Lifetime Of Equipment Research Articles

Smart PV Monitoring and Maintenance: A Vision Transformer Approach within Urban 4.0

The advancement to Urban 4.0 requires urban digitization and predictive maintenance of infrastructure to improve efficiency, durability, and quality of life. This study aims to integrate intelligent technologies for the predictive maintenance of photovoltaic panel systems, which serve as essential smart city renewable energy sources. In addition, we employ vision transformers (ViT), a deep learning architecture devoted to evolving image analysis, to detect anomalies in PV systems. The ViT model is pre-trained on ImageNet to exploit a comprehensive set of relevant visual features from the PV images and classify the input PV panel. Furthermore, the developed system was integrated into a web application that allows users to upload PV images, automatically detect anomalies, and provide detailed panel information, such as PV panel type, defect probability, and anomaly status. A comparative study using several convolutional neural network architectures (VGG, ResNet, and AlexNet) and the ViT transformer was conducted. Therefore, the adopted ViT model performs excellently in anomaly detection, where the ViT achieves an AUC of 0.96. Finally, the proposed approach excels at the prompt identification of potential defects detection, reducing maintenance costs, advancing equipment lifetime, and optimizing PV system implementation.

Alumina coatings on Ni-based superalloys: The impact of annealing on heavy oil fouling

As the sweet crude oil reserves decline, refiners must treat sulfur-rich heavy oil, requiring harsher operating conditions, which are detrimental to process equipment. Application of coatings on critical components protects surfaces against sulfidation, corrosion, and fouling, extends the equipment's lifetime, and reduces the frequency of costly turnarounds. In the present work, we coated Inconel 625 and Inconel 718 substrates with amorphous alumina thin films at room temperature using reactive RF magnetron sputtering. Annealing of the deposited coatings at 800, 900, and 1000 °C increased hardness, improved adhesion, and generated crystalline polymorphs, predominantly γ-Al2O3 at lower temperatures, while α-Al2O3 was present at 1000 °C. The annealed substrates formed thermally grown oxides (TGOs), which interacted with the alumina coatings. The TGOs followed grain boundaries in the case of IN718 and a crater-like pattern on IN625. Annealed substrate precipitates generated columnar-like protrusions responsible for inducing crack propagation, which exhibited TGO formation. After 2 h exposure to heavy oil (containing 0.06 g g−1 sulfur) at 450 °C and 11.3 MPa the as-deposited amorphous alumina presented no clear sign of adherent fouling, while the 1000 °C annealed crystalline alumina surfaces presented evidence of fouling.

Sustainable procurement of medical devices in an international context - Part 3

Background and Objectives This article is the third in a series of three manuscripts published in this journal. It aims to describe how sustainable procurement of medical devices (MDs) can be implemented in operational projects in the context of developing countries. It also further details how the biomedical/clinical engineer lead (BCEL) in charge of technical support during the MD procurement process can apply sustainability principles and concepts of value-based procurement. Material and Methods Based on the authors’ experience of more than 20 years in procurement projects and implementation of MDs, the role of the BCEL will be developed from a theoretical point of view with the description of the second and third pillars of a sustainable purchase following the needs assessment: the assessment of existing conditions along with local capacities and the evaluation of the use conditions during the lifetime of the medical equipment. The application of these principles in operational projects will be further discussed by analyzing literature and lessons learned from projects implemented in developing countries. Results/Proposal The BCEL has a key role in the sustainable procurement of MDs to design the technical specifications of the goods, related services, and post-sales conditions to maximize the benefit of the investment. As the specialist can analyze the local existing conditions and capacities while ensuring efficient use of the MDs during their lifespan, they can contribute to a sustainable implementation of MDs in developing countries. The BCEL shall also be able to analyze the local and international markets to find all possible technological solutions that meet the needs, local conditions, and capacities and ensure quality use during the lifespan of the purchased MD. The BCEL shall have competencies in identifying all the risks related to the use of the MD from the safety risks linked to its installation, use, and maintenance to the sustainability risks linked to obtaining the conditions that guarantee the use of the device and maintaining them as long as possible. Examples of these conditions include the presence of qualified and trained users, availability of maintenance and consumable budgets, availability and maintenance of infrastructure conditions (access, electrical power, water, drainage, medical gasses, etc.), and last but not least, presence of patients requiring a diagnosis or treatment using the purchased MD who were identified during the evaluation of the first pillar: a sound needs assessment. Conclusion As an evolution of the BCEL’s traditional biomedical and clinical engineering work, he/she shall assume the responsibility to guarantee the sustainability of the MD purchase. This quality assurance and control role is achieved by a sound theoretical background knowledge based on the three sustainable procurement pillars: the needs, existing and lifetime use conditions assessments, the analysis of the local and international markets, and a broad understanding of sustainability risks.

