability measures when they are set system operators and maintainers. A simple expression for the median time between operational failures for a socket subject to age-based replacement is also obtained. These ideas are considered briefly in the context of block replacement. Data from an actual case relating to the maintenance and replacement of train traction motors is used for illustration.     

Condition-based inspection scheme for condition-based maintenance

In condition-based maintenance (CBM) with periodic inspection, the item is preventively replaced if failure risk, which is calculated based on the information obtained from inspection, exceeds a pre-determined threshold. The determination of optimal replacement threshold is often based on minimisation of long-run average maintenance costs per unit time due to preventive and failure replacements. It is assumed that inspections are performed at equal time intervals and that the corresponding cost is negligible. However, in many practical situations where CBM is implemented, e.g. manufacturing processes, inspections require labours, specific test devices, and sometimes suspension of operations. Thus, when inspection cost is considerable, it is reasonable to inspect less frequently during the time the item is in healthier states, and, more frequently as time passes and/or the item degrades, namely, a condition-based inspection scheme. This paper proposes a novel two-phase approach for determination of replacement threshold and a condition-based inspection scheme for CBM. First, it takes into account failure and preventive replacement costs to determine the optimal replacement threshold assuming that inspections are performed at equal time intervals with no cost. This assumption is, then, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure to obtain a cost-effective condition-based inspection scheme. The proposed approach can be utilised in many CBM applications. For the sake of simplicity of presentation, the approach is illustrated through a simplified case study already reported by some researchers referenced in the paper.     

An economically designed, integrated quality and maintenance model using an adaptive Shewhart chart

This paper proposes a model for the economic design of a variable-parameter (Vp) Shewhart control chart used to monitor the mean in a process, where, apart from quality shifts, failures may also occur. Quality shifts result in poorer quality outcome, higher operational cost and higher failure rate. Thus, removal of such quality shifts, besides improving the quality of the outcome and reducing the quality cost, is also a preventive maintenance (PM) action since it reduces the probability of a failure and improves the equipment reliability. The proposed model allows the determination of the scheme parameters that minimize the total expected quality and maintenance cost of the procedure. The monitoring mechanism of the process employs an adaptive Vp-Shewhart control chart. To evaluate the effectiveness of the proposed model, its optimal expected cost is compared against the optimum cost of a fixed-parameter (Fp) chart.     

Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts

Offering extended warranty (EW) contracts for products such as automobiles is a good source of revenue for manufactures, insurers and third party companies. However, difficulties in the modeling of product’s failure process and assessing corrective and preventive maintenance actions’ effects on the reliability of product enforce the service providers to propose limited EW contracts with simple “minimal repair at failures” servicing strategy. In this paper for a product sold with a two-dimensional warranty, we model the failure process of product, the effect of imperfect preventive maintenance (PM) and corresponding servicing cost in terms of product’s age and usage. Then, we propose a mathematical optimization model to derive optimal number and degrees of preventive repairs to minimize the EW provider’s servicing cost. We also provide some guidelines to help the EW provider to design flexible EW contracts and determine their corresponding optimal maintenance strategies. To reproduce an illustrative numerical example, we use the failure history of a commercial vehicle produced in a plant in Iran. The provided results reveal that considering proper preventive maintenance strategy during the EW period may effectively reduces the cost of EW servicing.     

A study of availability-centered preventive maintenance for multi-component systems

This paper studies preventive maintenance (PM) in simultaneously considering three actions, mechanical service, repair and replacement for a multi-components system based on availability. Mechanical service denotes the activities including lubricating, cleaning, checking and adjusting, etc. which is set to alleviate strength degradation. Repair is defined on that not only slow down the degraded velocity but also restore the degraded strength partly. Replacement is settled to recover a component to its original condition. According to the definitions, the degradation of components is analyzed from its failure mechanisms and the improvements of various actions to it in reliability were measured by using two improved factors. Following the proposed model of reliability, the mean-up and mean-down times of each component are also investigated and the replacement intervals of components are determined based on availability maximization. Here, the minimum one among the intervals is chosen as the PM interval of system for programming the periodical PM policy. The selection of action for the components on every PM stage is decided by maximizing system benefit in maintenance. Repeatedly, the scheduling is progressed step by step and is terminated until the system extended life reaching to its expected life. The complete schedule provides the information, the actions adopted for the components, the availability and the total cost of system on each stage. Validly, a multi-components system is used as an example to describe the proposed algorithm.     

An inspection model for a multi‐component system subject to 2 types of failures

Group maintenance is common and of significant importance for complex systems in industrial applications. This paper proposes a novel inspection and replacement model for a multi‐component system whose components are all subject to 2 typical failure modes, ie, catastrophic failure and minor failure. A catastrophic failure stops the system immediately, whereas a minor failure is not fatal and could only be identified by periodic inspection. At either a catastrophic or a minor failure, replacement is immediate. The maintenance cost model could be constructed through calculating the distribution of the “forward time”, which denotes the time elapse to a catastrophic failure since the previous inspection. The objective of this paper is to minimize the expected cost per unit time of the system via the optimization of the inspection interval. A case study on offshore wind turbine blades is presented to illustrate the maintenance model.