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The Duane reliability growth model has a number of inherent limitations that make it unsuitable for monitoring reliability improvement progress. These limitations are explored and a model based on variance‐stabilizing transformation theory is explained. This model retains the ease of use while also avoiding the disadvantages of the Duane model. It represents a more useful graphical model for portraying reliability improvement at development team meetings. Computer simulations have shown that the new model provides a better fit to the data over the range of Duane slopes normally observed during a reliability growth program. The instantaneous mean time between failures (MTBF) equation for the new model is developed. Computer simulations show that its use results in higher values of instantaneous MTBF than that achieved by the Duane model. The new model also reduces the total test time for achieving a particular specified instantaneous MTBF. Finally, software failure data from an actual project illustrates the calculations and benefits of the new model.

The purpose of this paper is to focus on determining the optimal sales price for non-instantaneous deterioration items according to consideration of freshness and demand.

In this model, the authors have described the demand function which is dependent on price as well time. The products that the deterioration is considered as non-instantaneous have a determinate shelf life, and their demand rate will decrease over time after the beginning of the selling period. This paper depicts that the total profit of non-instantaneous deterioration items using the dynamic pricing strategy is higher than that using fixed pricing strategy.

Finally, to illustrate and validate the model, the authors have used some numerical examples. A new freshness function and the model to study pricing policy are developed as well applied to solve managerial decision problems.

This paper complements the lack of the existing theoretical research of pricing for non-instantaneous deterioration items under an e-commerce environment. A new freshness function and the model to study pricing policy are developed as well applied to solve managerial decision problems.

The paper aims to estimate the instantaneous breakdown voltage of the lightning discharge from simulated figures in an energized rod-plane configuration protected by a lightning rod. The same configuration of electrodes has been the subject of experimental investigations for the measurement of the instantaneous breakdown voltage using oscillographic monitoring. This study validates the simulation model by making a comparison with experimentation and involves the role of the inception field of the upward discharge in the propagation of this last one.

The research methodology is based on the development of a fractal lightning protection model based on real physical conditions of the discharge propagation, such as the downward discharge and the upward one emanating from protection. The voltage drop and the randomness character of the lightning discharge are also taken into account. The electrical field is an important parameter in discharge development; it is considered in this work at each step of the discharge propagation by the finite element method. The instantaneous breakdown voltage is measured and estimated by both empirical equations and simulated figures of lightning discharge

The established model that allows estimating the instantaneous breakdown voltage from simulated discharges and empirical equations gives results in a good agreement with experimentation. The involvement of the upward discharge inception field emanating from the lightning rod in the evolution of electrical discharge is illustrated.

The work presented in this paper aims to develop a new fractal lightning protection model taking into consideration physical phenomena intervening in the development of the lightning discharge.

The originality of this work consists of the combination between fractals modelling of the electrical discharge and the protection against lightning, in addition, to use one of the characteristics of the electrical discharge, which is the instantaneous breakdown voltage, to prove the importance of the inception field emanating from the upward discharge in the propagation criterion of this last one.

The purpose of this study is to determine distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process.

The law of iterated (or double) expectations is used to determine the mean and variance of the accumulated rate of interest on a cash management (or loan) account when interest accumulates at the instantaneous rates of interest implied by the square root process.

This study demonstrates how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.

This study has strong educational value in determining distributional properties of the accumulated rate of interest when the instantaneous rate of interest evolves in terms of the Cox et al. (1985) square root process and demonstrating how the accumulated rate of interest does not satisfy the strong mixing conditions necessary for convergence in distribution to the normal density function.

Instantaneous unloading with equal force is usually used to simulate the sudden failure of cables. This simulation method with equivalent force requires obtaining the magnitude and direction of the force for the failed cable in the normal state. It is difficult, however, to determine the magnitude or direction of the equivalent force when the shape of the cable is complex (space curve). This model of equivalent force may be difficult to establish. Thus, a numerical simulation method, the instantaneous temperature rise method, was proposed to address the dynamic response caused by failures of the cables with complex structural form.

This method can instantly reduce the cable force to zero through the instantaneous temperature rise process of the cable. Combined with theoretical formula and finite element model, the numerical calculation principle and two key parameters (temperature rise value and temperature rise time) of this method were detailed. The validity of this approach was verified by comparing it with equivalent force models. Two cable-net case with saddle curved surfaces were presented. Their static failure behaviors were compared with the dynamic failure behaviors calculated by this method.

This simulation method can effectively address the structural dynamic response caused by cable failure and may be applied to all cable structures.

An instantaneous temperature rise method (ITRM) is proposed and verified. Its calculation theory is detailed. Two key parameters, temperature rise value and temperature rise time, of this method are discussed and the corresponding reference values are recommended.

The purpose of this paper is to quantify the influence of alternating current (AC) interference on hydrogen evolution reaction of X80 steel.

The hydrogen evolution potential was obtained by cathodic potentiodynamic polarization curve. The instantaneous potential under AC interference was obtained by high-frequency acquisition with three-electrode system. Electrochemical impedance spectroscopy and Tafel polarization curves were used to study the influence mechanism of AC interference on instantaneous potential.