Analyisis Of Boiler Reliability Maintenance System With Availability Ratio At PT. XXX

This study investigates a food manufacturing firm's efforts to enhance operational efficiency by optimizing its maintenance strategy and spare parts management within the context of noodle production. The research focuses on reducing prolonged machine downtimes caused by boiler malfunctions, which negatively impact production targets. A novel approach combining total minimum downtime calculations and a hybrid corrective-preventive maintenance methodology has been proposed. To bolster this initiative, an efficient spare parts procurement scheme was implemented. Results demonstrate a substantial reduction in unplanned downtime following implementation, thereby improving overall productivity and profitability. Implications highlight the potential for widespread application across similar industries seeking to minimize disruptions while maximizing equipment lifetimes. highlight : Reduced downtime through improved boiler maintenance. Hybrid corrective-preventive maintenance for efficient operations. Optimized spare parts procurement for enhanced productivity. Keywords: noodle production, boiler maintenance, downtime reduction, spare parts management, hybrid maintenance.

Critical penetrating vibration evolution behaviors of the gas-liquid coupled vortex flow

The gas-liquid coupled vortex flow (GCVF), as a complex physical phenomenon, has been encountered in some sustainable productions, such as chemical cleaner production, continuous steel pouring processes, and energy conversion in the tidal power plant. Its critical penetrating state recognition is essential to improve sustainable production efficiency and equipment lifetime. Due to the gas-liquid coupling transport and fluid nonlinear excitation, the state recognition oriented to the GCVF critical penetrating still faces significant challenges. To address the above matter, a fluid-structure coupling modeling and solution method based on the level set and residue theorems is put forward to obtain the GCVF-induced vibration evolution mechanism at the critical penetrating state. A wavelet packet-based signal processing method is proposed to obtain the evolution law of the peak component of the GCVF-induced vibration. Research results found that the proposed modeling and method can better reveal the GCVF dynamic evolution regularities in the critical penetrating state. The GCVF-induced vibration exhibits energy peak and complex nonlinear pulse characteristics in the critical penetrating process. The relevant research work can provide multi-source sensing data support for the research and development of a fluid-induced vibration detection system, laying the foundation for sustainable metallurgy production, chemical cleaner extraction, and hydroelectric energy conversion.

The Potential Material Flow of WEEE in a Data-Constrained Environment—The Case of Jordan

