Learning and fatigue are consequences of task repetitiveness and have significant effects on an individual's performance. Despite the importance of the problem at hand, only a few studies have formulated their combined effect in a learning curve context. This paper contributes to this line of research, and unlike other models, proposes a learning curve model with a fatigue level-dependent learning rate. The proposed model has been validated using data from an order-picking task and its predictive ability has also been tested against potential models in the literature. The results show that the proposed learning curve outperforms the other models according to efficiency and balance criteria. The sensitivity analysis indicates the effect of the model's parameters on the selected system's measures and provides some managerial insights.

This paper presents a model for parallel replacement and improvement for a fleet of assets to minimize both the economic costs and greenhouse gas (GHG) emissions where the emissions are limited by an emissions trading system also known as cap-and-trade. The firm which owns the assets has the options of using, storing, improving, or salvaging them. Different technological types and their performances have been considered for the assets. The firm has the option of purchasing new assets from varying technologies and/or improving its existing assets to a higher-performance type. The model considers the possibility of both banking the emission allowances or trading them in the market. The model was applied to data from a fleet of excavators in Ontario, Canada. The model and the findings of this case study could help emitter firms to simultaneously manage the emissions and costs of their assets in a jurisdiction regulated by cap-and-trade.

We have investigated methodologies for predicting radiologists' workload in a short time interval by adopting a machine learning technique. Predicting for shorter intervals requires lower execution time combined with higher accuracy. To deal with this issue, an ensemble model is proposed with the fixed‐batch‐training method. To excel in the execution time, a fixed‐batch‐training method is used. On the other hand, the ensemble of multiple machine learning algorithms provides higher accuracy. The experimental result shows that this predictive model can produce at least 10% higher accuracy in comparison with the other available widely used short‐term time series forecasting models. In the studied medical system, this gain in accuracy for the earlier prediction of workload can reduce the Medicare relative value unit cost by $1.1 million annually, which we have formulated and shown in this paper. The proposed batch‐trained ensemble of experts model has also provided at least a 6% improvement in execution time compared with the other studied models.

One of the major problems in the application of machining processes is the cutting tool life estimation. In this regard, different studies with various assumptions have been conducted to analyze tool wear characteristics under various cutting conditions to achieve different objectives. Traditional models for the analysis of tool life are mostly based on deterministic approaches, and the variations in cutting conditions are overlooked, and the tool life is not precisely matched with predicted values by these methods. In recent years, researchers have considered using the stochastic approach in forecasting tool life. Among them, Weibull distribution has special significance. One problem in using these approaches is the accurate estimation of tool's life distribution functions based on the empirical information. In other words, although many researchers have considered Weibull an appropriate distribution for the cutting tool life modeling, however, the estimation of its parameters has certain inherent complexities. In this research, a hybrid methodology is presented to determine the parameters of the tool life distribution, by using the design of experiment (DOE) based on Box-Behnken design (BBD), total time on the test (TTT) transform, and golden section search (GSS). The estimation method of Weibull distribution parameters in this paper is compared with well-known techniques such as the least square method and maximum likelihood estimation. Finally, the proposed methodology was implemented in a case study, and the results were reported. The values of R2 for shape and scale parameters are 92.52% and 96.80%, respectively, which confirm the adequacy of the proposed methodology in the practical applications.

In failure-prone systems, it is important to take into considerations all the failure modes of each component to achieve the optimal system reliability. In this paper, a new series-parallel redundancy allocation problem is presented for a system in which the subsystems and components are subject to two different independent failure modes: short-circuit and open-circuit. It is assumed when a pre-determined number of a subsystem's components fail due to short- or open-circuit failure types, the subsystem fails. Moreover, when more than a pre-determined number of the system's subsystems fail due to short- or open-circuit failure types, the system fails. A new method based on the universal generating function is used to calculate the system's short-circuit failure probability, and the results are validated with the Monte-Carlo simulation. Then, a mathematical model for the considered RAP is presented to maximize the system's reliability. Finally, the proposed model is solved using a genetic algorithm.

In this paper, we develop a continuous-time discrete-state model for periodic inspection of a k-out-of-n cold-standby system with non-identical components. A perfect switching system detects the components' failures, and the failed component(s) are repaired during the next inspection interval, and then added to the standby queue. The system can be in different states depending on the combination of working components and the order of the components on the standby queue at the beginning of an inspection interval. We present a matrix-based approach to determine the system states and calculate the system-states transition probabilities and the transition matrix. We calculate the expected total cost of the inspection intervals by determining the system state at the beginning and end of each inspection interval and calculating the inspection cost matrix. The expected total inspection cost consists of the system downtime cost, components repair cost, system repair cost, and system inspection costs. Finally, we minimize the system's expected total cost by determining the system's optimal inspection interval. The results show that determining the optimal inspection interval decreases the system's total inspection interval cost up to 60 % in comparison with the cases when the inspection interval is selected arbitrarily.

