Long-run Cost Research Articles

Modeling Systems with Dependent Catastrophic and Degradation Failures Incorporating Uncertainty

This research examines the interval-valued availability and cost of a competing-risk system with dependent catastrophic and degradation failures incorporating uncertainty. Uncertainty indicates that the probability of the successful operation of the system is not precisely known. The considered system has three states: normal, degraded, and totally failed. While degradation failures lessen the system’s overall effectiveness and lead it to a degraded state, a catastrophic failure abruptly terminates the system’s operations and results in a totally failed state. The interrelationship between these two failures is illustrated by the fact that each degradation failure elevates the possibility of a catastrophic failure. To identify a failure, sequential inspections are performed on the system. If the system is found to be degraded, a minimal repair is executed. If a catastrophic failure is detected, a corrective repair is performed. By integrating the aforesaid points, a theorem describing the upper and lower limits of the model’s reliability is derived. Furthermore, some theorems defining the bounds of point availability, long-run availability, and the average long-run cost rate are established. A numerical example of an aluminum electrolytic capacitor is taken to demonstrate the results.

A reinforcement learning agent for maintenance of deteriorating systems with increasingly imperfect repairs

Efficient maintenance has always been essential for the successful application of engineering systems. However, the challenges to be overcome in the implementation of Industry 4.0 necessitate new paradigms of maintenance optimization. Machine learning techniques are becoming increasingly used in engineering and maintenance, with reinforcement learning being one of the most promising. In this paper, we propose a gamma degradation process together with a novel maintenance model in which repairs are increasingly imperfect, i.e., the beneficial effect of system repairs decreases as more repairs are performed, reflecting the degradational behavior of real-world systems. To generate maintenance policies for this system, we developed a reinforcement-learning-based agent using a Double Deep Q-Network architecture. This agent presents two important advantages: it works without a predefined preventive threshold, and it can operate in a continuous degradation state space. Our agent learns to behave in different scenarios, showing great flexibility. In addition, we performed an analysis of how changes in the main parameters of the environment affect the maintenance policy proposed by the agent. The proposed approach is demonstrated to be appropriate and to significatively improve long-run cost as compared with other common maintenance strategies.

Economic Estimation of the Long-Run Cost Function and Economies of Scale for the Date Crop in the Holy Governorate of Karbala-Al-Husseiniyah District for the Productive Season (2021)

Economic Estimation of the Long-Run Cost Function and Economies of Scale for the Date Crop in the Holy Governorate of Karbala-Al-Husseiniyah District for the Productive Season (2021)

The long-run costs of highly competitive exams for government jobs

Public sector recruitment exams can be highly competitive. Does this competition encourage candidates to develop generalizable skills, or do investments in exam preparation burden candidates who fail to get selected? I address this question by studying the impact of a partial public sector hiring freeze in the state of Tamil Nadu, India on male college graduates. The hiring freeze eliminated 86% of the usual vacancies. This increased the applicant-to-vacancy ratio for the remaining posts. Cohorts that were exposed to the hiring freeze delayed full-time employment, most likely in order to invest more time in exam preparation. A decade after the hiring freeze ended, the affected cohorts demonstrate a lower earning capacity, have delayed household formation, and appear more likely to remain unemployed. Together, these results suggest that highly competitive exams encourage candidates to make investments that are ultimately unproductive.

Planning maintenance when resources are limited: a study of periodic opportunistic replacement

Abstract Accepted by: M. Zied Babai We study an aged-based replacement policy with two control limits. The first triggers opportunistic replacement and the second triggers a guaranteed replacement. The policy is novel because: the instances for component replacement are restricted to instances of time, which we call slots, that arise periodically; and a slot provides an opportunity for replacement with a particular probability. The policy models contexts in which maintenance is periodic, and resources are limited or execution of maintenance is not guaranteed. The policy is important for practice because it is simple and reflects the common reality of time-based maintenance planning. Long-run cost per unit time and average availability are calculated in a renewal-reward framework. Numerical study indicates that, if opportunities are rare, guaranteed replacement is beneficial and opportunities should be taken early in the life of a system. Using the policy, a maintainer can evaluate the cost–benefit of investing more resources to reduce the time between slots. Specific analysis and policy comparisons can be carried out using a web-application developed by the authors.