The rising concerns about electric and electronic equipment waste (WEEE) come from the rapid increase in demand for appliances and the decreasing lifetimes of equipment. Setting a sustainable WEEE management system that exploits this secondary resource is paramount to maximize resource efficiency, mitigate its environmental impact, and stimulate the circular economy. This paper aims, for the first time, to quantify the material flow expected from recycling the generated WEEE, propose the number of plants required to recycle this secondary resource, and outline the expected economic and environmental benefits that could be achieved from recycling operations. The findings of material flow calculations show that the amount of steel, copper, and aluminum is predominant in the WEEE composition. Also, the expected metal content in WEEE in 2022 is approximately 26 kt, 3.3 kt, and 2.5 kt, respectively. These are expected to substantially increase to approximately 109 kt, 11.9 kt, and 9 kt for the three metals in 2050, respectively. Other valuable metals are doubling their quantities between 2022 and 2050 to reach approximately 1133 kg silver and 475 kg gold. Approximately, four treatment plants are required to recover these materials in 2030 with relative installation costs of USD 100 million. The forecasted financial revenues of recovering materials included in WEEE and indicators for environmental impact based on life cycle assessment (LCA) are calculated. The results of this study can serve as a preliminary reference for future usage in guiding effective planning for WEEE recycling and sustainable management in the country.

Computation Offloading Strategy Optimization with Multiple Heterogeneous Servers in Mobile Edge Computing

Computation offloading from a user equipment (UE) to a mobile edge cloud (MEC) is an effective way to ease the computational burden of mobile devices, to improve the performance of mobile applications, to reduce the energy consumption and to extend the battery lifetime of mobile user equipments. In this paper, we consider computation offloading strategy optimization with multiple heterogeneous servers in mobile edge computing. Queueing models are established for a UE and multiple heterogeneous servers from different MECs, and the average task response time of the UE and each MEC server and the average response time of all offloadable and non-offloadable tasks generated on the UE are rigorously analyzed. Three multi-variable optimization problems are formulated, i.e., minimization of average response time with average power consumption constraint, minimization of average power consumption with average response time constraint, and minimization of cost-performance ratio, so that computation offloading strategy optimization, power-performance tradeoff, as well as power-time product can all be studied in the context of load balancing. An efficient numerical method (which consists of a series of fast numerical algorithms) is developed to solve the problems of minimization of average response time with average power consumption constraint, minimization of average power consumption with average response time constraint, and minimization of cost-performance ratio. Numerical examples and data are also demonstrated to show the effectiveness of our method and to show the power-performance tradeoff, the power-time product, and the impact of various parameters. To the best of the author's knowledge, this is the first work in the literature that analytically addresses computation offloading strategy optimization with multiple heterogeneous servers in mobile edge computing.

Anomaly detection using electrical signature analysis and machine learning:application to a CNC mill.

Electrical Signature Analysis (ESA) is a powerful tool that uses the voltage and current signals of a machine to infer its health status. ESA can serve as a predictive maintenance tool for detecting common faults at an early stage, thus preventing expensive catastrophic failures and production outages, and extending equipment lifetime. In this study, a novel application of ESA and Machine Learning (ML) for working condition monitoring and health status assessment of a CNC mill is presented. Experimental results show the effectiveness of the proposed approach.

Recovery of Fluorinated Refrigerants from Decommissioned RAC Equipment in Germany—Implications for National Emission Reporting under the UNFCCC

Germany is obliged to report emissions of fluorinated greenhouse gases annually under the UNFCCC. This includes emissions of fluorinated refrigerants when decommissioning RAC equipment. To obtain this information, data on the recovery, recycling, and disposal of fluorinated greenhouse gases is necessary, but such data are scarce. The VDKF-LEC database contains information on the recovery of fluorinated refrigerants from decommissioned RAC equipment in Germany and an extracted dataset was used to obtain real-world information for the years 2017 to 2021. Recovery rates for different fluorinated refrigerants from decommissioned commercial and industrial refrigeration as well as stationary air-conditioning equipment were derived. Furthermore, average lifetimes of equipment for the different sectors were calculated. In the analysis, a dependency of charged refrigerant and age of the unit at decommissioning could be observed. Results from the analysis of the VDKF-LEC dataset were compared with reported data under the UNFCCC for Germany and other available data sources.