The utilization of real-time information in production scheduling decisions becomes possible with the help of new developments in Information Technology and Industrial Informatics, such as Industry 4.0. Regardless of the beliefs that the availability of such information will enhance scheduling decisions, several questions and concerns have been reported. One such question is to what extent can the availability of real-time information enhance scheduling decisions? Another concern is how can such information be utilized to advance scheduling decisions and when should it be used? Moreover, there is a general assumption that continuous rescheduling using real-time system updates is beneficial to some extent. However, this general assumption has not been extensively investigated in complex manufacturing systems, such as flexible job shops. Therefore, in this paper, our objective is to study the above-mentioned research questions by developing real-time scheduling (RTS) models for the flexible job-shop scheduling problem (FJSP) with unexpected new job arrivals and machine random breakdowns. We investigate how real-time updates on unexpected arrivals, the availability of machines (downtimes and recovery times), and the completion times of operations can be utilized to generate new schedules (i.e., rescheduling). The performance of the developed RTS models is also investigated under different settings for shop-floor events, different rescheduling strategies, rescheduling policies, and scheduling methods. Lastly, results, conclusions, and several promising research avenues are provided.

A new methodology for modeling large-scale scheduling problems in low-volume low-variety production systems is proposed through this paper. Such scheduling problems are constrained by limited time and resources, where each work center is assigned a unique statement of work, to be completed on-time with the budgeted number of resources. Products assembled in low-volume low-variety production systems are processed through a series of stations referred to as work centers, where varying levels and classifications of resources are deployed onto the product. Aircraft, heavy aero-structures, and heavy military equipment are examples of products assembled in low-volume low-variety production systems. To ensure products are delivered on-time and on-budget, it is crucial to execute to a detailed schedule, such that all precedence, resource, zonal, and other constraints and characteristics inherent in such production systems are successfully satisfied. Despite the criticality of detailed schedules in delivering products on-time and on-budget, limited research is reported on mixed-integer programming approaches for scheduling optimization of activities in low-volume low-variety production systems. The discrete-time linear mixed-integer mathematical programming model developed in this paper fills the gap in the current literature with a direct impact on the organizations' service levels and bottom line. The proposed mathematical programming models are validated through a real-world case-study of the assembly process of a narrow body aircraft to ensure compatibility in the modeling of large-scale industrial problems.

In production lines, several factors contribute to the manufacturing of final products. Among these factors, the production time, machine status, and energy consumption, before and during production, need to be investigated further. In this paper, we present a mathematical model which jointly optimizes production scheduling and maintenance planning in a single-machine production environment. The performance of the machine deteriorates with time, and the machine is subject to stochastic deterioration-based failures. We assume that the transitions between the machine's deterioration states follow an exponential distribution. We consider that processing times and energy consumption are affected by machine deterioration and failures. The main contribution of the paper is that maintenance and scheduling decisions are made based on the machine's degradation level (i.e., the machine's condition). We address the machine's deterioration as a discrete multi-state degradation process; and model the effects of the machine's deterioration and failures on the duration of job processing and the machine's energy consumption. Then, we develop a stochastic mixed-integer programming model that integrates decisions about maintenance and production scheduling. The model generates the optimal maintenance action for each degradation state, as well as the optimal inspection policy and job sequence, with the overall aim being to minimize the total cost, including: inspection costs, repair costs, machine energy consumption costs, and the makespan penalty for exceeding a predetermined threshold. Due to the complexity of the developed model, an effective genetic algorithm (GA) based on the properties of the considered problem is proposed. Finally, through a comparative numerical study, we show that making decisions according to the deterioration level of the machine results in more integrated and cost-effective plans compared to the current method of repairing the machine only once it has reached its failure state.

In this paper, we consider a single machine, which must process n jobs in sequence. The nmachine's failure process follows the two-stage Delay Time Model, i.e. it starts with an initial defect, and will lead to eventual failure if the defect is left unattended. An inspection may be performed before starting a job to detect a defect. We improve the machine's maintenance decision making process by considering the possibility of performing minimal repair or replacement at any event time with regard to the age of the machine. This assumption affects the complexity of the problems in terms of executing loops in MATLAB excessively. The objective is to find the optimal inspection policy and the jobs sequence, which minimize the total expected makespan. We will develop two models and derive their corresponding recursive formulas. For the optimization of the first model, we will combine the Genetic Algorithm with the recursive equations to jointly optimize the job sequence and inspection policy. In the second model, due to cumbersome recursive equations, we will adopt a simulation algorithm to obtain the required expected values in the objective function. We will provide numerical examples to present the application of the models, and study the influence of various input parameters on the best obtained policies. We conduct extensive computational experiments on randomly generated problems with different configurations to evaluate the efficiency of models.

Availability analysis of a fleet of assets requires modelling uncertainty sources that affect equipment reliability and maintainability. These uncertainties include complex, managerial causalities and risks which have been seldom examined in the asset management literature. The objective of this study is to measure the reliability, maintainability and availability of a fleet, considering the effect of common causal factors and extremely rare or previously unobserved events. We develop a fully probabilistic availability analysis model using hybrid Bayesian networks (BNs), to capture managerial, organizational and environmental causal factors that influence failure or repair rate, as well as those that affect both failure and repair rates simultaneously. The proposed methodology has been found more accurate in forecasting failure rate, repair rate, and average availability level of a fleet of assets, providing asset managers with an inference mechanism to not only measure the performance of the assets based on common causal factors, but also learn the actual level of such factors and thereby identify improvement areas. We have demonstrated the application of the model using a fleet of excavators located in Toronto, Ontario. The prediction accuracy of the proposed model is evaluated by use of a measure of prediction error.

