Random Repair Times Research Articles

Production planning in maintenance facilities under uncertain repair time

Production planning in maintenance facilities that rely on the availability of certified operators is a challenging task. This is primarily attributed to the need for the integration of workforce training with the operations schedule, in addition to the uncertain repair time of some components. We confine our attention to the repair and overhaul of advanced technological devices that are composed of several components. In this context, this study proposes a novel approach to embedding uncertain repair times of faulty components and develops a multi-stage stochastic programming model for integrated production and workforce planning in such facilities under independent random repair time. Our numerical experiments conducted on a range of problem instances expose the significant value of incorporating repair time uncertainty in this problem.

Markovchart: an R package for cost-optimal patient monitoring and treatment using control charts

Control charts originate from industrial statistics, but are constantly seeing new areas of application, for example in health care (Thor et al. in BMJ Qual Saf 16(5):387–399, 2007. https://doi.org/10.1136/qshc.2006.022194; Suman and Prajapati in Int J Metrol Qual Eng, 2018. https://doi.org/10.1051/ijmqe/2018003). This paper is about the Markovchart package, an R implementation of generalised Markov chain-based control charts with health care applications in mind and with a focus on cost-effectiveness. The methods are based on Zempléni et al. (Appl Stoch Model Bus Ind 20(3):185–200, 2004. https://doi.org/10.1002/asmb.521), Dobi and Zempléni (Qual Reliab Eng Int 35(5):1379–1395, 2019a. https://doi.org/10.1002/qre.2518, Ann Univ Sci Budapestinensis Rolando Eötvös Nomin Sect Comput 49:129–146, 2019b). The implemented ideas in the package were motivated by problems encountered by health care professionals and biostatisticians when assessing the effects and costs of different monitoring schemes and therapeutic regimens. However, the implemented generalisations may be useful in other (e.g., engineering) applications too, as they mainly revolve around the loosening of assumptions seen in traditional control chart theory. The Markovchart package is able to model processes with random shift sizes (i.e., the degradation of the patient’s health), random repair (i.e., treatment) and random time between samplings (i.e., visits) as well. The article highlights the flexibility of the methods through the modelling of different disease progression and treatment scenarios and also through an application on real-world data of diabetic patients.

Modeling a sequentially inspected system prone to degradation and shocks

PurposeIn certain environments, the system may not fail completely, but undergoes degradation, and the system productivity might decrease. Meanwhile, at the same time, the system may be vulnerable to shocks. A single-unit system prone to degradation and shocks is proposed in this study, and emphasis is placed upon determining its availability and cost rate.Design/methodology/approachThe considered single-unit system is expected to have three states, namely, normal, degraded and failed. As the system enters the degraded state, it is said to be partially failed. The degraded state incurs higher degradation than the normal state and is more prone to shocks. Inspections are used to determine the state and failure type of the system. Inspections are predetermined to be carried out sequentially at time where 0 < a ≤ 1, until the detection of degradation/failure. Perfect repairs are conducted instantly on spotting the partial/complete failure. Two cases have been considered of repair taking constant times and random times.FindingsExplicit results on the reliability, availability (both point and limiting availability) and long-run average cost rate (LRACR) of a sequentially inspected single-unit system prone to degradation and shocks under constant and random repair times are given. Numerical example of an oil pipeline system is taken to clarify the acquired results.Originality/valueA sequentially inspected single-unit system prone to degradation and shock is studied unlike done previously.

Minimal repair models with non-negligible repair time

In existing minimal repair models, it is usually supposed that the repair time of systems is negligible, and thus the occurrences of breakdowns obey non-homogeneous Poisson Process within a replacement interval. However, for the case that the mean working time of a system is not far longer than its mean repair time, ignoring repair time may lead to a large error in calculating the system long-run average cost rate. In this paper, taking random repair time into account, we generalize several calendar time-based minimal repair policies, including periodic replacement policy with minimal repair, reference time policy, and bivariate T−N maintenance policy. By using probability decomposition technique and indicator function method, the system long-run average cost rate under each minimal repair policy is gained explicitly. Various special cases are discussed. An application of the periodic replacement policy with minimal repair is presented in warranty field. Finally, a comprehensive sensitivity analysis is conducted to investigate the relative error on the long-run average cost rate caused by ignoring repair time, and to compare calendar time-based minimal repair policies with age-based minimal repair policies in terms of the long-run average cost rate.