Analysis of physicochemical and tribological properties of nano alumina-based gear oil developed from effluent of lube oil blending plant

Industrial wastewater, also known as effluent has been identified as one of the leading sources of environmental pollutions worldwide. The establishment of lube oil blending plants in Nigeria has led to a continuous discharge of industrial effluent in densely populated areas. This threatens the well-being of humanity, plants, aquatic lives and construction soils. This research paper focused on developing a nano alumina-based effluent gear oil from effluent of lube oil blending plants as an alternative means of mitigating its threats on the environment. Nano lubricant are used in gearboxes for better thermal, friction and anti-wear properties. This is due to the small size and high specific surface area to volume ratio of the nanoparticles. Furthermore, due to their excellent mechanical and thermal properties, easy dispersal in most fluids, inexpensiveness, ease of manufacture, and aspect ratio, the Al2O3 nanoparticles are recently being used by researchers as an additive in gear oils to improve tribological properties, increase power efficiency, extend equipment lifetimes, and lower operating cost. In this work, the alumina nanoparticle was synthesized using co-precipitation method, after which it was characterized using Fourier Transform Infrared (FTIR) and X-ray Diffraction (XRD) analysers. After the development of Al2O3-based gear oil from the effluent, the physicochemical and tribological properties of the alumina-based effluent gear oil samples were investigated with varied weight percentages of Al2O3 nanoparticles. The Differential Scanning Calorimetry (DSC) and Computational Fluid Dynamics (CFD) thermal analyses of nano alumina-based gear sample was investigated after obtaining the suitable sample among the sample blends developed. The dispersion of the nanoparticle in the effluent oil improved the specific gravity and pour point whereas a slight reduction was observed in kinematic viscosity at 100 °C, viscosity index and flash point. However, viscosity index and flash point values are conforming to the minimum requirements of API EP 85W90 and ISO 100 standard values. The anti-wear property was observed to significantly improved by 26.14%, at 0.4 wt% nanoparticles concentration. The results showed that, the pure effluent oil recovered is more thermally stable than the 0.4 wt% nano alumina-based effluent gear oil sample, whereas the nano gear oil sample has a higher thermo-oxidative stability than the pure effluent oil. Finally, temperature profiles from the simulation results also ensured a better performance of the 0.4 wt% alumina-based effluent gear oil developed, at 1500 rpm speed of rotation by 6.7% and 8.9% and at 4000 rpm is by 5.9% and 7.8% than the API EP 85W90 and pure effluent oil samples respectively. Hence, based on the results obtained, the study indicated that the effluent oil from lube oil blending plants can be used as gear oil with the dispersion of alumina nanoparticles.

On the impact of tidal generation and energy storage integration in PV-rich electric distribution systems

Deep decarbonization of power system operations requires the maximal utilization of available renewable resources. At distribution-level operations, however, grid operators can face numerous challenges in integrating renewables at scale owing to the inherent intermittence of renewable energy resources. These include phenomena such as voltage fluctuations, which are typically mitigated through control actuators such as on-load tap changers (OLTC) as well as energy storage devices, such as battery energy storage systems (BESS). On the one hand, high intermittence of the available renewable portfolio may require increasingly aggressive control of actuators, thereby accelerating the probability of equipment failure. On the other hand, integrating BESS operations and having a diverse renewable generation portfolio can typically help stagger power/energy flow to mitigate the aforementioned adverse impacts. In this paper, we employ a Bayesian framework for equipment lifetime estimation to understand the impact of including tidal energy resources and BESS in distribution system operations for feeders having substantial distribution photovoltaic generation. Our results indicate that while tidal energy alone may slightly decrease equipment reliability, the adverse impact on reliability is significantly magnified by a generation portfolio consisting of tidal generation and photovoltaic generation. We also study the tidal and photovoltaic hosting capacity problem with and without energy storage systems using equipment reliability as an added constraint. We conclude that energy storage increases the reliability-constrained hosting capacity of the distribution system.

