Long-run Cost Research Articles

Reliability analysis of periodically inspected systems with competing risks under Markovian environments

We develop a reliability and maintenance model for a periodically inspected system with competing risks subject to a randomly evolving operating environment, which is modeled as a continuous-time homogeneous absorbing Markov process. The natural wear rate and shock arrival rate are both modulated by Markovian environments. Specifically, three competing failure processes are considered. System failures may occur when an extremely harsh environment arrives, when the magnitude of a shock load exceeds a fixed value, or when the overall cumulative degradation caused jointly by the natural wear and abrupt additions due to shocks hits a preset threshold. Explicit formulas for reliability functions and first failure time moments of systems are derived. A Monte-Carlo simulation algorithm to obtain the first failure time of the system when shock arrivals are governed by non-homogenous Poisson processes is proposed. An optimal maintenance policy using periodic inspection is developed by minimizing the average long-run cost rate where the decision variable is the inspection interval. A case study of micro-engine systems is given to illustrate the developed reliability and maintenance model, which exhibits that an increased failure threshold value improves the system reliability and reduces the minimum average long-run cost rate.

Availability analysis and maintenance optimization for multiple failure mode systems considering imperfect repair

This paper studies the availability and optimal maintenance policies for systems subject to competing failure modes under continuous and periodic inspections. The repair time distribution and maintenance cost are both dependent on the failure modes. We investigate the instantaneous availability and the steady state availability of the system maintained through several imperfect repairs before a replacement is allowed. Analytical expressions for system availability under continuous and periodic inspections are derived respectively. The availability models are then utilized to obtain the optimal inspection and imperfect maintenance policy that minimizes the average long-run cost rate. A numerical example for Remote Power Feeding System is presented to demonstrate the application of the developed approach.

Replacement Policy for Heterogeneous Items Subject to Gamma Degradation Processes

A hybrid preventive maintenance policy for heterogeneous degrading items is discussed. It combines the classical age-replacement strategy, when a system is replaced either on failure or at the predetermined age, with replacement of the system when degradation reaches the predetermined level at some intermediate time. Items come from two subpopulations with different reliability characteristics. Non-homogeneous gamma processes model degradation of an item from each subpopulation. We justify probabilistically the superiority of the proposed policy over that for homogeneous populations and over the policy without possibility of additional replacement. The corresponding long-run cost rate is derived for the suggested cost structure. Some detailed numerical illustrations are presented and relevant sensitivity analysis for the main parameters of the model is performed.

An adaptive predictive maintenance model for repairable deteriorating systems using inverse Gaussian degradation process

Predictive maintenance is a promising solution to keep the long-run operation of industrial systems at high reliability and low cost. In this spirit, we aim to develop an adaptive predictive maintenance model for continuously deteriorating single-unit systems subject to periodic inspection, imperfect repair and perfect replacement. The development consists of four steps: degradation modeling, maintenance effect modeling, maintenance policy elaboration, and performance evaluation. Compared with existing models, ours differs in three main aspects. Firstly, we take into account the past dependency of maintenance actions in the degradation modeling via the random effect of an inverse Gaussian process. Secondly, we use both the system remaining useful life and maintenance duration to enable dynamic maintenance decision-making. Finally, we take advantage of the semi-regenerative theory to analytically evaluate the long-run cost rate of maintenance policies whose decision variables are of different nature. We validate and illustrate the developed adaptive predictive maintenance model by various numerical experiments. Comparative studies with benchmarks under different maintenance costs and degradation characteristics confirm the flexibility and cost-effectiveness of the model.

The potential health and economic value of SARS-CoV-2 vaccination alongside physical distancing in the UK: a transmission model-based future scenario analysis and economic evaluation

