Production disruptions in high-tech mass production companies producing many parts every single minute will lead to considerable economic impact and affect manufacturing efficiency. The root causes of disruptions are classified into three categories: human-related, machine-related, and material related. Using different management, hiring and training strategies, companies are generally successful in reducing human related and material related disruptions. However, machine related disruptions (MRDs) are still occurring even in companies employing a solid maintenance program. The MRDs poses random pauses of various durations in a production. Forecasting the characteristics of such pauses (downtimes) can assist in real-time manufacturing process adjustment and real-time re-scheduling of a production. This study aims at utilizing available recorded MRDs for forecasting time to forthcoming MRD and its duration. Our general approach is to evaluate the performance of different data mining-based learning techniques for predicting both the duration and time to forthcoming MRDs and determining the outperforming approach. We consider a smart factory located in the northern part of Toronto great area active in the field of thermoplastic injection molding of various components. We use the historical data on the MRDs recorded from 2013 to 2019 to conduct the investigation. In this study a set of different classifiers, including rule-based, function-based, tree-based and lazy are implemented for forecasting each of the duration and time to forthcoming MRD. The part ID, machine ID, mold age, and the ordinal number of the forthcoming MRD are considered as the input attributes of the developed data mining-based classifiers. In order to determine how effectively the data mining-based methods perform, we calculate different performance criteria including the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Bias, Correlation Coefficient (CC), and R2. The overall accuracy rate for some tree-based algorithms is significant (CC exceeded 0.92 and MAE<0.06). It shows the capabilities of data mining-based approaches in forecasting the durations and times to MRDs. The obtained trained models are accurate enough to be coupled with stochastic optimization algorithms for real-time manufacturing process adjustment and re-scheduling when a MDR takes place.

In this paper, we consider a degrading flexible job-shop manufacturing system and optimize jointly optimize scheduling, maintenance and inventory. In this production system, we are given n jobs of different routings and processing times, which need to be scheduled on m machines with varying processing power, and each job can be processed on all machines. The machines may fail due to the deterioration or the random breakdown of their tools. We model the condition of the machines' tools as a discrete multi-state degradation process using a continuous-time Markov chain. We assume that the transitions between the machines' tools deterioration states follow an exponential distribution. We aim to simultaneously optimize jobs' sequencing, maintenance planning, as well as the level of the machines' tool inventory at the beginning of the mission horizon. The objective is to minimize the total cost of the production system. The machines' tools are subject to several failures during the jobs' processing and are replaced after a failure. Failure of the machines' tools may damage the product (job) quality, and then, this product (job) needs to be reprocessed from the beginning after a tool replacement. At the beginning of each job's processing, based on the maintenance policy, a machine's tool may be inspected or not. If the tool is inspected, it may be replaced based on a pre-defined state-based threshold. Due to the available budget constraint, we should order the machines' redundant tool(s) at the beginning of the production's mission horizon. We present a mathematical model that minimizes the total production cost. The production cost includes inspection cost, maintenance cost, the penalty for exceeding a pre-defined threshold for the job completion time, and the cost of purchasing the redundant tools. Since the considered production scheduling problem is NP-Hard in the strong sense, we used a Genetic Algorithm (GA) and Teaching-Learning-Based Optimization (TLBO) algorithm to solve the presented model.

In practice, production lines are dynamic and subject to several disruptions, unforeseen events, and requirements. Examples of such disruptions and events include random machine breakdowns, new order arrivals, order cancellations, due date changes, and shortage of material. Production schedules are adapted to such events by conducting rescheduling continuously, using real-time information about the current status of work-in-progress, machines, and resources on a shop-floor. This level of connectivity and real-time information sharing is achieved with the help of advanced initiatives in manufacturing technologies and industrial informatics such as Industry 4.0. Industry 4.0, driven by many emerging technologies, such as cyber-physical systems (CPS), internet of things (IoT), and internet of services (IoS), delivers real-time actionable data for smart decision-making in manufacturing. Several optimization approaches have been proposed to take advantage of such technology by incorporating the use of real-time information in the optimization process. Recently, with the increasing power of new machine learning (ML) algorithms in solving real-world problems, several ML approaches have been introduced to production planning and scheduling. In this paper, to achieve the Industry 4.0 vision in production control, we apply a reinforcement learning (RL) approach to real-time scheduling (RTS). The proposed RL based RTS uses a multiple dispatching rules (MDRs) strategy to enhance the production performance. A case study of a smart manufacturing firm is considered to apply the proposed approach. The firm is located in Ontario (Canada) and specializes in thermoplastic injection molding of various components and assemblies. The production schedules on the shop floor are sensitive to the changes resulting from random breakdowns and their associated maintenance activities. The production managers are using the data from the continuous monitoring system to update production schedules. The updating process is conducted manually based on their knowledge and a single dispatching rule (SDR) strategy. We believe that the proposed RTS system will help the company utilize the installed Industry 4.0 concepts and achieve the Industry 4.0 vision in the production control. The performance of the proposed RTS system is compared to the current strategy applied in the company. Results show the efficiency of the proposed RTS system compared to the current strategy.