Economic modelling and optimisation of SPRT-based quality control schemes for individual observations

In many industrial processes, it may not be practical to obtain sample sizes larger than one due to various reasons. As a result, practitioners must rely on control charts based on individual observations for statistical process monitoring and control. The sequential probability ratio test (SPRT) chart is an appropriate solution for such situations. Existing literature predominantly delves into the statistical aspects of designing or optimising an SPRT chart, neglecting the economic and associated design aspects. However, past experience suggests that statistical design may not always be optimal from an economic perspective. This paper aims to bridge this research gap by proposing a two-stage Markov chain approach to develop an economic model for the optimal design of the SPRT chart with individual observations. Following the principles of economic-statistical designs, optimal parameters are determined by solving a mixed-integer non-linear programming problem that minimises the long-run cost per item while ensuring compliance with practical constraints. Through an extensive study, we find that the economic performance of the SPRT chart surpasses that of competing individual control charts in many cases. This indicates that the economic-statistical design of the SPRT chart can yield significant economic benefits while maintaining desirable statistical properties. Moreover, enhancements have been introduced to refine the optimal design of the SPRT chart, retaining excellent overall performance across a wide range of shifts. Finally, we provide two industrial examples to illustrate the effectiveness of the proposed SPRT chart.

Optimal Bivariate Order-Replacement Policies for a Multi-State Repairable System with Reliability Constraint

A bivariate order-replacement policy for a multi-state repairable system with imperfect repair is put forward in this paper, where the decisions on when to order a spare part and when to place a replacement are based on the number of failures. The geometric processes are generalized to depict the characteristics that the successive working times are shorter and shorter while the consecutive repair times are longer and longer. According to the renewal reward theorem, a constrained optimization model for the order-replacement policy is formulated, in which the aim is to minimize the expected long-run cost rate (ELRCR) under the constraint that system availability is not less than a predetermined availability requirement. General representations of the ELRCR and system availability are derived and an approximation result of the optimization model is given under certain assumptions. Illustrative examples are provided to validate the applicability of the proposed order-replacement model and show the advantage of the order-replacement policy for the multi-state repairable system.

Availability and cost models for sequentially inspected systems with dependent catastrophic and soft failures

This paper introduces a novel availability and cost model designed for competing-risk systems that integrate interdependent catastrophic and soft failures. Catastrophic failures halt system operations instantly, while soft failures result in efficiency reductions. The linkage between these failure types is reflected in the fact that each soft failure instantly raises the hazard rate of catastrophic failure. The system under consideration is inspected sequentially wherein upon detecting a soft failure; an immediate minimal repair is performed. After a repair, the system is inspected again in the aforesaid way. If a catastrophic failure is discovered, the system is replaced immediately. This paper formulates expressions for upper and lower reliability limits by incorporating these aspects. Furthermore, it presents theorems that establish bounds for point availability, long-run availability, and the average long-run cost rate. The proposed framework’s validity is confirmed through a numerical case study involving a refrigerator. The outcomes highlight the effectiveness of the model in addressing systems vulnerability to interdependent failures and provide insights into its application.

Strategic choices of migrants and smugglers in the Central Mediterranean sea.

The sea crossing from Libya to Italy is one of the world's most dangerous and politically contentious migration routes, and yet over half a million people have attempted the crossing since 2014. Leveraging data on aggregate migration flows and individual migration incidents, we estimate how migrants and smugglers have reacted to changes in the border enforcement regime, namely the rise in interceptions by the Libyan Coast Guard starting in 2017 and the corresponding decrease in the probability of rescue to Europe. We find support for a deterrence effect in which attempted crossings along the Central Mediterranean route declined, and a diversion effect in which some migrants substituted to the Western Mediterranean route. At the same time, smugglers adapted their tactics. Using a strategic model of the smuggler's choice of boat size, we estimate how smugglers trade off between the short-run payoffs to launching overcrowded boats and the long-run costs of making less successful crossing attempts under different levels of enforcement. Taken together, these analyses shed light on how the integration of incident- and flow-level datasets can inform ongoing migration policy debates and identify potential consequences of changing enforcement regimes.

Estimating the Long-Run Cost Function of the Potato Crop in Al-Nasr and Al-Salam Sub-District for the Fall Season 2021

The research aims to estimate the long-term cost function of the potato crop for the Fall harvest (2021), and calculate the optimal size of production, the optimal area, and the output supply function, The research relied on the cross-sectional data obtained by the researcher through the personal interview, and it included 181 farms out of 599 farms, which constitute 30.2% of the total farms in Al-Nasr and Al-Salam district, according to the statistics of the study area division, The research used Eviews 10 and Excel software to estimate the long-run cost function and represent its economic derivatives, The results showed that the optimal cost-reducing production volume is 5663.33 kg/dunum, and the average actual production volume was 5484.80 kg/dunum, The optimal area of the field is 24.35 dunums, while the average actual area was 4.06 dunums, The study showed that the lowest price that a farmer can offer his crop is 195.642 thousand dinars / ton, The results also showed that more than half of the sample farms operate according to economies of scale, The study recommends the necessity of cultivating at optimum sizes and taking advantage of economies of scale to reduce waste in costs to the least possible.