Review of Micro Hydro Power Plant (MHPP) as a Solution to Reach Remote Areas of Electricity

A micro hydro power plant (MHPP) is a small-scale power plant that converts the potential energy of the air into mechanical work, turning turbines and generators to generate electrical power. Small scale, which is around 0-100 kW. The construction of a Micro-hydro Power Plant (MHPP) is an alternative supply of electrical energy, especially in rural areas that are not covered by the electricity grid State Power Plant. MHPP has a high potential as an alternative to renewable energy sources. Thus, the reliability of the system built is a must forget quality electricity. In a power plant, what is considered is the stability of the output voltage generated by the generator; this is necessary to keep the consumer's equipment from being damaged. Unstable voltage can also Age-reduce equipment (lifetime) owned by consumers.
 Keywords: Micro Hydro Power Plant 2; Alternative, 3; Electric Power

Performance of high-concentration photovoltaic cells cooled by a hybrid microchannel heat sink

The electrical performance and equipment lifetime of high-concentration photovoltaic cells depends heavily on efficient cooling. In this paper, we applied a hybrid configuration to the cooling of a high-concentration photovoltaic cell, an innovative pattern derived from a comprehensive study on the combination of oblique microchannel and micro pin fin. Results from this study found that an elliptical pin fin pattern conforming with streamlines most effectively removed heat flux with a Nusselt number of 65.44 at a Reynolds number 1250. Then, the performance evaluation of a photovoltaic cell with a concentration ratio of 1000 was carried out on the hottest day of each season in Shiraz under actual boundary conditions. With an average flow rate of 30 ml/min in the spring, the implementation of this hybrid design resulted in the photovoltaic cell achieving an electrical efficiency of 40.16 while still maintaining a constant surface temperature of 301 K. Unlike a straight microchannel, which failed to maintain a constant cell temperature throughout summer’s hottest hours, this hybrid configuration succeeded in sustaining cooling with an average flow rate of 90 ml/min. In the winter and autumn, the pump’s average power consumption required for cooling was about 25 and 38 mW, respectively. Moreover, the maximum output electrical power in the summer was 2.8 W, with pumping power contributing to 1500 mW.

Hydrophilic Nature of Polytetrafluoroethylene through Modification with Perfluorosulfonic Acid-Based Polymers

Polytetrafluoroethylene (PTFE), commercially known as Teflon, is a fluoropolymer with a structure containing (CF2–CF2)n. It has high resistance to acids, alkalis and corrosive chemicals. PTFE is hydrophobic in nature with a water contact angle of 140°. Being hydrophobic in nature is a knotty problem, particularly in electrical applications, as it may lead to short circuits and result in reducing the lifetime of electrical equipment. Herein we describe the surface modification of PTFE from hydrophobic to hydrophilic without altering its bulk property. The surface hydrophilicity is achieved by two different techniques, viz., polymer coating (aquivion and nafion) and plasma treatment. Several characterization techniques including FTIR, Raman, XPS, WCA and SEM were used to analyze the surface of PTFE. It was found that 5% of the polymer solution and N2 plasma treatment for 2 min can produce huge differences in the surface property, as evidenced by the reduction in water contact angle from 140° (neat Teflon) to 80° (surface-modified Teflon). The surface morphology of neat PTFE is completely changed and collapsed as evidenced by the SEM images. The FTIR, Raman and XPS analyses confirm the presence of additional hydrophilic functional groups after the polymer coating and plasma treatment. Hence, this method represents a unique approach to modifying the surface property of Teflon, while maintaining its bulk property.

