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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. [ABSTRACT FROM AUTHOR]

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 d1, and the system fails upon the occurrence of the first shock above a critical level d2 (> d1). 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Combinatorial techniques have anim portant role to com pute the joint reliability importance (J RI) of some coherent system s. We obtain combinatorial formula for calcu lation of the JR I of two com p onents in a generalised version of consecutive type systems consisting of nlinearly ordered comp onents 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. [ABSTRACT FROM AUTHOR]

A system can be classified with respect to the physical arrangement of its components and the functioning principle. A circular consecutivek-within-m-out-of-n:F system consists ofncircularly ordered components and fails if and only if there aremconsecutive components that include among them at leastkfailed components. A circular consecutivek-within-m-out-of-n:F system turns into circular consecutivek-out-of-n:F for m = k andk-out-of-n:F system for m = n. In this study, signature-based analysis of circular consecutivek-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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]