Implications of Bank Equity Price Declines for Inflation

This Economic Commentary examines the relationship between bank equity price index returns and inflation in advanced economies. While large declines in bank equity price indices are generally followed by declines in the ratio of bank credit to GDP, a measure of credit supply, and economic activity as measured by GDP, they have essentially no effect on inflation. These findings suggest that the collapse of several regional banks in early 2023 would not, on its own, put downward pressure on inflation.

The Long-Run Costs of Higher Inflation

This Economic Commentary provides an overview of several frictions and the channels through which they affect economic welfare under elevated trend inflation above 2 percent. These frictions, associated with financial transactions, price and wage stickiness, and cognitive limitations, suggest that inflation imposes significant costs on society. Higher inflation may lead to a steeper Phillips curve, a situation which increases the volatility of inflation and interest rates.

Dynamic analysis of healthcare providers’ cost efficiency

ABSTRACT This study uses quarterly longitudinal data to examine the cost efficiency of 20 New Zealand District Health Boards between 2011 and 2018. A random-effects dynamic stochastic frontier model is applied to estimate the persistence of Health Boards’ cost efficiency while considering both observed and unobserved heterogeneity. The findings reveal that New Zealand Health Boards, on average, spent approximately 7.5% more than the estimated costs of efficient operation, primarily due to high persistence in cost inefficiency. Notably, Health Boards serving rural areas faced even higher levels of long-run cost inefficiency, resulting in an overspending of about 15% of annual budgets. The results of this study highlight that most Health Boards demonstrated excellent short-term performance relative to the long-run equilibrium level of cost inefficiency. However, the more significant concern lies in high long-run cost inefficiency within the sector attributed to structural and regulatory issues. Policymakers are urged to address these underlying problems to improve overall cost efficiency in the health sector.

Condition-Based Maintenance for Performance Degradation Under Nonperiodic Unreliable Inspections

With the development of monitoring technology, increasing attention has been paid to condition-based maintenance (CBM). Also, if condition information for maintenance can be obtained with fewer inspections, the cost of the entire maintenance process could be reduced. However, in application, the monitoring equipment cannot maintain always a reliable operating state, for example, due to various uncertain factors, such as sensor errors, component tolerances, and environment disturbances, the inspections from the sensors are often unreliable. Motivated by these simple observations, we propose a non-periodic condition-based maintenance policy under unreliable inspections. The time interval of the non-periodic inspections is obtained via an inspection scheduling function. The unknown parameters of the component degradation process are updated by gradient descent, while simultaneously the maintenance decision variables are adjusted. A catastrophe strategy-based particle swarm optimization is used to set the optimal decision variables by minimizing the long-run cost rate. Application to laser degradation data illustrates the effectiveness of the proposed method.

Economics of in-space industry and competitiveness of lunar-derived rocket propellant

Economic parameters are identified for an in-space industry where the capital is made on one planet, it is transported to and teleoperated on a second planet, and the product is transported off the second planet for consumption. This framework is used to model the long-run cost of lunar propellant production to help answer whether it is commercially competitive against propellant launched from Earth. The prior techno-economic analyses (TEAs) of lunar propellant production had disagreed over this. The “gear ratio on cost” for capital transport, G, and the production mass ratio of the capital, φ, are identified as the most important factors determining competitiveness. The prior TEAs are examined for how they handled these two metrics. This identifies crucial mistakes in some of the TEAs: choosing transportation architectures with high G, and neglecting to make choices for the capital that could achieve adequate φ. The tent sublimation technology has a value of φ that is an order of magnitude better than the threshold for competitiveness even in low Earth orbit (LEO). The strip mining technology is closer to the threshold, but technological improvements plus several years of operating experience will improve its competitiveness, according to the model. Objections from members of the aerospace community are discussed, especially the question whether the technology can attain adequate reliability in the lunar environment. The results suggest that lunar propellant production will be commercially viable and that it should lower the cost of doing everything else in space.

Optimal block replacement based on expert judgement method

Applying the theory of uncertainty is a good approach to study the reliability of a system when there is a little frequency of suitable data. Based on this theory, the policy of block replacement with minimal repair is considered assuming the system lifetime follows a power law process. The unknown parameters are estimated according to evidence theory that affects the epistemic uncertainty. The Dempster-Shafer as well as Yager rules are applied to aggregate the judgements and mental estimates of two or more experts. After determining the unknown parameters, a judgement interval is derived for the optimal replacement time using the long-run cost criterion.