A framework for the assessment of optimal and cost-effective energy decarbonisation pathways of a UK-based healthcare facility

In light of the global energy and climate crises, integration of low-carbon technologies into energy systems is being considered to mitigate the high energy costs and carbon footprint. The wide range of available capacities, efficiencies, and investment costs of these technologies and their different possible operating schedules can unlock several pathways towards decarbonisation. This paper presents an optimisation framework for a public healthcare facility to determine the optimal operation schedule of the site's energy system. A detailed techno-economic analysis of low-carbon power generation, conversion, and energy storage technologies that can be incorporated into the system based on real historical data was carried out for different scenarios. The results reveal that a heat pump with a capacity of 1800 kW can replace gas boilers on-site to meet the heat demand while recovering the investment in 5 years and providing an operating and carbon cost saving of 22.47% compared to the base case. The analysis shows that a more electrified mode of operation is favoured during high gas prices, thus making electrical energy storage more attractive than thermal energy storage. While handling real data, the optimisation algorithm was sensitised to discriminate conventional energy supplies from clean energy sources by considering their carbon impact so that it minimises energy bills in a smart and eco-friendly way. The optimisation algorithm and the subsequent techno-economic analysis provide a comprehensive framework to decision-makers for facilitating energy investment decisions. The framework can be used based on the short and long term goals of the energy system, visualising the evolution of financial benefits over equipment lifetime, and understanding the environmental impacts of integrating renewable energy.

Theoretical and experimental investigation of reverse osmosis (RO) desalination solar system using the solar panel, battery, and water turbine for high-pressure recovery of output brine

Drinking water shortage is one of the most critical risks threatening current communities. The number of freshwater resources is decreasing due to industrialization and population growth in addition to unprecedented consumption. Brine desalination processes are the solution that helps to overcome this crisis. Among desalination techniques, reverse osmosis (RO) is the leading technique in this field. In this study, we investigate a desalination system, a photovoltaic/water turbine (PV/WT) panel based on the RO technique to provide the water required for several rural families living in Ilam at a small scale. This paper examines the exergy and economic analysis to measure the lifetime of equipment by using ESS Software. Results show that the lifetime of equipment equals 350, 73, 183, and 360$ for PV, WT, battery (B), and RO, respectively. On the other hand, the output rate of the PV panel and RO purification machine equals 12% and 35%, respectively. Also, three hybrid arrangements are examined: PV + RO, PV + B + RO, and PV + WT + B + RO, and the most efficient arrangement is introduced in which, the maximum water desalination volume is 150L per day, and the TDS rate of output water is decreased up to 120 ppm, and the produced drinking water throughout the project equals 25 m3. Moreover, solar and WT panels generate 120 and 20 kw/h of electricity over the project time, respectively.

Sludge Reduction and Surface Investigation in Electrochemical Machining by Complexing and Reducing Agents

Electrochemical machining (ECM) is widely applied to manufacture parts with complex geometries, used in electronic components and the automotive, military, and aeronautics industries. These parts have a surface shaped by controlled anodic dissolution at high current density levels, using a neutral solution of inorganic salts (i.e., NaCl or NaNO3) as the electrolyte. Such conditions generate a high amount of sludge that deposits onto the surfaces of equipment, devices, cathodes, and working pieces, requiring daily and complicated sludge management during the series production in the industry. Thus, the main goal of the present work is to propose a simple way to reduce sludge generation in the ECM industrial process. To do so, complexing (EDTA) or reducing (ascorbic acid) agents were added to the electrolyte composition, creating parallel reactions to keep the metallic ions from precipitating. The complexing agent EDTA resulted in a 30% reduction in sludge mass, using an alkaline solution (pH > 10.0). The reducing agent, ascorbic acid, resulted in a 90% reduction in sludge mass, using an acidic solution (pH < 5.0). This sludge reduction has the potential to contribute significantly to increasing equipment, devices, and cathode lifetime, as well as reducing costs associated with centrifuge or filter maintenance (sludge removal from electrolyte) and increasing the productivity of industrial ECM processes.