This paper investigates integrated maintenance and production scheduling in an unrelated parallel-machine production environment. We address three different preventive maintenance (PM) policies, namely (1) PM at fixed predefined time intervals, (2) optimal PM period that maximizes machines' availability, and (3) optimal PM period that maintains a minimum reliability threshold for a given production period t. We incorporate the three PM policies into a mixed-integer mathematical model that jointly optimizes maintenance and production scheduling. The objective is to minimize maximum completion time and maintenance costs. The weighted-sum method is adopted to joint these two objectives as they have different units. Due to the complexity of the proposed model, a problem-specific designed simulated annealing (SA) algorithm is used to solve it. The effect of the three adopted maintenance policies on the delivery times of products and cost of maintenance activities is illustrated through a small case study.

Summary & Conclusions: The objective of the majority of production planning problems is to find the order of jobs on each machine minimizing functions of the jobs' processing times, such as makespan and flow time. However, production environment is subject to many sources of uncertainty including machine unavailability periods, which may have a major impact on the production plan. Often times, a production line is interrupted due to periodic repair and preventive maintenance. In addition, machines may become unavailable due to unexpected failures. In many industrial settings unexpected machine failures can be potentially costly as a result of its consequences in terms of machine down times, product quality and client satisfaction. In this context, decision makers may want to jointly optimize the order of the jobs on the machine as well as the maintenance operations considering failures in a production environment such that the total expected makespan is minimized. In this paper, we deal with an integrated optimization model for production scheduling and inspection of a single machine. The failure process of the machine follows a two-stage Delay Time Model (DTM), i.e. it starts with an initial defect, which leads to eventual failure if the defect is left unattended. Once a job is interrupted due to failure on the machine, it must be restarted from the beginning when the machine becomes available. To reduce the risk of machine's breakdown during processing of the jobs, an inspection can be performed prior to start of any job on the machine which exposes down time to the system. We consider the possibility of either minimal repair or replacement of the machine depending on its age at inspection time. We develop a recursive formula to jointly find the optimal inspection policy and production schedule which minimizes the total expected makespan. The problem defined in this paper might be applicable in many industrial and management contexts. Especially when some objective functions such as makespan is of greater importance for the decision makers. We present the application of our proposed model by use of data from a production line consisting of a multiple spindles boring machines which are able to process a number of jobs. We implement a branch and bound algorithm to optimize the model and then evaluate the efficiency of the branch and bound algorithm. The results of the study indicate the optimal solution depends on the input parameters of the model, most specifically, the down time parameters and the distributions of defect arrival and delay time.

The adaption of state-of-the-art inventions in information technology and industrial informatics in manufacturing has led to the advent of Industry 4.0, commonly known as the fourth industrial revolution. Industry 4.0 will take manufacturing productivity and quality to new levels and create enormous opportunities for business and revenue growth. Unlike classical manufacturing systems, Industry 4.0-based manufacturing systems are supported by several advanced technologies (known as Industry 4.0 concepts), which include cyber-physical systems (CPS) and internet of things (IoT), among other Industry 4.0 concepts. The adoption of such technology (i.e., Industry 4.0) allows for the delivery of real-time actionable data for smart decision-making. In order to fully realize the potential of such technologies, real-time decision making should be present in all aspects of the manufacturing process. This includes two core components of manufacturing: maintenance and production scheduling.