SummaryBackgroundIn response to the COVID-19 pandemic, the UK first adopted physical distancing measures in March, 2020. Vaccines against SARS-CoV-2 became available in December, 2020. We explored the health and economic value of introducing SARS-CoV-2 immunisation alongside physical distancing in the UK to gain insights about possible future scenarios in a post-vaccination era.MethodsWe used an age-structured dynamic transmission and economic model to explore different scenarios of UK mass immunisation programmes over 10 years. We compared vaccinating 75% of individuals aged 15 years or older (and annually revaccinating 50% of individuals aged 15–64 years and 75% of individuals aged 65 years or older) to no vaccination. We assumed either 50% vaccine efficacy against disease and 45-week protection (worst-case scenario) or 95% vaccine efficacy against infection and 3-year protection (best-case scenario). Natural immunity was assumed to wane within 45 weeks. We also explored the additional impact of physical distancing on vaccination by assuming either an initial lockdown followed by voluntary physical distancing, or an initial lockdown followed by increased physical distancing mandated above a certain threshold of incident daily infections. We considered benefits in terms of quality-adjusted life-years (QALYs) and costs, both to the health-care payer and the national economy. We discounted future costs and QALYs at 3·5% annually and assumed a monetary value per QALY of £20 000 and a conservative long-run cost per vaccine dose of £15. We explored and varied these parameters in sensitivity analyses. We expressed the health and economic benefits of each scenario with the net monetary value: QALYs × (monetary value per QALY) – costs.FindingsWithout the initial lockdown, vaccination, and increased physical distancing, we estimated 148·0 million (95% uncertainty interval 48·5–198·8) COVID-19 cases and 3·1 million (0·84–4·5) deaths would occur in the UK over 10 years. In the best-case scenario, vaccination minimises community transmission without future periods of increased physical distancing, whereas SARS-CoV-2 becomes endemic with biannual epidemics in the worst-case scenario. Ongoing transmission is also expected in intermediate scenarios with vaccine efficacy similar to published clinical trial data. From a health-care perspective, introducing vaccination leads to incremental net monetary values ranging from £12·0 billion to £334·7 billion in the best-case scenario and from –£1·1 billion to £56·9 billion in the worst-case scenario. Incremental net monetary values of increased physical distancing might be negative from a societal perspective if national economy losses are persistent and large.InterpretationOur model findings highlight the substantial health and economic value of introducing SARS-CoV-2 vaccination. Smaller outbreaks could continue even with vaccines, but population-wide implementation of increased physical distancing might no longer be justifiable. Our study provides early insights about possible future post-vaccination scenarios from an economic and epidemiological perspective.FundingNational Institute for Health Research, European Commission, Bill & Melinda Gates Foundation.

Optimal Condition-based Opportunistic Maintenance and Spare Parts Provisioning for a Two-unit System using a State Space Partitioning Approach

Making optimal decisions on preventive maintenance (PM) and spare parts provisioning for a multi-unit system is a practical problem in many industrial applications. In practice, decision makers must deal with a high level of complexity because of complex interactions among multiple units. In this work, we study optimal condition-based opportunistic maintenance (CBOM) and spare parts provisioning policies for a two-unit system experiencing continuous deterioration. A state space partitioning approach considering the deterioration states of the system along with the spare parts inventory state is proposed to analyse the requirements and actions for different maintenance types under the constraints of spare parts and those for spare parts holding and ordering. The explicit representations of stationary probability densities of combined states and their numerical solutions are deduced to obtain the corresponding probabilities of interest. Based on the results and the semi-regenerative process theory, an expected long-run cost rate model is developed to determine the optimal joint strategy. To illustrate the use of the proposed approach in practice, a wind turbine system consisting of main bearings and gearboxes is studied. The numerical results and sensitivity analysis validate the proposed approach and its practical values in solving such complex industrial problems.

Illiquidity and the Cost of Equity Capital: Evidence from Actual Estimates of Capital Cost

Illiquidity measures appear to be related to monthly realized returns but do they actually impact the long-run costs of capital for firms? We make progress on this issue by analyzing the relation between the well-known Amihud (2002) liquidity measure and actual cost-of-capital (CoC) estimates, which rely on imputing the internal rate of returns on firms’ equity cash flows. Using U.S. data, after controlling for well-known determinants of CoC, we find that illiquidity is strongly and negatively related to CoC estimates. This result obtains even as we confirm that illiquidity is positively related to monthly realized returns. Liquidity risk and the probability of informed trading bear no relation to CoC. While our results do not rule out that short horizon investors demand compensation for illiquidity, our results run contrary to the notion that corporations should care about illiquidity, liquidity risk, or information risk, while setting discount rates for long-term projects.

Conventional and Current way of Interpretation and Cost Forecasting

This study discuses Short-term cost interpretation, regression analysis with time-series data, long term cost interpretation, Regression analysis using cross-section data, cost forecasting and Changes in the productivity of production factors. Short-term cost interpretation lead to short-term decisions, the concept of incramental costs has a very important role which includes variable costs and changes in fixed costs. Long term cost interpretation to analyze the production function of several different firms, long-run cost estimates can be used. Based on these conditions, the estimation of long-term costs uses cross-section data. Forecasting costs for various levels of output in the coming period requires an assessment of changes in the efficiency of the production process physically, plus changes in the prices of production factors used in the production process.