An imperfect age-based and condition-based opportunistic maintenance model for a two-unit series system

Maintenance strategies have been studied extensively and applied successfully to reduce the operation costs of industrial assets. However, the study for heterogeneous two-unit systems is rarely based on the usage and condition information of units, simultaneously. This paper originally proposes a novel imperfect opportunistic maintenance model for a two-unit series system considering random repair time and two types of failures, where unit 1 and unit 2 are respectively subject to soft failure and hard failure. The system maintenance actions are performed not only based on the deterioration level of unit 1 but also on the usage of unit 2. To utilize the economic dependence between the two units, the opportunistic maintenance policy is adopted in the series system. When a unit fails or is being repaired, the other unit has an opportunity to be simultaneously maintained once it meets the requirement of opportunistic maintenance. Herein, opportunistic maintenance action is imperfect maintenance, which means that the deterioration level of unit 1 and the usage of unit 2 restore to a lower level than the as-good-as new status after repair. Nonetheless, once both units meet the requirement of replacement actions, they will be perfectly replaced by new ones. The objective is to minimize the system average maintenance cost by optimizing the thresholds of opportunistic maintenance and perfect replacement of two units. Finally, an illustrative example is presented to demonstrate the superiority of the proposed maintenance model.

The Simultaneous Effect of Holding Safety Stock and Purchasing Policies on the Economic Production Quantity Model Subject to Random Machine Breakdown

In this paper, we develop an economic production quantity (EPQ) model under machine breakdown and two types of repair (corrective and preventive). also, study the simultaneous effect of holding safety stock and purchasing policy. In order to avoid shortages occurring as a result of the random repair time, in addition to keep safety stock, we suppose that the manufacturer could purchase some quantities from an external supplier. This paper addresses the following question: how the manufacturer determine the optimal values of safety stock, production and purchasing lot sizes, simultaneously, to minimize the expected total cost? The introduced model is then compared with the situations in which the manufacturer only keeps safety stock or just uses an external supplier, respectively. The results through the analysis show that using the simultaneous policy when the system is prone to shortages due to long repair times, have more improvement in the performance of the system rather than using the safety stock or purchasing policies, separately.

Performance Evaluation and Improvement of Chipset Assembly &amp; Test Production Line Based on Variability

“Factory physics principles” provided a method to evaluate the performance of a simple production line, whose fundamental parameters are known or given. However, it is difficult to obtain the exact and reasonable parameters in actual manufacturing environment, especially for the complex chipset assembly & test production line (CATPL). Besides, research in this field tends to focus on evaluation and improvement of CATPL without considering performance interval and status with variability level. A developed internal benchmark method is proposed, which established three-parameter method based on the Little′s law. It integrates the variability factors, such as processing time, random failure time, and random repair time, to meet performance evaluation and improvement. A case study in a chipset assembly and test factory for the performance of CATPL is implemented. The results demonstrate the potential of the proposed method to meet performance evaluation and emphasise its relevance for practical applications.

Availability analysis for general repairable systems with repair time threshold

ABSTRACTAvailability analysis is an important issue in many practical fields. This paper investigates the availability for general repairable systems with repair time threshold. Based on practical applications, a repair time threshold is introduced. If the period of a repair is less than a predefined time threshold, then the system may be considered as working during this period, i.e., the effect of the repair could be neglected. Otherwise, if the period of a repair is longer than the given threshold, then the system is considered as working from the beginning of the system failure until the repair time exceeding the threshold, i.e., the time point of the system down could be delayed. We consider both constant and random repair time threshold. This paper valuates the user-perceived availability, when the user does not experience any service interruption because the duration of repair is too short. The results can be applied in reliability engineering, queueing theory and many other fields. A numerical example for ventilator system is presented to demonstrate the application of the developed approach.