We propose an algorithm for estimating the effectiveness of maintenance on both age and health of a system. One of the main contributions is the concept of virtual health of the device. It is assumed that failures follow a nonhomogeneous Poisson process (NHPP) and covariates follow the proportional hazards model (PHM). In particular, the effect of maintenance on device's age is estimated using the Weibull hazard function, while the effect on device's health and covariates associated with condition-based monitoring (CBM) is estimated using the Cox hazard function. We show that the maintenance effect on the health indicator (HI) and the virtual HI can be expressed in terms of the Kalman filter concepts. The health indicator is calculated from Mahalanobis distance between the current and the baseline condition monitoring data. The effect of maintenance on both age and health is also estimated. The algorithm is applied to the case of railway point machines. Preventive and corrective types of maintenance are modelled as different maintenance effect parameters. Using condition monitoring data, the health indicator (HI) is calculated as a scaled Mahalanobis distance. We derive reliability and likelihood functions and find the least squares estimates (LSE) of all relevant parameters, maintenance effect estimates on time and health indicator and remaining useful life (RUL).

Equipment repair/replacement decision is an important aspect of asset management, which aims to find the best time to retire an in-use system considering its lifecycle costs. Previous lifecycle analysis techniques assume that the distribution of equipment's failure and repair time remain unaltered during the usage phase. In reality, however, the actual parameters that represent equipment's reliability and maintainability could change by several causal factors, including the quality of preventive and corrective maintenance, which can be dynamically adjusted through management intervention. Another dimension of repair/replacement problem is the environmental impact of equipment, which is important to be considered because of carbon pricing schemes as well as the international concerns about global warming. Not every aspect of this issue has been addressed in the published replacement decision models. Most importantly, the causality between equipment failure behaviour and its greenhouse gas (GHG) emissions has been seldom examined. The contribution of this paper is twofold. First, an economic repair/replacement model is developed in two phases: 1) deterministic phase, in which the mathematical structure of the total repair and replacement costs are defined, and 2) probabilistic phase, which incorporates the uncertainty of input parameters, risk events, quality of preventive maintenance, and repair perfection. Second, the economic model is extended to a combined model, in which the emissions associated with different phases of equipment lifecycle are considered. An inference mechanism is proposed to predict the emissions of operation phase of in-use equipment based on its failure behaviour. A plastic shredder case study is presented to illustrate the application of the proposed approach.

Many studies have been conducted to forecast and analyze the price of carbon in an emission trading scheme, also known as a cap-and-trade market. Exhaustive forecasting studies have been seldom (if ever) performed in the Western Climate Initiative (WCI) market. Because of the distinctive market dynamics in the WCI, the results of research on other markets may not be applicable to forecast the carbon price in this market. Moreover, there is a continuous debate about modelling the causality between driving forces (including energy prices, economic growth, weather, etc.) and carbon price. The objective of this paper is to forecast carbon price in the WCI market, by modelling the uncertainty of the driving forces and their causal relationship with carbon price. A probabilistic model is developed using Bayesian networks to infer the possible ranges of each driving force that could have an escalation/depreciation effect on price as well as the magnitude of this impact. The model is developed based on retrospective and prospective information on the selected driving forces in all the jurisdictions of the WCI market, providing the most probable price(s) over the period 2018–2030.

In this paper, a new approach for solving scheduling problems in low-volume low-variety production systems is proposed. Products assembled in such production systems follow a pre-defined processing order through a series of unique work centers, each budgeted with multiple classifications of resources, responsible to complete a pre-defined statement of work, over the span of an imposed takt-time. Aircraft, heavy aero-structures, and heavy mining and military equipment are examples of products assembled in such production systems. Despite prominent scholarly advancements in sequencing and scheduling optimization of a wide range of production systems, limited research has been reported on mathematical programming approaches for scheduling optimization of activities in low-volume low-variety production systems. This paper fills the gap in the current literature, through the formulation of a set of multi-objective mixed-integer linear mathematical programming models, developed for solving discrete-time work center scheduling problems in low-volume low-variety production systems. Three mathematical models are proposed in this paper, two of which are formulated for scheduling optimization of activities within a work center, differentiated by their objectives and underlying assumptions, reflective of two distinct industrial approaches to scheduling. Additionally, an alternative optimization model is proposed for evaluating a work center's maximum capacity given the complete saturation of resources, recommended for capacity studies and early detection of bottlenecks. The models proposed in this paper are validated and verified for compatibility and reliability through a real-world case study with a global leader in the aerospace industry.

The objective of traditional fleet optimization models has been to find the economic life of the assets, neglecting their environmental impacts. However, due to the effect of carbon pricing schemes, in addition to the international concerns about global warming and carbon emissions, it is essential for affected fleet owners to incorporate environmental burdens into their asset management systems. The contribution of this paper is twofold. First, a fleet optimization model is proposed, which factors in the environmental impacts of a fleet of assets over a finite horizon, in addition to its total cost of ownership. As an indicator of environmental impacts, the greenhouse gas (GHG) emissions associated with the fleet ownership is considered. GHG emissions are converted into a monetary value, using the expected price of carbon in Ontario's cap-and-trade program, as a new member of Western Climate Initiative (WCI) market. Thus, the second contribution of this study is to develop a model to predict the price of carbon in this market. The optimization model is then applied to a fleet of excavators located in Ontario, Canada, and the price of carbon in WCI market is forecasted over the planning horizon of the optimization model.

