In this paper, the probability distribution of wind power from a dispersed array of wind turbine sites is studied considering forced outage rates of wind turbines. The wind speeds at distinct sites are assumed to be dependent and the dependence is modeled by copulas. In particular, the probability distribution of the aggregate power from two sites is exactly derived. The probability distribution of the aggregate power is also derived under the particular case when site 1 consists of n1 identical wind turbines of type 1 and site 2 consists of n2 identical wind turbines of type 2. Numerical results are presented to illustrate the theoretical findings for a chosen copula function.

This paper studies the discrete time component level and system level reliability evaluation by considering a certain protection mechanism that is used to increase reliability. In particular, the discrete time version of the protection mechanism which was previously studied under continuous time setting is considered. An exact matrix-based expression is also obtained for the reliability of the discrete time consecutive k-out-of-n:G system equipped with protection block. The case when the lifetimes have a phase-type distribution is also taken into consideration. The novelty of the paper lies not only in the consideration of the discrete-time version but also in the new formulation of the reliability of the consecutive k-out-of-n:G system having a protection block.

It is important in many respects to have information about the number of failed components in the system when or before a system fails. This paper investigates the mean number of failed components at or before the failure time of the linear consecutive k-out-of-n:F system which is a useful structure to model various engineering systems such as transportation and transmission systems. In particular, closed form expressions for the mean number of failed components within the system that have discretely distributed components lifetimes are obtained. The results are used to estimate the unknown parameter of the components' lifetime distribution and to find the optimal replacement cycle that minimizes the expected cost per unit of time under a certain age-based replacement policy.

In this work, we assess the power production of a single wind turbine and wind farm under probabilistic distributions where wind speed and wind turbine availability are dependent on each other. In our developments, the wind speed distribution is assumed to be discrete. Our method of finding the corresponding distributions is based on classical probabilistic techniques.

The year 2020 was the beginning of the Covid-19 pandemic, and the turning point for the industries poorly affected by the unexpected conditions. This paper focused on the impact of a range of factors on China's exports of metal manufacture in 2020, in particular the impact of the COVID-19 pandemic on it. Using cross-sectional data, the paper collected relevant data for 151 countries in 2020. We applied trade gravity model by considering important parameters impacting on China's exports of metal manufacture such as GDP, distance, population, the total number of cases of COVID-19, employment rate, economic degrees of freedom, the political environment and the free trade agreement between China and other countries. Then, by collecting the data set for 2021, this paper compares the models for 2020 and 2021 with the aim of making a comparison of the impact of the pandemic on China's exports of metal manufactures. We also do some analysis about the trend of the effect of COVID-19 in the future. The paper continues with calculation of China's export potential for metal manufacture for its 151 partner countries including 54 of them are at the Trade Potential Untapped level, 38 at the Trade Potential Growing level and 59 at the Trade Potential Mature level based on gravity model. This paper also offers different detailed trade policies for the distinct levels of trade potential in the light of the impact of the COVID-19.

A system experiences random shocks over time, with two critical levels, d 1 and d 2 , where $d_{1} \lt d_{2}$ . k consecutive shocks with magnitudes between d 1 and d 2 partially damaging the system, causing it to transition to a lower, partially working state. Shocks with magnitudes above d 2 have a catastrophic effect, resulting in complete failure. This theoretical framework gives rise to a multi-state system characterized by an indeterminate quantity of states. When the time between successive shocks follows a phase-type distribution, a detailed analysis of the system’s dynamic reliability properties such as the lifetime of the system, the time it spends in perfect functioning, as well as the total time it spends in partially working states are discussed.

In this paper, particular shock models are studied for the case when the times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. The well-known shock models such as delta shock model, extreme shock model, and the mixed shock model which is obtained by combining delta and extreme shock models are considered. The probability generating function and recursive equation for the distribution of the system's lifetime are obtained for the cases when the interarrival times between shocks and the magnitudes of shocks are independent and when they are dependent. System reliability is computed for particular interarrival distributions such as geometric, negative Binomial and generalized geometric distributions.

This paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system’s lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system’s lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system’s lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated.

Combinatorial techniques have an important role to compute the joint reliability importance (JRI) of some coherent systems. We obtain combinatorial formula for calculation of the JRI of two components in a generalised version of consecutive type systems consisting of n linearly ordered components such that system fails if and only if (iff) there are at least m l-overlapping runs of k consecutive failed components (n >= m(k - l) + l, l < k). Overlapping runs mean having common elements which is denoted by l: We concentrate on both s-independent & identical components and exchangeable components. Explicit combinatorial formulae are provided for computing the JRI of the above mentioned cases. For both cases, we also compare the results with linear m-consecutive-k-out-of-n:F system (nonoverlapping case when l = 0). In addition, some numerical and illustrative examples are presented.