Connectivity modeling and optimization of linear consecutively connected systems with repairable connecting elements

Linear consecutively connected systems (LCCSs) are systems containing a linear sequence of ordered nodes. Connection elements (CE) characterized by diverse connection ranges, time-to-failure and time-to-repair distributions are allocated to different nodes to provide the system connectivity, i.e., a connection between the source and sink nodes of the LCCS. Examples of LCCSs abound in practical applications such as flow transmission systems and radio communication systems. Considerable research efforts have been expended in modeling and optimizing LCCSs. However, most of the existing works have assumed that CEs either are non-repairable or undergo a restrictive minimal repair policy with constant repair time. This paper makes new technical contributions by modeling and optimizing LCCSs with CEs under corrective maintenance with random repair time and different repair policies (minimal, perfect, and imperfect). The characteristics of CEs can depend on their location because the distance between adjacent nodes and conditions of CE operation and maintenance at different nodes can be different, which further complicates the problem. We first propose a discrete numerical algorithm to evaluate the instantaneous availability of each CE. A universal generating function based method is then implemented for assessing instantaneous and expected system connectivity for a specific CE allocation. As the CE allocation can have significant impacts on the system connectivity, we further define and solve the optimal CE allocation problem, whose objective is to find the CE allocation among LCCS nodes maximizing the expected system connectivity over a given mission time. Effects of different parameters including repair efficiency, mission time and repair time are investigated. As illustrated through examples, optimization results can facilitate optimal decisions on robust design and effective operation and maintenance managements of LCCSs.

Approximations of time-dependent unreliable flow lines with finite buffers

Flow lines process discrete workpieces on consecutive machines, which are coupled by buffers. Their operating environment is often stochastic and time-dependent. For the flow line under consideration, the stochasticity is generated by random breakdowns and successive stochastic repair times, whereas the processing times are deterministic. However, the release rate of workpieces to the line is time-dependent, due to changes in demand. The buffers between the machines may be finite or infinite. We introduce two new sampling approaches for the performance evaluation of such flow lines: one method utilizes an approximation based on a mixed-integer program in discrete time with discrete material, while the other approximation is based on partial and ordinary differential equations in continuous time and with a continuous flow of material. In addition, we sketch a proof that these two approximations are equivalent under some linearity assumptions. A computational study demonstrates the accuracy of both approximations relative to a discrete-event simulation in continuous time. Furthermore, we reveal some effects occurring in unreliable flow lines with time-dependent processing rates.

Optimal backup frequency in system with random repair time

This paper considers single-component repairable systems performing backup procedures to avoid repeating the entire work from scratch and thus facilitate fast system recovery in the case of failures. The mission succeeds if a specified amount of work can be accomplished within the maximum allowed mission time or deadline. The repair time is randomly distributed within a specified interval. Both failure and repair times are represented by known distributions. We first suggest a numerical algorithm to evaluate mission reliability, conditional expected cost and completion time of a successful mission. The backup frequency optimization problem is then formulated and solved for finding the inter-backup interval that maximizes mission reliability or minimizes expected mission cost while satisfying a desired level of mission reliability. Impacts of parameters including the maximum allowed mission time, data backup and retrieval times, repair and failure time distributions, and repair efficiency on mission reliability, cost and time as well as on the optimal solution are investigated through examples.

Optimal loading of system with random repair time

This paper considers single-component repairable systems supporting different levels of workloads and subject to random repair times. The mission is successful if the system can perform a specified amount of work within the maximum allowed mission time. The system can work with different load levels, each corresponding to different productivity, time-to-failure distribution, and per time unit operation cost. A numerical algorithm is first suggested to evaluate mission success probability and conditional expected cost of a successful mission for the considered repairable system. The load optimization problem is then formulated and solved for finding the system load level that minimizes the expected mission cost subject to providing a desired level of the mission success probability. Examples with discrete and continuous load variation are provided to illustrate the proposed methodology. Effects of repair efficiency, repair time distribution, and maximum allowed time on the mission reliability and cost are also investigated through the examples.

A stochastic alternating renewal process model for unavailability analysis of standby safety equipment

The paper presents a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis is formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability is derived and numerically solved for a given maintenance policy. The paper also incorporates an age-based preventive maintenance policy with random repair time. In case of aging equipment, the asymptotic limit or average unavailability should be used with a caution, because it cannot model an increasing trend in unavailability as a result of increasing hazard rate (i.e. aging) of the time to failure distribution.