A k-out-of-n:G system and a system with components subject to soft and hard failures are both inspected non-periodically. For the k-out-of-n system, components fail "silently" (i.e. are hidden), and the entire system fails when (n-k+1)st component fails. For the system with hard-type and soft-type components, hard failures cause system failure, while soft failures are hidden and do not cause immediate failure of the system, but still reduce its reliability. Every system failure allows for an opportunistic inspection of hidden soft-type components in addition to the scheduled inspections. The available maintenance types are replacement and minimal repair. For hard-type components, the maintenance decision is determined by the optimal age before replacement. For the soft-type components with hidden failures, we do not know their age, and so decide on the appropriate type of maintenance using the optimal number of minimal repairs before replacement. The hidden nature of soft-type component failures precludes the use of a tractable analytic expression, so we use simulation and genetic algorithm (GA) to jointly optimise the non-periodic policies on maintenance and inspection and to ensure these incur minimal expected total cost over a finite planning horizon. Due to increasing computational complexity associated with the number of inspections and maintenance policies to be evaluated, the genetic algorithm presents a promising method of multi-objective optimisation for complex multicomponent systems.

In response to recent climate change, which is believed to be attributed to the release of greenhouse gas (GHG) emissions, many countries are placing CO2 abatement programs such as carbon tax and cap-and-trade. Projects do have a significant share in GHGs and therefore their environmental performance, like their schedule and cost performance, should be monitored and controlled. Although many large projects would pass an environmental assessment in the project evaluation phase, the issue of environmental performance monitoring during the project execution phase has not been addressed in project management methodologies. The objective of this paper is to develop a model to estimate project GHG emissions, and to measure project GHG performance using the developed metrics, which can be used at any point in time over the life of a project. A comprehensive study is conducted to collect information on GHG emission factors of various project activity data (such as material use, energy and fuel consumption, transportation, etc.), and a user form interface is developed to calculate the total GHG of an activity. Also, a breakdown structure is proposed which supports managing all the project GHG accounts. The monitoring and control model is formulated based on the logic used in earned value management (EVM) methodology. The proposed model is then implemented to a work package of a real construction project. The results present the project initial GHG plan and show that the model is able to calculate project GHG variance by the reporting date and predict project final GHG based on a project GHG performance index. The method presented in this paper is general and can be applied to any type of projects in an organization that aims to reduce its carbon footprint. The same structure can be applied to monitor and control any other environmental impact associated with project execution process.

We will discuss the joint optimization of the jobs sequence as well as inspection policy for a single system expected to process n jobs with different processing times. The system has a two-stage failures process, i.e. first a defect arises in the system, and if the defect is not detected, the system eventually fails. The interrupted job due to failure should be restarted after corrective replacement of the system. The possibility of inspecting the system before starting a job is considered to detect a potential defect. We develop two models to find the optimal policy based on either total expected makespan, or total expected cost. In the cost optimization model, we assume a common due date for all jobs and incur a penalty cost per unit time that the makespan exceeds the due date. We develop a recursive formula to obtain the expected makespan, and the number of failures and preventive replacements and the application of our proposed models to a system, which is supposed to process four jobs. We compare the results of the direct calculation (recursive formula) with a Monte Carlo simulation model, and discuss how changing the models’ parameters can impact the optimal policy.

Background. Modeling breast cancer progression and the effect of various risk is helpful in deciding when a woman should start and end screening, and how often the screening should be undertaken. Methods. We modeled the natural progression of breast cancer using a hidden Markov process, and incorporated the effects of covariates. Patients are women aged 50–59 (older) and 40–49 (younger) years from the Canadian National Breast Screening Studies. We included prevalent cancers, estimated the screening sensitivities and rates of over-diagnosis, and validated the models using simulation. Results. We found that older women have a higher rate of transition from a healthy to preclinical state and other causes of death but a lower rate of transition from preclinical to clinical state. Reciprocally, younger women have a lower rate of transition from a healthy to preclinical state and other causes of death but a higher rate of transition from a preclinical to clinical state. Different risk factors were significant for the age groups. The mean sojourn times for older and younger women were 2.53 and 2.96 years, respectively. In the study group, the sensitivities of the initial physical examination and mammography for older and younger women were 0.87 and 0.81, respectively, and the sensitivity of the subsequent screens were 0.78 and 0.53, respectively. In the control groups, the sensitivities of the initial physical examination for older and younger women were 0.769 and 0.671, respectively, and the sensitivity of the subsequent physical examinations for the control group aged 50–59 years was 0.37. The upper-bounds for over-diagnosis in older and younger women were 25% and 27%, respectively. Conclusions. The present work offers a basis for the better modeling of cancer incidence for a population with the inclusion of prevalent cancers.

In this paper, we consider a repairable system whose failures follow a non-homogenous Poisson process with the power law intensity function. The system is subject to corrective and multiple types of preventive maintenance. A corrective maintenance has a minimal effect on the system; however, a preventive maintenance may reduce the system's age. We assume the effects of different preventive maintenance on the system are not identical and derive the likelihood function to estimate the parameters of the failure process as well as the effects of preventive maintenance. Moreover, we derive the conditional reliability and the expected number of failures between two consecutive preventive maintenance types. The proposed methods are applied to a real case study of four trucks used in a mining site in Canada.