Methods to improve reliability and operational flexibility by integrating hybrid community mini-grids into power systems

Decarbonization and decentralization are major trends in the transformation of conventional power systems. The increase of the penetration of renewable electricity generation into generation mix contributes to the reduction of greenhouse gas emissions. At the same time, one has to ensure that the reliability and operational flexibility as measured by respective metrics meet specified standards. This calls for a solution of a set of engineering, economic, and institutional problems, the list of which depends on the features specific to countries and regions in question. This is due to differences in the requirements established by technical regulations, the rules governing wholesale and retail electricity and capacity markets, the mix of electricity consumption, as well as the principles underpinning the management of capacity expansion and operation of power systems. The purpose of this article is to provide the rationale for the feasibility and efficacy of integrating hybrid community mini-grids into power systems. The balance of community mini-grids in terms of power and capacity allows them to operate both in the grid-connected and islanded modes without disrupting power supply to consumers. The main sources of electricity in hybrid community mini-grids are distributed generation (DG) facilities, including those based on renewables as well as energy storage systems (ESS). Load dispatching of community mini-grids is performed by an intelligent automatic control system (ACS) governed by decentralized algorithms, which provides coordinated operation of emergency control and power flow automatics. Integration of community mini-grids into power systems can be accomplished through several transmission lines that form an interconnection. The controlled flow of power through such an interconnection allows for significant system-wide technical and economic effects. We propose a technique to provide the rationale for the efficacy of creating community mini-grids. The technique is based on calculations of reliability metrics. The integration of hybrid community mini-grids into power systems makes it possible to increase the availability and uninterrupted supply of electricity to consumers, as well as the lifetime of power grid equipment.

Valuation of used machinery based on the new model of its degradation

We propose a new model of equipment degradation. In it, the machine is subjected to random latent failures, the danger of which depends on the equipment condition and after each failure the intensity of the equipment's benefits decreases by a random amount. Equipment that brings negative benefits is subject to decommissioning. The model parameters are found based on known information about the average value and the coefficient of variation of the equipment lifetime. Market value of equipment is determined by discounting the flow of benefits from its future use. This allows us to find the dependence of the equipment’s market value on the benefits it brings. Assessing the market value of new equipment is usually not difficult, but it is much more difficult to do this for used equipment items. Appraisers are usually unable to estimate the value of the work performed by equipment, and when valuing a used equipment, they have to rely on its age. To do this, the market value of a similar new equipment is usually reduced by a depreciation factor or multiplied by Percent Good Factor (PGF, relative value), depending on the age of equipment being valued. However, equipment of the same age may be in different conditions and, therefore, have a different market value. Therefore, such PGFs, in fact, relate to the average equipment that has survived to the appropriate age. Appraisers determine them by formulas or tables that are usually not supported by proper justifications. The proposed model makes it possible to build the dependence of the average PGF on age and calculate the market value of the work performed by machines, even if such works are not traded on the market. It turns out that it is possible to take into account the influence of the utilization cost of the machine and inflation in the model. The results of experimental calculations performed using the model (with calibration parameters selected appropriately) are in good agreement with the market prices of some types of construction equipment.

Likelihood Maximization of Lifetime Distributions With Bathtub-Shaped Failure Rate

Equipment lifetime distributions with bathtub-shaped failure rate can be fitted to data by the maximum likelihood criterion. In the literature, a commonly used method is to find a point in the parameter space where the partial derivatives of the log-likelihood function are zero. As the log-likelihood function is typically nonconvex, this approach may yield a suboptimal fit. In this work, we maximize the log-likelihood function, using a multistart of 100 optimization procedures, by three nonlinear optimization algorithms: 1) Nelder–Mead with adaptive parameters; 2) sequential least squares quadratic programming (SLSQP); 3) limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with box constraints (L-BFGS-B). We perform a systematic study of refitting ten key lifetime distributions with bathtub-shaped failure rate from the literature to two widely studied datasets. The multistart nonlinear optimization yields better fits than those reported in the literature in 14 out of 19 distribution-dataset pairs, for which reference parameters are available. Based on the results, if gradient information of the log-likelihood function is available, our recommended optimization algorithm for the purpose is SLSQP.