A novel approach for optimal replacement threshold and inspection scheme for condition based maintenance

PurposeThe purpose of this paper is the simultaneous determination of optimal replacement threshold and inspection scheme for a system within condition-based maintenance (CBM) framework.Design/methodology/approachA proportional hazards model (PHM) is used for risk of failure and a Markovian process to model the system covariates. Total expected long-run cost (including replacement, inspection and downtime costs) is formulated in terms of replacement threshold and inspection scheme. Through an iterative procedure, for all different values of replacement thresholds, their associated optimal inspection scheme is determined using an effective search algorithm. By evaluating the corresponding costs, the optimal replacement threshold and its associated optimal inspection scheme are, then, identified.FindingsThe mathematical formulation, that takes into account all different costs, required for the simultaneous determination of optimal replacement threshold and optimal inspection scheme for an item subjected to CBM using PHM is provided. The proposed approach is compared against classical age policy and one state-of-the-art policy through a numerical example. The results show that the proposed approach outperforms other comparing policies.Practical implicationsIn practical situations where CBM is implemented, inspections and downtime often incur cost. Under such circumstances, findings of this paper can be utilized for the determination of optimal replacement threshold and optimal inspection scheme so that the CBM cost is minimized.Originality/valueIn most of the reported researches, it is often assumed that inspections have no cost and/or that the time for replacements (either preventive or at failure) is negligible. In the contrary, in this paper the author takes all cost factors including inspection costs, replacement time(s) and their associated downtime costs into account in the simultaneous determination of optimal replacement threshold and optimal inspection scheme.

Performance analysis and optimization of a cold standby system subject to [formula omitted]-shocks and imperfect repairs

This paper analyzes and optimizes the economic performance of a cold standby system subject to δ-shocks and imperfect repairs. Specially, the system consists of two components with different reliability characteristics. It is assumed that shocks arrive according to a Poisson process. When a component is active during operation, it will fail whenever the interarrival time between successive shocks is less than a threshold influenced by the number of repairs performed on this component. For reliability analysis, geometric process models are utilized to characterize the lifetime and repair time of the active component subject to δ-shocks and imperfect repairs. Using the supplementary variable method, some reliability measures of the system are obtained. Moreover, an explicit expression for the long-run cost per unit time is derived to quantify the system's economic performance. Finally, the optimal repair policy is determined based on this economic performance measure, and a sensitivity analysis is conducted to provide managerial insights for the efficient operation of such a system.

Energy-efficient, EDFA lifetime-aware network planning along with virtualized elastic regenerator placement for IP-over-EON

In this paper, we focus on energy-efficient network planning (including traffic provisioning) along with optimal placement of virtualized elastic regenerators (VERs) for IP-over-elastic optical networks based on a static traffic profile, using a mixed integer linear programming-based optimization model. The proposed model judiciously exploits flexibility of IP core routers, sliceable bandwidth variable transponders (SBVTs) and VERs to accommodate the traffic demands with the minimum power consumption (PC). Optical layer traffic grooming allows to simultaneously originate/terminate multiple lightpaths of different capacities, data slots and maximum transparent reach by a single SBVT. The proposed model also allows to use all functionalities of VER, such as simultaneous regeneration, distance-adaptive transmission option selection, frequency slot merging to be used concurrently for the given static traffic profile. In addition, the proposed model includes lifetime awareness of Erbium-doped fiber amplifier (EDFA) to reduce EDFA failure and associated repairing cost in long run. Using the proposed model, we enhance the average EDFA lifetime by restricting average EDFA occupancy, represented by the ratio of the (average) number of lightpaths being amplified in an EDFA and the maximum possible number of lightpaths that can be amplified in it, even though in the process, the overall PC in network may increase, with reference to the scenario with no EDFA occupancy restriction. The variation in PC and average EDFA lifetime for different permissible (user-defined) average EDFA occupancy are studied. We exhaustively study performance of the model under different network conditions.