INTRODUCTION: This study set out to explore if breast cancers of different sizes are detected with varying sensitivity. In addition, we attempt to determine the effect of tumor size on screening detectability. SUBJECTS AND METHODS: Data arising from the Canadian National Breast Screening Study (CNBSS) was used to perform all analyses. The CNBSS consists of two randomized controlled trials, which includes data on detection methods, age, and allocation groups. We stratified tumor size by 5 mm; age into 40-49 and 50-59 years age groups; and cancer detection or presentation methods into mammography only, physical breast examination only, both mammography and physical breast examination, interval cancers, and incident cancers. RESULTS: This study revealed that a difference in tumor size exists for age (smaller tumor sizes are found in older women) and breast cancer detection or presentation modes. More specifically, breast cancers detected by mammography screening are statistically smaller than those detected by physical breast examination or those presenting as incident or interval cancers. This study also found that tumor size affects screening detectability for women in their 50's but not in their forties. That is, a statistically significant difference between mammography screening alone and physical examination alone was observed for women between the ages of 50-59 for tumor sizes up to 20 mm, including prevalent cases, and up to 15 mm when prevalent cases were excluded. CONCLUSION: The results of this study suggest that smaller breast cancers are more likely to be detected among women in their 50s.

This paper proposes a model to find the optimal non-periodic inspection interval over a finite planning horizon for two types of multi-component repairable systems. The first system contains hard-type and soft-type components, and the second system is a k-out-of-m system with m identical components. The failures of components in both systems follow a non-homogeneous Poisson process. A component can be a single part such as battery or line cord, or a subsystem, such as circuit breaker or charger in an infusion pump, which depending on their failures could be either replaced or minimally repaired according to their ages at failure. The systems are inspected at scheduled inspections or when an event of opportunistic inspection or a system failure occur. We develop a model to find the optimal inspection scheme for each system, which results in the minimum total expected cost over the system's lifecycle. We first develop a simulation model to obtain the total expected cost for a given non-periodic inspection scheme, and then integrate the simulation model with a genetic algorithm to obtain the optimal scheme more efficiently.

In the present paper, a system with components subject to soft and hard failures is considered. It is assumed that hard failures are revealed and fixed immediately and present an additional opportunity for inspection (opportunistic inspection), but soft failures are hidden and only corrected at periodic inspections. The objective is to find the optimal maintenance policy for all components and the optimal periodic inspection for the entire system. Two models are considered in this context. In the first model, hard-type and soft-type components are subject to minimal repair or corrective replacement, and soft-type components undergo opportunistic inspections. In the second model, in addition to the assumptions of the first model, hard-type components may be preventively replaced at periodic inspections. In our models, we base the maintenance decision for the soft-type components on the optimal number of minimal repairs until replacement, and for the hard-type components – on the optimal age before replacement. A recursive equation is provided for deriving the required expected values. Hidden failures preclude us from expressing the terms of the objective function in closed form. For this reason, the optimal periodic inspection interval for the system minimizing its total expected life cycle cost is found for both models using simulation.

In the present paper, a k-out-of-n system with hidden failures is considered. The system is inspected periodically over a finite lifecycle. Hidden component failures accumulate and cause system failure when their cumulative number reaches n − k + 1. Every system failure presents an additional opportunity for inspection and, therefore, is called “opportunistic”. The objective is to find the optimal periodic inspection policy and the optimal maintenance action at each inspection for the entire system. Three types of maintenance are considered: minimal repair, preventive replacement and corrective replacement. In view of the failures being hidden, the maintenance decision is based on the optimal number of minimal repairs before replacement (of either type). Due to the unavailability of a closed-form solution, joint optimisation of inspection and maintenance policies resulting in the minimum total expected cost is performed using exhaustive search and genetic algorithm (GA), both with integer inspection period constraint, and a GA implementation with quasi-continuous inspection period. Although both exhaustive search and GA with integer inspection period provide identical results, the genetic algorithm presents a more efficient procedure and requires less computational time, which becomes more noticeable with increasing complexity of the problem, as in the case of GA with quasi-continuous inspection period. Based on the simulation results, some insights are made regarding the system’s operation and cost optimisation. Expressions are derived for the expected number of system failures in terms of the cost ratio and component failure intensity. In addition, a criterion is derived for establishing acceptable level of expected system failures over the system’s lifecycle. This can be useful when designing the system or analysing its performance.

In technology-related industries, such as smartphones manufacturing, two phenomena can be observed for the products: the first is the obsolescence of an existing product, usually due to the appearance of a new product which decreases the attractiveness of the existing one; the second is the stochastic nature of the market demand and its price sensitivity. These two imply that the demand decreases over a product's lifecycle, and thus, the manufacturer and/or retailer may need to decline the retail price of the product during its lifecycle. In this paper, we assume that a dominant manufacturer wholesales a technological product to a retailer who has single or two buying opportunities. For either single- or two-buying-opportunity setting, we consider two models: (1) the retailer decreases the retail price at the product's midlife with no compensation from the manufacturer; (2) the manufacturer provides a rebate to the retailer for the retail price decline at the midlife. For the two-buying-opportunity setting, the rebate is that the manufacturer decreases the wholesale price at the midlife. The variables include the manufacturer's wholesale price and rebate, the retailer's order quantities and retail prices. We also compare the performance of the proposed models to the wholesale-price-only and the buyback policies.