A production inventory model with flexible manufacturing, random machine breakdown and stochastic repair time

Article history: Received January 26 2014 Received in Revised Format July 5 2014 Accepted July 5 2014 Available online July 12 2014 This paper derives a production inventory model over infinite planning horizon with flexible but unreliable manufacturing process and the stochastic repair time. Demand is stock dependent and during the period of sale it depends on reduction on selling price. Production rate is a function of demand and reliability of the production equipment is assumed to be exponentially decreasing function of time. Repair time is estimated using uniform probability density function. The objective of the study is to determine the optimal policy for production system, which maximizes the total profit subject to some constraints under consideration. The results are discussed with a numerical example to illustrate the theory. © 2014 Growing Science Ltd. All rights reserved

Evaluation of reliability indices accounting omission of random repair time for distribution systems using Monte Carlo simulation

This paper describes a methodology for reliability assessment of electrical distribution system accounting random repair time omission for each section. A distributor segment in a distribution system has failure rate and repair time which decide mean up time (MUT) and mean down time (MDT) at load points. Usually the reliability analysis is based on exponential failure and repair laws. The repair time is a random variable. Certain values of repair times are smaller which may be neglected based on the tolerance time of consumers at each load point. Complete reliability analysis with repair time omission has been presented. Modified mean up time, mean down time and unavailability (h/year) have been obtained at each load point using state transition sampling technique. These have been obtained accounting outage due to random repair time omission. The methodology has been implemented on two distribution systems.

Two-moment approximations for analysing a series of automated workstations

In this research we develop two-moment approximation equations for the analysis of a series of automated workstations with infinite buffer capacity. An automated workstation is a server with deterministic processing times that experiences random operating times between failures, and then subsequent random repair times. The distribution of job inter-departure times from a workstation receiving input from an automated workstation is derived. From this distribution, expressions for the mean and variance of job inter-departure times from a workstation are obtained. These are then used as a basis for ‘linking’ workstations in a two-workstation aggregation approach. This method is compared to modelling such a system as a series of G/G/1 queues. The analysis method is easily implemented in a spreadsheet. Extensive computational experiments demonstrate the effectiveness of the overall approach.

Cost evaluation for an imperfect-repair model with random repair time

A repair can bring the state of a failed system to a level which is somewhere between new and prior to repair. In most repair models proposed in the literature so far, the repair time is assumed to be negligible, and so the length of repair time has not been a factor in developing the maintenance models. However, it is more realistic to assume that it takes a certain amount of repair time. In this paper, we discuss an imperfect repair model with random repair times. We first derive a formula that can be used to evaluate the expected numbers of perfect and minimal repairs. The expected costs during (0, t], t>0 fixed, are also evaluated based on the convolution of the failure and repair distributions of the system.

Availability of a periodically inspected system with random repair or replacement times

The availability of systems undergoing periodic inspections is studied in this paper. A perfect repair or replacement of a failed system is carried out requiring either a constant or a random length of time. In Model A, the system is assumed to be as good as new on completion of inspection or repair. For Model B, no maintenance or corrective actions are taken at the time of inspection if the system is still working, and the condition of the system is assumed to be the same as that before the inspection. Unlike that studied in a related paper by Sarkar and Sarkar (J. Statist. Plann. Inference 91 (2000) 77.), our model assumes that the periodic inspections take place at fixed time points after repair or replacement in case of failure. Some general results on the instantaneous availability and the steady-state availability for the two models are presented under the assumption of random repair or replacement time.

Optimal (m-FailureP-Repairmen) policies with random repair time

The failure times of N machines are i.i.d. exponential random variables with parameter λ. This paper extends the repair model given by [3] to the case where the repair crew is more than one repairmen (P⩾1). We developed and implemented an algorithm for finding optimal policies for the new model. The experiments show that bringing more than one repirman is always the optimal solution

A renewal reward approximation for the variance of electric power production costs

The cost of producing electric power over a specified study horizon is a random quantity influenced by random failures and repair times for the generating units and variations in demand over time. Previous approaches for determining the variance of the production cost have required implicit or explicit enumeration of a large set of availability or capacity states for the generation system. In this paper, a simplifying assumption makes possible' a renewal reward model for the production cost. Formulas are provided to estimate the asymptotic variance for intermediate to long study horizons and their results are illustrated with a numerical example.