In this paper, we consider a single-machine manufacturing system in which data about the status of its critical components are instantly available. We aim to optimize simultaneously the jobs sequence and maintenance actions to minimize the total cost of the considered production system. Since the machine parts are subject to several failures during the production, the maintenance actions are either to imperfect repair or replacement, taking into considerations that parts' imperfect repair do not make these parts as good as new. The manufacturing system's cost includes the machine's parts repair or replacement cost, and the penalty if the jobs completion time exceeds a predefined threshold. We assume that the lifetime of the machine's parts has a Weibull distribution. We study a machine cutting tool and engine among others. We consider that the failure of the cutting tool decreases the product's (job) quality, and this product (job) needs to be restarted processing after the imperfect repair or replacement of the tool. For this part, we consider an age-based threshold; if the tool has failed before the threshold, the maintenance action is imperfect repair; otherwise, the tool is replaced by the new one. One of the model objectives is to find the optimal value of this threshold. If the engine fails during the processing of the job, the maintenance action is imperfect repair. The failures of the engine have no effect on the product quality; thus, the product process resumes after engine imperfect repair. The tool and engine imperfect repairs affect the life distribution parameter (scale parameter of Weibull distribution, $\theta$), but tool replacement makes the tool as good as new and presents a mathematical model with the aim of minimizing the total production cost when the system is subject to these two-failure modes. Since the lifetime of the machine's parts follows a Weibull distribution, we use a Monte Carlo simulation for calculating the jobs' completion time and the system's total cost. Job scheduling and maintenance planning problems are NP-hard problems, so we use a Genetic algorithm (GA) to solve the presented model.

We propose a method of estimating the maintenance efficiency and investigating how the efficiency impacts the system's health indicator. We assume power law (Weibull) form of the time-dependent portion of failure intensity and the Cox proportional hazards assumption for the covariate portion of failure intensity. We model the effects of preventive and corrective maintenance as multiplicative on both time and either health indicator, or raw observed covariates. Thus, we incorporate both time- and covariate-dependent parts, as well as the maintenance effects in one failure intensity function. The effects of preventive or corrective types of maintenance are modelled as different maintenance effect parameters. We derive the likelihood function and obtain the least squares estimates (LSE) of covariate coefficient(s), Weibull shape and scale parameters, as well as the preventive and corrective maintenance effect estimates on time and covariate(s). The application of the proposed model is shown in a real case study of railway point machines subject to periodic preventive maintenance and corrective maintenance on failures.

In recent years, there has been growing concern on energy efficiency in the manufacturing enterprises. Since scheduling problem has a direct impact on energy consumption, developing the effective production scheduling is among the priorities in industries. Moreover, in practice, production and maintenance operations have been viewed as major source of energy consumption in industrial system. In this paper, we propose a stochastic mathematical model for a joint production and maintenance operations scheduling problem in a flexible job shop industrial environment in which both traditional and energy efficient aspects are modeled. The objective of this research is to minimize the expected makespan in the scheduling problem focusing on CO2 emissions reduction in an actual workshop which breakdowns can happen at any moment and make machines unavailable for processing operations. In fact, energy usage associated with the CO2 emissions of the industrial shop floor are formulated in the constraints with respect to different states of operation and idle. To address this problem effectively, the Genetic Algorithm (GA) is applied for the proposed stochastic model to minimize the expected makespan. From an operation management viewpoint, the proposed model provides a scientific and helpful guideline for manufacturing system to plan production and maintenance simultaneously, with both economic and environmental benefits.

Many nations are implementing or plan to implement a carbon pricing program in response to global warming and climate change issues. A significant amount of greenhouse gas (GHG) emissions can be attributed to projects, mainly construction works. Therefore, projects' environmental impact should be estimated before the project commencement and be monitored during its implementation phase. In this paper, we propose a probabilistic model to quantify the uncertainty of project GHG emissions using Bayesian networks (BNs) and simulation techniques. The model provides a quantitative risk analysis mechanism to estimate the total emissions of the project as well as an update of the final emissions using information on the completed activates.