We investigate the maintenance and inventory policy for a k-out-of-n system where the components' failures are hidden and follow a non-homogeneous Poisson process. Two types of inspections are performed to find failed components: planned periodic inspections and unplanned opportunistic inspections. The latter are performed at system failure times when n − k +1 components are simultaneously down. In all cases, the failed components are either minimally repaired or replaced with spare parts from the inventory. The inventory is replenished either periodically or when the system fails. The periodic orders have a random lead-time, but there is no lead-time for emergency orders, as these are placed at system failure times. The key objective is to develop a method to solve the joint maintenance and inventory problem for systems with a large number of components, long planning horizon, and large inventory. We construct a simulation model to jointly optimize the periodic inspection interval, the periodic reorder interval, and periodic and emergency order-up-to levels. Due to the large search space, it is infeasible to try all possible combinations of decision variables in a reasonable amount of time. Thus, the simulation model is integrated with a heuristic search algorithm to obtain the optimal solution.

In this paper, we consider a k-out-of-n load-sharing system with n identical components sharing a certain amount of load. Each time a component fails, its load is distributed to the remaining components; we assume an increase in load increases the hazard rates of the remaining components. The system is periodically inspected to detect failed components. Two cases may occur in an inspection interval: if the number of failed components is less than n-k+1, then the failed components are only rectified at periodic inspections; if the number of failures reaches n-k+1, then the system fails, and at this time, all the failed components are inspected and rectified. A failed component is replaced or minimally repaired according to a probability which depends on its age at the failure time. The components' failures follow a Non-Homogenous Poisson Process (NHPP), and their intensity functions depend on their ages and the loads to which they are exposed at any moment. In this paper, we develop a model to find the optimal inspection interval for such a system, which minimizes the total expected cost incurred over the system lifecycle. We derive the analytical solution for the special case of a 1-out-of-2 system, and discuss its computational difficulties. We then present a simulation algorithm to find the required expected values in the objective function. Several numerical examples are presented to illustrate the proposed model.

In this paper, we study breast cancer screening policies using computer simulation. We developed a multi-state Markov model for breast cancer progression, considering both the screening and treatment stages of breast cancer. The parameters of our model were estimated through data from the Canadian National Breast Cancer Screening Study as well as data in the relevant literature. Using computer simulation, we evaluated various screening policies to study the impact of mammography screening for age-based subpopulations in Canada. We also performed sensitivity analysis to examine the impact of certain parameters on number of deaths and total costs. The analysis comparing screening policies reveals that a policy in which women belonging to the 40–49 age group are not screened, whereas those belonging to the 50–59 and 60–69 age groups are screened once every 5 years, outperforms others with respect to cost per life saved. Our analysis also indicates that increasing the screening frequencies for the 50–59 and 60–69 age groups decrease mortality, and that the average number of deaths generally decreases with an increase in screening frequency. We found that screening annually for all age groups is associated with the highest costs per life saved. Our analysis thus reveals that cost per life saved increases with an increase in screening frequency.

Purpose: The objective of this paper is to develop a model, which optimizes jointly the inspection frequency and the inventory level for a k-out-of-n system with repairable components whose failures are hidden.Scope: The system is periodically inspected to detect failed components, and the components are either minimally repaired or replaced with spares from the inventory. The system fails between periodic inspections if n−k+1 components are down; in that case, all failed components are inspected and rectified if possible. Otherwise, the failed components are rectified at periodic inspections. An emergency spare is ordered at a system failure, if the inventory is empty and all failed components require replacement. Methodology: Using analytical approach to find the optimal solution is computationally intensive and not practical; a simulation model is developed to solve the problem.Results: The proposed model harmonizes the maintenance and inventory policies and finds the joint optimal solution which results in a minimum total cost. Conclusion: The joint optimization model results in a lower cost compared to separate maintenance and inventory optimization models. Novelty: Few joint models for k-out-of-n systems exist, and none of them investigate repairable components whose failures are hidden and follow a non-homogeneous Poisson process.

There are similarities between the condition-based maintenance of a system and monitoring the health status of a person over time and taking preventive maintenance or proactive medical actions. In this paper, we first explain the classical statistical model for the optimization of condition-based maintenance decisions and describe how system degradation can be modeled using the evolution of certain covariates over time. We then describe the modeling of cancer progression using a hidden Markov model. A case study of progression modeling of breast cancer based on the data from a randomized controlled trial is presented.

There are similarities between the condition-based maintenance of a system and monitoring the health status of a person over time and taking preventive maintenance or proactive medical actions. In this paper, we first explain the classical statistical model for the optimization of condition-based maintenance decisions and describe how system degradation can be modeled using the evolution of certain covariates over time. We then describe the modeling of cancer progression using a hidden Markov model. A case study of progression modeling of breast cancer based on the data from a randomized controlled trial is presented.