Designing optimal proactive replacement strategies for degraded systems subject to two types of external shocks

This article mainly investigates a proactive replacement policy for a stochastically deteriorating system concurrently subject to two types of shocks. First, the closed-form representation of system reliability function suffering from both a degradation process and environmental shocks is derived based on the degradation-threshold-failure (DTS) modeling framework. An age- and state-dependent competing risks model with mutual dependence between the two failure processes is embedded into system reliability modeling, where two types of shocks are taken into consideration upon arrival of an external shock including a minor one and a major one. Based on which, a bivariate maintenance policy is put forward for the deteriorating system, where the system is proactively replaced before failure at a planned time, or at an appropriate number of minimal repairs, whichever takes place first. The expected long-run cost rate (ELRCR) is formulated, and optimal solutions are evaluated analytically for two special cases. Finally, an illustrative example is redesigned to validate the theoretical results, exploring the significance of two types of shocks and mutual dependence in system reliability modeling, and illustrating the potential applications in maintenance decisions in various manufacturing systems.

Availability modeling of systems incorporating uncertainty & multiple failure modes using critical repair time & copula

This paper investigates the availability of a system incorporating uncertainty in the inspection period, including multiple failure modes (FMs). We decrease or increase the inspection period depending on the occurrence or nonoccurrence of system failure during any particular inspection, i.e. if, during an inspection, a defect is detected, we reduce the inspection period for the next inspection, and if no defect is found, we increase the inspection period. Also, the proposed model is examined under a pre-defined critical repair time incorporating the Gumbel-Hougaard copula. This paper considers a repairable system having α number of FMs. Random failure times are associated with every single FM, and whenever the system collapses from the ath FM, a subsequent corrective repair is conducted, which requires a random amount of time (a = 1, 2,…, α). Then the point and long-run availability of the proposed model are derived, and a sensitivity analysis is done to examine how inspection time affects the system’s availability. Additionally, the system’s average long-run cost rate is analyzed, and the model is employed to determine the optimal inspection period that optimizes the system’s ALRCR. Lastly, the results are verified via a numerical illustration of a power transformer.

EMISSIONS TAX AND EXECUTIVE COMPENSATION: A PUBLIC–PRIVATE JOINT MECHANISM TO PROMOTE ENVIRONMENTAL AND ENERGY MANAGEMENT

It is widely accepted that a market-based instrument such as a tax on greenhouse gas emissions is effective in motivating firms to improve energy efficiency, environmental management and invest in environmentally-related research and development (R&D). However, modern corporations tend to separate ownership and management, and decision-making executives who are myopic may not share the firm owners’ concern about their firm’s exposure to long-run costs and risks associated with climate change. Hence, executive wage contracts should include rewards for environmental performance, particularly in energy efficiency and developing R&D to reduce emissions. This paper examines the effect of implementing executive compensation that is partially indexed to abatement in a monopolist firm, in which decision-making is delegated to a manager under an emissions tax policy. In equilibrium, it is shown that the new wage compensation leads to more abatement, greater production of output, and higher wages for the manager compared with a conventional wage scheme where wages are solely indexed to profits. Hence, the government imposes a lower emissions tax on the firm. More importantly, this public–private joint mechanism results in net social welfare improvement in equilibrium. However, whether the monopolist’s profit is higher in the new wage scheme depends non-monotonically on the abatement efficiency technology and the extent of wage indexation to profitability.

Strategic Successive Refinement With Interdependent Decoders Cost Functions

In decentralized and decision-oriented communication paradigms, autonomous devices strategically implement information compression policies. In this work, we study a strategic communication game between an encoder and two decoders. An i.i.d. information source, observed by the encoder, is transmitted to the decoders via two perfect links, one reaching the first decoder only and the other reaching both decoders, as in the successive refinement setup. All three communicating devices are assumed to be rational, i.e. they want to minimize their respective cost functions, that depend on the source variable and the output symbols of both decoder. The game takes place as follows: the encoder commits to implementing an encoding strategy which induces a Bayesian game among the two decoders. The encoder is the Stackelberg leader and the two decoders are the Stackelberg followers, they select simultaneously the output sequences that minimize their respective long-run costs. We characterize the asymptotic behavior of the long-run optimal cost of the encoder, when the decoders implement decoding strategies that form a Bayes-Nash equilibrium. We show that this optimal cost converges to a single-letter expression which involves two auxiliary random variables and single-letter incentive constraints of the decoders.