Coherent systems and Marshall-Olkin run shock models are combined. Coherent systems consisting of n components receive some kind of shocks from n+1 different sources similar to Marshall-Olkin type. More precisely, when the component j receives k consecutive fatal shocks from the source j or k consecutive fatal shocks from the source n+1, it fails, j = 1, …,n. When the interarrival time of shocks has phase-type distribution, reliability, mean time to failure (MTTF) and mean residual life (MRL) function of the coherent systems are studied. Numerical examples and graphical representations are provided.

Integrating multiple wind farms into power systems may reduce the fluctuation in total power output of wind farms and hence it decreases the system risk resulting from the wind speed variability. In this paper, a wind power system consisting of two wind farms is modeled and analyzed considering the dependence between wind speeds at two sites. In particular, the system is modeled as a threshold system and reliability values of wind turbines are also taken into account in capacity based calculations. The results are illustrated for the available bivariate wind speed data in the literature.

It is important to elicit information about the potential power output of a wind turbine and a wind farm consisting of specified number of wind turbines before installation of the turbines. Such information can be used to estimate the potential power output of the wind farm which will be built in a specific region. The output power of a wind turbine is affected by two factors: wind speed and turbine availability. As shown in the literature, the correlation between wind speed and wind turbine availability has an impact on the output of a wind farm. Thus, the probability distribution of the power produced by the farm depending on the wind speed distribution and turbine availability can be effectively used for planning and risk management. In this paper, the theoretical distribution of the wind farm power is derived by considering the dependence between turbine availability and the wind speed. The theoretical results are illustrated for real wind turbine reliability and wind speed data.

An extreme shock model when there is a change in the distribution of the magnitudes of shocks is defined and studied. Such a model is useful in practice since a sudden change in environmental conditions may cause a larger shock. In particular, the reliability and mean time to failure of the system is obtained by assuming that the times between arrivals of shocks follow phase-type distribution. The optimal replacement policy that is based on a control limit is also proposed. The results are illustrated when the number of shocks until the change point follows geometric distribution.

For a system that is subject to shocks, it is assumed that the distribution of the magnitudes of shocks changes after the first shock of size at least d(1), and the system fails upon the occurrence of the first shock above a critical level d(2) (> d(1)). In this paper, the distribution of the lifetime of such a system is studied when the times between successive shocks follow matrix-exponential distribution. In particular, it is shown that the system's lifetime has matrix-exponential distribution when the intershock times follow Erlang distribution. The model is extended to the case when the system fails upon the occurrence of l consecutive critical shocks.

Majority of the people have been paid attention towards renewable and clean sources of energy like wind. Due to the uncertainties related to wind turbines, issues of energy storage are noteworthy. One of the aptest methods of energy storage is the production of hydrogen from the wind. The main aim of this paper is to investigate the potential of wind energy assisted hydrogen production in three selected stations of Fiji Islands using various wind turbines. From the analysis of results and discussion, Vestas V110-2.0 provides acceptable capacity factors among all inspected wind turbines with the highest value of 77.06% for the station at Labasa. Additionally, the highest energy production was from the Vestas V110-2.0 wind turbine with an annual production of 13,501,620 kWh. The conversion system used in this study resulted in a linear relationship between generated wind energy and the amount of hydrogen produced. Therefore, the highest amount of yearly hydrogen production (240.19 ton-H) is related to the largest examined wind turbine, installed in the station at Labasa.

In this paper, the influence of a cold standby component on a coherent system is studied. A method for computing the system reliability of coherent systems with a cold standby component based on signature is presented. Numerical examples are presented. Reliability and mean time to failure of different systems are computed.

A system can be classified with respect to the physical arrangement of its components and the functioning principle. A circular consecutive k-within-m-out-of-n:F system consists of n circularly ordered components and fails if and only if there are m consecutive components that include among them at least k failed components. A circular consecutive k-within-m-out-of-n:F system turns into circular consecutive k-out-of-n:F for m = k and k-out-of-n:F system for m = n. In this study, signature-based analysis of circular consecutive k-within-m-out-of-n:F system is performed. A new approximation to this system is provided based on maximum number of failed components and an illustrative example is given for different values of n, m, k to compare the approximate results with simulated and exact results.

A consecutive k-within-m-out-of-n:F system consists of n linearly ordered components and fails if and only if there are m consecutive components which include among them at least k failed components. This system model generalizes both consecutive k-out-of-n:F and k-out-of-n:F systems. In this article, we study the dynamic reliability properties of consecutive k-within-m-out-of-n:F system consisting of exchangeable dependent components. We also obtain some stochastic ordering results and use them to get simple approximation formulae for the survival function and mean time to failure of this system.