This paper proposes a mathematical model for replacement of a fleet of assets considering technology improvement and varying utilization. The objective is to simultaneously minimize the total ownership cost of a fleet of assets and the total greenhouse gas (GHG) emissions caused by the fleet. The model allows the assets to be kept in storage in any time period, and over which, such assets do not age. We modeled previous utilization to make a more realistic difference between assets. To take into account the economic and environmental factors, we include purchasing new assets, O&M of in-use assets, holding in-storage assets, and salvaging items. Using carbon price of an emission trading market, we convert the GHG emissions of the above items to a monetary value. In addition, GHG cap and budget limit of the fleet owner is formulated. The outputs of the model include optimal decision on which assets should be in-use, in-storage, and salvaged in each period. Additionally, the model determines how many new assets should be purchased and added to the fleet in each period. The applicability of the model is shown by use of data from a fleet of excavators and CPLEX software. The proposed model can help companies to reduce their carbon footprint by employing the new economic-environmental based replacement model, in which GHG emissions of assets are taken into consideration.

Maintenance and production scheduling are interconnected activities which should be planned jointly to minimize their total cost as well as jobs tardiness. Although, the joint optimization of maintenance planning and production scheduling has been addressed extensively in literature, no study has considered production and maintenance optimization based on the concept of delay-time model (DTM). DTM has been effectively utilized in industry for inspection optimization of various systems, such as oil-hydraulic extrusion press, production plant, and industrial vehicles. The DTM considers a two-stage failure process for a system, in which an initial defect will eventually lead to a failure, if left unattended. The elapsed time between a defect occurrence and the failure (in the absence of inspection) is called delay-time, which provides a window of opportunity to inspect the system and fix the defect. In this paper, we consider a single system in a manufacturing plant which is required to process n independent jobs, while a job cannot be preempted for another job. We assume that the system has a single dominant failure mode, and model the system's failure using the DTM concept, in which the time to a defect appearance and the delay time follow certain distributions. The delay time distribution is independent of the time to defect. The system can be completely renewed by preventive replacement before a job to reduce the probability of a defect arrival and its subsequent failure while the job is being processed. An unattended defect may lead to a failure, which causes the system shutdown. The system is then replaced after a failure, and the job is restarted. We assume that the time required for a preventive replacement of the system is shorter than the time required for corrective replacement after a failure. We will jointly optimize preventive maintenance and production scheduling which results in the minimum total expected cost consisting of tardiness penalty and preventive and corrective maintenance costs. More specifically, we will determine the optimal sequence of the jobs as well as the decision on whether or not preventive replacement should be performed before a specific job. We will formulate the objective function and derive analytic expressions to obtain the total expected cost for a given sequence of jobs and a preventive replacement scheme. The application of the proposed model is shown in a case study. The results of the study indicate the optimal job sequence obtained from the joint optimization problem could differ from the case where the optimal sequence is obtained in a standalone scheduling problem. Moreover, the optimal solution depends on the input parameters of the model, most specifically, the job processing times and the distributions of defect arrival and delay time.

This paper addresses a reverse logistics system with two sources of supply, namely remanufacturing and purchasing options. The amount of return is stochastic and dependent on customers' demand. The primary goal of this research is to investigate the impact of transportation mode selection on the overall performance of the system. Using simulation modeling, we study the impact of two modes of transportation (truck vs. train). The preliminary simulation results suggest that even a more expensive mode of transportation (truck) can result in a lower total cost if the alternate mode (train) does not offer a competitive price. This work is the first step in a comprehensive study for determining conditions under which one mode of transportation is recommended over another.

Canada's mining sector contributed $54 billion to its GDP in 2013. Mining operations are an important element of Canada's economy and rely heavily on mobile equipment for the transportation of rock-ore. Failure of mobile equipment, when it is required to be in available state prevents the successful flow of mining operations, and can result in production losses averaging in millions of tons, annually. Consequently, the availability - and by extension, reliability - of mobile equipment have a direct economic impact on mine productivity. A mobile equipment's failures are the greatest contributors to its unavailability - and are observed to occur randomly. Typically, to help diagnose and curb mobile equipment failures, corrective and preventive maintenance policies are implemented. Maintenance personnel are concerned with quantifying the effect of multiple preventive maintenance policies on mobile equipment reliability and availability. Generally, this is performed by modelling the reliability of repairable systems. In most studies, it is assumed that repairable systems are subject to only one type of repair/maintenance, and the effect of repair/maintenance is captured using a single repair factor in an age reduction or intensity reduction model. In this paper, we consider a repairable system whose failures follow a Non-Homogenous Poisson Process, and the system is subject to corrective and several types of preventive maintenance. While the effect of corrective maintenance is minimal, a preventive maintenance may reduce the age of the system effectively. We assume different effects for different preventive maintenance types, and develop the likelihood function to estimate the failure process and preventive maintenance effects, simultaneously. We also derive the conditional reliability and the expected number of failures between two consecutive preventive maintenance types. The proposed methods are applied to a case study of two trucks used in a mining site. The proposed methods provide excellent predictions with the potential of becoming very useful in practice and of leading to further generalizations of repairable systems analyses.