It was concluded that the hydrogen evolution reaction could occur on X80 steel under AC interference. There were critical AC current densities of about 100 to 200 A/m2, beyond which the cathode reaction of X80 steel changed from oxygen absorption to hydrogen evolution. Besides the pH value, the initial polarization potential EZ and impedance module of the steel/electrolyte interface under AC interference were also the factors that affected the critical AC densities in different solutions.

This research quantified the hydrogen evolution capacity of X80 steel under AC interference, which could be applied to clear the effect of AC interference on hydrogen evolution reaction.

At the current stage of electrical technology development, it is relevant to take into account the quality of electrical energy. It can be implemented if an assessed energy quality indicator is available. The amount of electrical energy is determined by active power, which is transmitted over a certain time period. In some cases, reactive power is included in the metering system. The distortion power is justifiably criticized and is not taken into account. The purpose of this paper consists in the substantiation of the indicator of the distortion of the periodic polyharmonic current electrical energy power, by separating from the instantaneous power such harmonics, which formed by same frequencies current and voltage harmonics.

Using the method of calculating linear polyharmonic current circuits, the following quantities are identified in instantaneous power: active, reactive and apparent powers of each harmonic. These components are known from references as canonical.

By the method of instantaneous power harmonic analysis, the components formed by current and voltage harmonics of the same frequency and different frequencies are distinguished.

The RMS value of the instantaneous power due to current and voltage harmonics of different frequencies is justified in the work. This quantity allows you to distinguish the instantaneous power distortion level in comparison with the existing quantity.

The results can be used to assess the level of instantaneous power distortion level in commercial and technical metering systems.

The definition of instantaneous power distortion by extracting the canonical components from it and determining the root mean square value of the remainder is proposed.

The purpose of this paper is to present a 3D finite element model of the electromagnetic fields in an AC three‐phase electric arc furnace (EAF). The model includes the electrodes, arcs, and molten bath.

The electromagnetic field in terms of time in AC arc is also modeled, utilizing a 3D finite element method (3D FEM). The arc is supposed to be an electro‐thermal unit with electrical power as input and thermal power as output. The average Joule power, calculated during the transient electromagnetic analysis of the AC arc furnace, can be used as a thermal source for the thermal analysis of the inner part of furnace. Then, by attention to different mechanisms of heat transfer in the furnace (convection and radiation from arc to bath, radiation from arc to the inner part of furnace and radiation from the bath to the sidewall and roof panel of the furnace), the temperature distribution in different parts of the furnace is calculated. The thermal model consists of the roof and sidewall panels, electrodes, bath, refractory, and arc. The thermal problem is solved in the steady state for the furnace without slag and with different depths of slag.

Current density, voltage and magnetic field intensity in the arcs, molten bath and electrodes are predicted as a result of applying the three‐phase AC voltages to the EAF. The temperature distribution in different parts of the furnace is also evaluated as a result of the electromagnetic field analysis.

This paper considers an ideal condition for the AC arc. Non‐linearity of the arc during the melting, which leads to power quality disturbances, is not considered. In most prior researches on the electrical arc furnace, a non‐linear circuit model is usually used for calculation of power quality phenomena distributions. In this paper, the FEM is used instead of non‐linear circuits, and calculated voltage and current densities in the linear arc model. The FEM results directly depend on the physical properties considered for the arc.

Steady‐state arc shapes, based on the Bowman model, are used to calculate and evaluate the geometry of the arc in a real and practical three‐phase AC arc furnace. A new approach to modeling AC arcs is developed, assuming that the instantaneous geometry of the AC arc at any time is constant and is similar to the geometry of a DC arc with the root mean square value of the current waveform of the AC arc. A time‐stepping 3D FEM is utilized to calculate the electromagnetic field in the AC arc as a function of time.

This paper aims to find a new method that could be applied to the high and mid-grade prosthesis knee joint.

Based on analysis, calculation, modeling, simulation and experimental study of the motion law of knee joint, this paper not only determines the structure and parameters of the knee joint and calculates the instantaneous center but also analyzes the stance stability and completes the optimization. With the help of experimental tests (fatigue test and gait curve test), the quality and performance of the designed knee joint is verified.

The experimental results show that the gait curve of the designed knee joint is much closer to health people. The designed prosthesis knee joint, with adjustable swing speed and gait curve which are close to health limb, has a better performance when compared to the ordinary knee joint with four-bar linkage structure.

This paper developed a prosthesis knee joint based on a novel design method that could be applied to the “high and mid” grade prosthesis knee joint and verified its function on an amputee performed the lower amputation, which could provide theoretical support for researches and designs related to prosthesis knee joint in future.

In any machining process, the surface profile of the workpiece is continuously changing with respect to time and input parameters. In a conventional machining process, input parameters are feed and depth of cut whilst other parameters are considered to be constant throughout the process.

The direct and indirect participation of this instantaneous curvature can be used to optimize the strategy of cutting operation in terms of different parameters like heat generation-induced stresses, etc. The concepts of the metric tensor and Riemannian curvature tensor are made use in this study as a representation of curvature itself. The objective of this study is to create a mathematical methodology that can be implemented on a highly flexible machining process to find an optimum cutting strategy for a particular output parameter.

The study also includes different case studies for the validation of this newly introduced mathematical methodology.

The study will also find its position in other mechanical processes like forging and casting where instantaneous curvature affects various mechanical properties.