Optimal sampling plan for an unreliable multistage production system subject to competing and propagating random shifts

Sampling plans play an important role in monitoring production systems and reducing quality- and maintenance-related costs. Existing sampling plans usually focus on one assignable cause. However, multiple assignable causes may occur, especially for a multistage production system, and the resulting process shift may propagate downstream. This article addresses the problem of finding the optimal sampling plan for an unreliable multistage production system subject to competing and propagating random quality shifts. In particular, a serial production system with two unreliable machines that produce a product at a fixed production rate is studied. It is assumed that both machines are subject to random quality shifts with increased nonconforming rates and can suddenly fail with increasing failure rates. A sampling plan is implemented at the end of the production line to determine whether the system has shifted or not. If a process shift is detected, a necessary maintenance action will be initiated. The optimal sample size, sampling interval, and acceptance threshold are determined by minimizing the long-run cost rate subject to the constraints on average time to signal a true alarm, effective production rate, and system availability. A numerical example on an automatic shot blasting and painting system is provided to illustrate the application of the proposed sampling plan and the effects of key parameters and system constraints on the optimal sampling plan. Moreover, the proposed model shows better performance for various cases than an alternative model that ignores shift propagation.

Who is unhappy for Brexit? A machine-learning, agent-based study on financial instability

In this paper, we assess the happiness cost of Brexit in the UK and the EU, using data from the Gallup World Poll. We implement a two-stage learning machine, using a naive Bayes classifier to extract happiness preferences of the population and then passing these onto an artificial neural network of attributes to generate dynamic happiness functions for each household, on an agent-based modelling framework. We find that there is a significant long-run cost in terms of both happiness and unemployment, which primarily affects the most vulnerable portion of the population. In addition, despite the expected instability in City's financial centre, the UK financial sector seems to be well equipped to deal with the repercussions, thus minimising the welfare costs for the country. Our findings extend the discussion of the economic costs of Brexit, by adding the welfare cost of the ensuing financial instability.

Who Is Unhappy for Brexit? A Machine-Learning, Agent-based study on Financial Instability

In this paper, we assess the happiness cost of Brexit in the UK and the EU, using data from the Gallup World Poll. We implement a two-stage learning machine, using a naive Bayes classifier to extract happiness preferences of the population and then passing these onto an artificial neural network of attributes to generate dynamic happiness functions for each household, on an agent-based modelling framework. We find that there is a significant long-run cost in terms of both happiness and unemployment, which primarily affects the most vulnerable portion of the population. In addition, despite the expected instability in City’s financial centre, the UK financial sector seems to be well equipped to deal with the repercussions, thus minimising the welfare costs for the country. Our findings extend the discussion of the economic costs of Brexit, by adding the welfare cost of the ensuing financial instability.

Time‐based replacement policies for a fault tolerant system subject to degradation and two types of shocks

AbstractA single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed‐form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time‐based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long‐run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented.

Time Heals all Wounds? a Capabilities Approach for Analyzing Intimate Partner Violence

ABSTRACT The capabilities approach has redefined what constitutes economic well-being and is now used globally to track progress in human development. Yet, its application in examining violence against women has been limited to identification of impacts on universal capabilities and protective or risk factors for violence. This study examines the long-term consequences of intimate partner violence as capability deprivations. This framework allows for a more complete articulation of the costs faced by survivors. Additionally, this approach allows for consideration of the temporal dimension of capability deprivations associated with intimate partner violence. Such deprivations are cyclical, in the translation of resources into capabilities and into functionings, and linear, over the lifespan. Ultimately, the capabilities approach can help evaluate policies that disproportionately impact survivors over time. Two examples from the United States are included. HIGHLIGHTS Intimate partner violence (IPV) is both a serious, direct deprivation of bodily integrity and a cause and consequence of deprivations across other capabilities. Compared to static frameworks, the capabilities approach allows for better recognition of the long-run costs of IPV. Organizations working with survivors should move away from resource-based perspectives and toward using the capabilities approach to identify and remove barriers survivors face in translating resources to capabilities to functionings. Examining the US-based Purple Paw Program for pet fostering and the Patient Protection and Affordable Care Act reveals how conceptualizing IPV in terms of capabilities can aid in targeting policies toward supporting survivors.