Redundantly-configured k-out-of-n systems have wide applications in various industries. Even though the reliability and availability of k-out-of-n systems have been studied in the literature, not many models have been proposed for inspection and maintenance optimization of such systems. In addition, for majority of k-out-of-n systems, it is assumed that a failed component is always rectified by replacement, which is not a realistic assumption for many systems in the real world. In this paper, we consider a k-out-of-n system with components whose failures follow a non-homogeneous Poisson process with power law intensity function. The system is periodically inspected, and if the number of failed components in an inspection interval does not exceed n-k+1, the failed components are detected and rectified only at a periodic inspection. However, if the number of failures reaches n-k+1, the system fails and this is when all the failed components are detected and fixed. When a failure is detected, we should decide whether to minimally repair the component or replace it. Thus, two types of optimal decisions should be made simultaneously: obtaining the optimal maintenance action for a failed component and finding the optimal periodic inspection interval for the entire system. We formulate a model to obtain jointly the optimal maintenance actions and the periodic inspection interval which results in the minimum total expected cost of the system over a finite planning horizon. The optimal maintenance decision is the optimal number of minimal repairs that should be performed before a component is replaced. The total cost includes the cost of periodic inspections, the penalty cost for system failures, minimal repairs and replacements of the components, and the penalty cost for the downtime of the components before they get rectified. We then develop a simulation model to obtain the required model parameters. The application of the proposed model is shown in case studies of a 1-out-of-5 (parallel), 2-out-of-5 and 5-out-of-5 (series) systems. The 1-out-of-5 system incurs the smallest optimal total expected cost of inspection and maintenance, while the 5-out-of-5 system incurs the highest optimal cost. The optimal inspection period is the longest for the 5-out-of-5 system, since the greater number of failures provides a greater number of opportunistic inspections, which reduces the need for frequent periodic inspections.

In this paper, we consider a system with components subject to soft and hard failures. Hard failures are detected and fixed immediately, but soft failures are hidden and only rectified at periodic inspections. The objective is to find the optimal maintenance policy (minimal repair vs. replacement) for all components and the optimal periodic inspection for the whole system. We first obtain the optimal ages to replace the components with hard failures, and the optimal number of minimal repairs before replacement for the components with soft failures. We then develop a simulation model to get these optimal maintenance policies as inputs, and find the optimal periodic inspection which minimizes the total expected cost for the system over its lifecycle.

This paper proposes a model to find the optimal non-periodic inspection interval over a finite time horizon for a repairable system with hard-type and soft-type components whose failures follow a non-homogeneous Poisson process. The failure of a hard-type component (a hard failure) is self-announcing and the system stops when one of them occurs. A hard failure is fixed immediately. The failure of a soft-type component (a soft failure) does not cause the system to stop functioning, but rather stays hidden until either the next scheduled inspection occurs or a hard failure happens before the next inspection, which makes an opportunistic inspection takes place. In this paper, we assume that both types of components are either minimally repaired or replaced when they fail. We formulate the objective function of the model which is minimizing the total expected cost of the system over a finite planning horizon. The total cost includes the cost of the components’ minimal repairs, replacements, downtimes, and the scheduled inspections. We consider a binary variable for a possible scheduled inspection’s time, for which 1 indicates performing a planned inspection at that time, and 0 shows no inspection to be performed. Thus, our goal is to find the vector of binary decision variables which results in the minimum total cost of the system. We first develop a simulation model to obtain the total expected cost for a given non-periodic inspection scheme. We then join the simulation model with a genetic algorithm to obtain the optimal scheme.