In this paper, we consider the recurrent failures of several repairable units, which can only be observed at periodic inspection times. A unit is not aging over the period between a failure and its detection. The failure times are interval censored by the periodic assessment times. The observed data consists of censoring intervals of failure times and the unobserved data are the actual ages of the units at the failure times. We formulate the likelihood function and use several iterative algorithms to find the maximum likelihood estimate (MLE) of the parameters. The complete Expectation–Maximization (EM) algorithm, the EM gradient, full Newton–Raphson (NR), and the Simplex method are used. We derive recursive equations to calculate the expected values required in the algorithms. We estimate the parameters for four failure datasets, assuming that the failures follow a non-homogeneous Poisson process (NHPP). Three datasets are obtained from a hospital for the components of general infusion pump, and the fourth dataset is simulated. Since the estimation could take a long time, we compare the performance of the algorithms in terms of the required number of iterations to converge, the total execution time, and the precision of the estimated parameters. We also use Monte Carlo and Quasi-Monte Carlo simulation as the substitutes for the recursive procedures in the Expectation step of the EM gradient and compare the results.

While controversies regarding optimal breast cancer screening modalities, screening start and end ages, and screening frequencies continue to exist, additional population-based randomized trials are unlikely to be initiated to examine these concerns. Simulation models have been used to evaluate the efficacy and effectiveness of various breast cancer screening strategies, however these models were all developed using US data. Currently, there is a need to examine the optimal screening and treatment policies in the Canadian context. In this commentary, we discuss the current controversies pertaining to breast cancer screening, and describe the fundamental components of a simulation model, which can be used to inform breast cancer screening and treatment policies.

Mortality due to causes other than breast cancer is a potential competing risk which may alter the incidence probability of breast cancer and as such should be taken into account in predictive modelling. We used data from the Canadian National Breast Screening Study (CNBSS), which consist of two randomized controlled trials designed to evaluate the efficacy of mammography among women aged 40–59. The participants in the CNBSS were followed up for incidence of breast cancer and mortality due to breast cancer and other causes; this allowed us to construct a breast cancer risk prediction model while taking into account mortality for the same study population. In this study, we use 1980–1989 as the study period. We exclude the prevalent cancers from the CNBSS to estimate the probability of developing breast cancer, given the fact that women were cancer-free at the beginning of the follow-up. By the end of 1989, from 89,434 women, 944 (1.1 %) were diagnosed with invasive breast cancer, 922 (1.0 %) died from causes other than breast cancer, and 87,568 (97.9 %) were alive and not diagnosed with invasive breast cancer. We constructed a risk prediction model for invasive breast cancer based on 39 risk factors collected at the time of enrolment or the initial physical examination of the breasts. Age at entry (HR 1.07, 95 % CI 1.05–1.10), lumps ever found in left or right breast (HR 1.92, 95 % CI 1.19–3.10), abnormality in the left breast (HR 1.26, 95 % CI 1.07–1.48), history of other breast disease, family history of breast cancer score (HR 1.01, 95 % CI 1.00–1.01), years menstruating (HR 1.02, 95 % CI 1.01–1.03) and nulliparity (HR 1.70, 95 % CI 1.23–2.36) are the model’s predictors. We investigated the effects of time-dependent factors. The model is well calibrated with a moderate discriminatory power (c-index 0.61, 95 % CI 0.59–0.63); we use it to predict the 9-year risk of developing breast cancer for women of different age groups. As an example, we estimated the probability of invasive cancer at 5 years after enrolment to be 0.00448, 0.00556, 0.00691, 0.00863, and 0.01034, respectively, for women aged 40, 45, 50, 55, and 59, all of whom had never noted lumps in their breasts, had 32 years of menstruating, 1–2 live births, no other types of breast disease and no abnormality found in their left breasts. The results of this study can be used by clinicians to identify women at high risk of breast cancer for screening intervention and to recommend a personalized intervention plan. The model can be also utilized by a woman as a breast cancer risk prediction tool.

Background: Evaluating the cost-effectiveness of breast cancer screening requires estimates of the absolute risk of breast cancer, which is modified by various risk factors. Breast cancer incidence, and thus mortality, is altered by the occurrence of competing events. More accurate estimates of competing risks should improve the estimation of absolute risk of breast cancer and benefit from breast cancer screening, leading to more effective preventive, diagnostic, and treatment policies. We have previously described the effect of breast cancer risk factors on breast cancer incidence in the presence of competing risks. In this study, we investigate the association of the same risk factors with mortality as a competing event with breast cancer incidence. Methods: We use data from the Canadian National Breast Screening Study, consisting of two randomized controlled trials, which included data on 39 risk factors for breast cancer. The participants were followed up for the incidence of breast cancer and mortality due to breast cancer and other causes. We stratified all-cause mortality into death from other types of cancer and death from non-cancer causes. We conducted separate analyses for cause-specific mortalities. Results: We found that “age at entry” is a significant factor for all-cause mortality, and cancer-specific and non-cancer mortality. “Menstruation length” and “number of live births” are significant factors for all-cause mortality, and cancer-specific mortality. “Ever noted lumps in right/left breasts” is a factor associated with all-cause mortality, and non-cancer mortality. Conclusions: For proper estimation of absolute risk of the main event of interest common risk factors associated with competing events should be identified and considered.