Integrated decision making for attributes sampling and proactive maintenance in a discrete manufacturing system

An integrated optimal design of attributes sampling and proactive maintenance for a discrete manufacturing system is studied in this paper. In the system, the failure of a critical component causes the process to shift. The new mathematical model for online sampling of the discrete manufacturing system is based on the binomial and truncated negative binomial distributions. In addition to performing scheduled maintenance and unscheduled corrective maintenance at the time of a true alarm, an additional maintenance opportunity when a false alarm occurs is also considered. The optimal scheduled maintenance time and sampling parameters are determined by solving a mixed integer nonlinear programming problem to minimise the long-run cost rate. A numerical example is provided to illustrate the proposed integrated attributes sampling and maintenance plan. The results show that the integrated approach outperforms the alternatives that consider different models separately. More importantly, showing the benefit of doing maintenance upon a false alarm provides a stakeholder with a new idea in managing a deteriorating manufacturing system.

An study of cost effective maintenance policies: Age replacement versus replacement after N minimal repairs

In this paper we consider the inspection and maintenance of a system under two types of age-dependent failures, revealed minor failures (R) and unrevealed catastrophic failures (U). Periodic inspections every T units of time are carried out to detect U failures, leading to the system replacement when one is discovered. R failures are followed by a minor repair. In addition the system is preventively replaced at MT or after the Nth R failure whichever comes first. The costs of minimal repair and replacement after N minor failures depend on age and history of failures. Non-perfect inspections are assumed, providing false positives when no U failure has happened or false negatives when a U failure is present. The long-run cost per unit of time along with the optimum policy (T*, M*, N*) are obtained. We explore conditions under which both strategies of preventive maintenance are profitable, comparing with suboptimal policies when only one of them is performed. Maintenance of infrastructures illustrates the model conditions.

Condition-Based Maintenance Planning for Systems Subject to Dependent Soft and Hard Failures

Most systems can fail in multiple ways, and the failure modes are usually positively correlated. This phenomenon complicates the reliability analysis and makes the corresponding maintenance planning challenging. This article proposes a condition-based maintenance policy for systems that are subject to both degradation-induced soft failure and sudden hard failure, where a higher degradation level leads to a higher hazard rate of the hard failure. The Wiener process is adopted for the degradation process, and the Weibull model is used to describe the baseline hazard rate of the hard failure. The degradation level is then treated as a time-varying covariate that affects the hazard rate of the hard failure, and the closed-form of the reliability function is derived by using the Brownian bridge theory. An inspection/replacement maintenance policy is employed, and the long-run cost rate is formulated based on the semiregenerative property of the system state. The optimal inspection interval and the preventive replacement threshold are then jointly determined by minimizing the long-run cost rate. A numerical study on a hydraulic sliding spool system is conducted to validate the derived reliability function and the maintenance policy.

The costs of disability in Australia: a hybrid panel-data examination

BackgroundOver four million people in Australia have some form of disability, of whom 2.1 million are of working age. This paper estimates the costs of disability in Australia using the standard-of-living approach. This approach defines the cost of disability as additional income required for people with a disability to achieve a similar living standard to those without a disability. We analyse data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey using a hybrid panel data model. To the best of our knowledge, this is the first study to examine the costs of disability in Australia using a high quality, large, nationally-representative longitudinal data set.MethodsThis study estimates the costs of disability in Australia by using the Standard of Living (SoL) and a dynamic model approach. It examines the dynamics of disability and income by using lagged disability and income status. The study also controls for unobserved individual heterogeneity and endogeneity of income. The longitudinal specification in this study allows us to separate short- and long-run costs of disability using a hybrid panel data regression approach.ResultsOur results show that people with a disability need to increase their adult-equivalent disposable income by 50% (in the short-run) to achieve the same standard of living as those without a disability. This figure varies considerably according to the severity of the disability, ranging from 19% for people without work-related limitations to 102% for people with severe limitations. Further, the average cost of disability in the long-run is higher and it is 63% of the adult-equivalent disposable income.ConclusionsFirstly, our results show that with the same level of income, the living standard is lower in households with people with a disability compared to households without members with a disability. This indicates a strong relationship between poverty and disability. However, current poverty measures do not take into account disability, therefore, they fail to consider substantial differences in poverty rates between people with and without a disability. Secondly, the estimated costs reflected in this study do consider foregone income due to disability. Therefore, policymakers should seriously consider adopting disability-adjusted poverty and inequality measurements. Thirdly, increasing the income (e.g. through government payments) or providing subsidised services for people with a disability may increase their financial satisfaction, leading to an improved living standard. The results of this study can serve as a baseline for the evaluation of the National Disability Insurance Scheme (NDIS).