In this paper, we propose a replacement decision model for a truck, which takes into account both economic aspects of the vehicle and the amount of emission released during its use phase. From an economic perspective, we consider the truck's acquisition, fuel and maintenance costs, and the resale value. For the emission consideration, we calculate the amount of CO2 produced based on the estimated vehicle's miles traveled, emission factor, and fuel use. The latter is a function of the fuel economy, which depends on the truck's model year and its current age. We consider a finite planning horizon and develop an optimal replacement policy based on dynamic programming (DP). From the model, we obtain the optimal annual cost limits (ACLs) for a truck with a certain age at the beginning of a year assuming that the truck still needs to operate over the remaining planning horizon. The optimal ACLs minimize the sum of the economic and emission related costs in the model. At the end of each year, according to the optimal ACLs, we determine whether to replace or repair the truck. We repair the truck if the estimated total cost of maintenance, fuel and emission for the upcoming year does not exceed the ACL, and replace it immediately, otherwise. The truck is disposed at the end of the planning horizon. We will present the application of the proposed model as a case study, and compare our results with the results of the model in which no environmental consideration is considered. The comparison reveals that the latter recommends more repair as the optimal decision; while our model more recommends that the total cost should be compared with the cost limits to choose the optimal repair/replacement decisions.

In this paper, we will present a model for joint optimization of periodic inspection and inventory levels for a k-out-of-n system. The component failures follow a Non-Homogeneous Poisson Process and failed components can only be revealed at inspection times. We have two types of inspections; planned periodic inspections and non-planned opportunistic inspections. Opportunistic inspections are performed when the system fails, which occurs when n-k+1 components are down at the same time. Failed components are either minimally repaired or replaced with spare parts from the inventory. The inventory policy needs to support the inspection policy so that spare parts are available when needed. The inventory is replenished to level S at periodic inspections, after a random lead-time. However, when the system fails within an inspection interval, the inventory is replenished to level s, with no lead-time (because it is an emergency order). We assume that placing an emergency order is more expensive, and that it depends on the number of spares which is ordered. A simulation model is developed to find the expected total cost for given inspection interval τ and inventory levels S and s. In order to find the combination of τ, s and S, that minimizes the total cost over the system life cycle, we use a genetic algorithm. It is necessary to use a search heuristic method because the size of the search space makes it not feasible to find the optimal solution by trying all combinations of τ, s and S.

In this paper we consider a k-out-of-n load sharing system, in which the failure of a component increases the hazard rates of the surviving components. The components failures follow a power law intensity function. The system is periodically inspected to detect failed components if the number of failures is less than n-k+1. However, the system fails when the number of failures equals to n-k+1, which is when all components are opportunistically inspected and repaired if they are in a failed state. Two models of load-sharing are considered: a tampered failure rate model, in which only the scale parameter of the power law is affected due to a change in load, and the cumulative exposure (CE) model, in which both the scale parameter and the ages of the surviving components are affected. We propose a model to find the optimal inspection interval for such systems, and describe the application of the model in several case studies. The results reveal that a system with the CE model requires to be inspected more frequently to avoid a high penalty incurred due to system failure. Moreover, shorter inspection interval is also required for a system with higher load intensity.

In this paper, we consider a k-out-of-n system, with components whose failures follow a Non-Homogeneous Poisson Process (NHPP). The system is periodically inspected to detect the failed components. The failed components can either be minimally repaired or replaced at periodic inspection times. Components are replaced with new spare parts from the inventory. The system fails between inspections if the total number of failed components exceeds n-k+1, in that case all the failed components are inspected and rectified if possible. The objective of the paper is to jointly find the optimal inspection interval and inventory level. Most studies in the literature consider a system with single item or a number of identical components that all have to work simultaneously and are completely replaced after a failure.

In this paper, we consider a k-out-of-n load-sharing system. The system starts to work with n components and each time a component fails the load is shared among the remaining components, so it increases their hazard rates. The system is periodically inspected to detect failed components. If the number of failed components is less than n-k+1 in an inspection interval; the failed components are either replaced or minimally repaired according to an age-dependent probability. If the number of failures exceeds the limit, the system fails and in this case all the components will be inspected and repaired if necessary. The failures of the components depend on the load at any moment and follow a Non-homogenous Poisson Process (NHPP). We developed a model to find the optimal inspection interval for the system over a finite time horizon, which minimizes the total expected cost incurred over the life-cycle of the system.