This article proposes a model to find an optimal periodic inspection interval over a finite time horizon for a multi-component system. The system’s components are subject to either hard or soft failures. Hard failures are detected and fixed instantaneously. Soft failures are unrevealed and can only be detected at inspections. Soft failures do not stop the system from operating; however, they may reduce its level of performance from its designed value. The system is inspected periodically to detect soft failures; however, a hard failure instance also provides an opportunity called opportunistic inspection to inspect and fix soft failures. Two models are discussed in this article. The first model assumes that components with soft and hard failures are minimally repaired. The second model assumes the possibility of either minimal repair or replacement of a component with soft failure, with some age-dependent probabilities. Recursive procedures are developed to calculate the expected number of minimal repairs and replacements and expected downtimes of components with soft failure. Examples of the calculation of the optimal inspection intervals are given. The data used in the examples are adapted from a hospital’s maintenance data for general infusion pump.

This paper proposes two optimization models for the periodic inspection of a system with “hard-type” and “soft-type” components. Given that the failures of hard-type components are self-announcing, the component is instantly repaired or replaced, but the failures of soft-type components can only be detected at inspections. A system can operate with a soft failure, but its performance may be reduced. Although a system may be periodically inspected, a hard failure creates an opportunity for additional inspection (opportunistic inspection) of all soft-type components. Two optimization models are discussed in the paper. In the first, soft-type components undergo both periodic and opportunistic inspections to detect possible failures. In the second, hard-type components undergo periodic inspections and are preventively replaced depending on their condition at inspection. Soft-type and hard-type components are either minimally repaired or replaced when they fail. Minimal repair or replacement depends on the state of a component at failure; this, in turn, depends on its age. The paper formulates objective functions for the two models and derives recursive equations for their required expected values. It develops a simulation algorithm to calculate these expected values for a complex model. Several examples are used to illustrate the models and the calculations. The data used in the examples are adapted from a real case study of a hospital’s maintenance data for a general infusion pump.

Trend analysis is a common statistical method used to investigate the operation and changes of a repairable system over time. This method takes historical failure data of a system or a group of similar systems and determines whether the recurrent failures exhibit an increasing or decreasing trend. Most trend analysis methods proposed in the literature assume that the failure times are known, so the failure data is statistically complete; however, in many situations, such as hidden failures, failure times are subject to censoring. In this paper we assume that the failure process of a group of similar independent repairable units follows a non-homogenous Poisson process with a power law intensity function. Moreover, the failure data are subject to left, interval and right censoring. The paper proposes using the likelihood ratio test to check for trends in the failure data. It uses the Expectation–Maximization (EM) algorithm to find the parameters, which maximize the data likelihood in the case of null and alternative hypotheses. A recursive procedure is used to solve the main technical problem of calculating the expected values in the Expectation step. The proposed method is applied to a hospital's maintenance data for trend analysis of the components of a general infusion pump.

This paper proposes a model to find an optimal periodic inspection interval over finite and infinite time horizons for a multi-component repairable system subject to hidden failures. The components' failures can only be rectified at periodic inspections, when a failed component is either minimally repaired, or replaced with some age dependent probabilities. We calculate the excepted cost with delayed replacement or minimal repair of a component. Recursive procedures are developed to calculate probabilities of failures in every interval, expected number of minimal repairs, and expected downtimes for optimization over finite and infinite time horizons. Numerical examples of the calculation of the optimal inspection frequencies are given. The data used in the examples is adapted from a hospital's maintenance data for a general infusion pump.

This paper proposes a method to analyze statistically maintenance data for complex medical devices with censoring and missing information. It presents a classification of the different types of failures and establishes policies for analyzing data at the system and component levels taking into account the failure types. The results of this analysis can be used as basic assumptions in the development of a maintenance/inspection optimization model. As a case study, we present the reliability analysis of a general infusion pump from a hospital.

Clinical engineering departments in hospitals are responsible for establishing and regulating a Medical Equipment Management Program to ensure that medical devices are safe and reliable. In order to mitigate functional failures, significant and critical devices should be identified and prioritized. In this paper, we present a multi-criteria decision-making model to prioritize medical devices according to their criticality. Devices with lower criticality scores can be assigned a lower priority in a maintenance management program. However, those with higher scores should be investigated in detail to find the reasons for their higher criticality, and appropriate actions, such as ‘preventive maintenance’, ‘user training’, ‘redesigning the device’, etc, should be taken. In this paper,we also describe how individual score values obtained for each criterion can be used to establish guidelines for appropriate maintenance strategies for different classes of devices. The information of 26 different medical devices is extracted from a hospital's maintenance management system to illustrate an application of the proposed model.

This paper proposes a model to find the optimal periodic inspection interval on a finite time horizon for a complex repairable system. In general, it may be assumed that components of the system are subject to soft or hard failures, with minimal repairs. Hard failures are either self-announcing or the system stops when they take place and they are fixed instantaneously. Soft failures are unrevealed and can be detected only at scheduled inspections but they do not stop the system from functioning. In this paper we consider a simple policy where soft failures are detected and fixed only at planned inspections, but not at moments of hard failures. One version of the model takes into account the elapsed times from soft failures to their detection. The other version of the model considers a threshold for the total number of soft failures. A combined model is also proposed to incorporate both threshold and elapsed times. A recursive procedure is developed to calculate probabilities of failures in every interval, and expected downtimes. Numerical examples of calculation of optimal inspection frequencies are given. The data used in the examples are adapted from a hospital's maintenance data for a general infusion pump.