Breast cancer will affect one out of 9 women in Canada and is responsible for the death of 31% of them. Better modelling of breast cancer progression is key to evaluating approaches to reduce breast cancer incidence and mortality. This paper uses a four-state model to describe the progression of breast cancer: 1. healthy/non-detectable cancer, 2. preclinical (screening detectable cancer), 3. clinical (symptoms are evident), 4. death due to causes other than breast cancer. We model the natural progression of breast cancer from healthy state to clinical cancer using a partially hidden Markov chain. The effects of covariates are also studied. We incorporate prevalent cancers which are detected at the initial screen of any screening program. We then develop a simulation model to predict the expected number of prevalent cancers, screen-detected cancers and clinical cancers for a group of women aged 40- 49. We used data from the Canadian National Breast Screening Study (CNBSS) to both inform and validate our model.

In this paper we use a five-state model to describe the progression of invasive breast cancer. The states of the model are: 1. Healthy or non-detectable cancer, 2. Preclinical (screening detectable cancer), 3. Clinical (symptoms are evident), 4. Death due to breast cancer, and 5. Death due to causes other than breast cancer. We model the natural progression of breast cancer from healthy state to clinical cancer using a partially observable Markov model. We model the survival time from cancer diagnosis to breast cancer mortality using a Weibull Proportional Hazards Model (PHM). The effect of covariates in both models are also studied. We then combine the two models and develop a simulation model to evaluate the effect of different screening intervals in reducing breast cancer mortality. We use the data from the Canadian National Breast Screening Study (CNBSS), which consists of two randomized screening trials designed to evaluate the effect of mammography on women aged 40-59. The results reveal that screening can be effective in detecting breast cancer at earlier stages, so reducing breast cancer mortality. We estimated a higher reduction for older women.

In this paper we assume that the failures of a system follow a non-homogenous Poisson process (NHPP) with a power law intensity function. NHPP is a model commonly used to describe a system with minimal repairs. In many situations, such as hidden failures, failure times of a system are subject to censoring. Current trend analysis methods in the literature for NHPP consider only right censoring and do not address recurrent failure data with left or interval censoring and periodic or non-periodic inspections. We use the likelihood ratio test to check for trend in the failure data. We use the EM algorithm and a recursive method to calculate the likelihood for estimating the parameters of the power law process in the case of null and alternative hypotheses (no trend and trend assumptions). As an example, the proposed method is applied to the failures of a medical infusion pump. It was found that the likelihood ratio test and the proposed recursive method can be applied successfully to censored data, although the method may be computationally intensive for larger datasets. We also compared the likelihood method to an ad-hoc method using the mid points of censoring intervals instead of unknown failure times. The comparison showed that using the midpoints is not reliable and may result in incorrect conclusion about the trend. The proposed method can be applied to other repairable systems used in industry.

This paper proposes a model to find the optimal periodic inspection interval over a finite time horizon for a multi-component repairable system subject to hidden failures. Component failures can only be rectified at periodic inspections. At inspection, a failed component is either minimally repaired or replaced, according to certain age dependent probabilities. A penalty cost is incurred for the elapsed time from a failure to its detection at the next inspection. This model finds the optimal inspection interval with minimum expected cost. The main technical problem of finding the excepted cost with delayed replacement or minimal repair of a component is solved in this paper. Recursive procedures are developed to calculate the probabilities of failures in every interval, the expected number of minimal repairs, and expected downtimes while seeking optimization over a finite time horizon. A numerical example of the calculation of the optimal inspection frequency is given. The data used in the examples are adapted from a hospital’s maintenance data for a general infusion pump.

The Canadian Council on Health Services Accreditation (CCHSA) requires hospitals to establish a Medical Equipment Management Program (MEMP) to ensure that equipment used in patient care is safe, available, accurate, and affordable. This study focuses on a risk-based policy in inspection and maintenance of medical devices. It proposes a methodology how to include high-risk components in the hospital's inspection and maintenance plan. This methodology provides a tool for decision makers to reduce the probability and consequences of failure. And this will, in turn, result in better service quality, patient safety enhancement, and minimization of inspection and maintenance cost.