It is well known that two different underlying dynamics lead to different patterns of income/wealth distribution such as the Boltzmann–Gibbs form for the lower end and the Pareto-like power-law form for the higher-end. The Boltzmann–Gibbs distribution is naturally derived from maximizing the entropy of random interactions among agents, whereas the Pareto distribution requires a rational approach of economics dependent on the wealth level. More interestingly, the Pareto regime is very dynamic, whereas the Boltzmann–Gibbs regime is stable over time. Also, there are some cases in which the distributions of income/wealth are bimodal or polymodal. In order to incorporate the dynamic aspects of the Pareto regime and the polymodal forms of income/wealth distribution into one stochastic model, we present a modified agent-based model based on classical kinetic wealth exchange models. First, we adopt a simple two-class society consisting of the rich and the poor where the agents in the same class engage in random exchanges while the agents in the different classes perform a wealth-dependent winner-takes-all trading. This modification leads the system to an extreme polarized society with preserving the Pareto exponent. Second, we incorporate a solidarity formation among agents belonging to the lower class in our model, in order to confront a super-rich agent. This modification leads the system to a drastic bimodal distribution of wealth with a varying Pareto exponent over varying the solidarity parameter, that is, the Pareto-regime becomes narrower and the Pareto exponent gets larger as the solidarity parameter increases. We argue that the solidarity formation is the key ingredient in the varying Pareto exponent and the polymodal distribution. Lastly, we take two approaches to evaluate the level of inequality of wealth such as Gini coefficients and the entropy measure. According to the numerical results, the increasing solidarity parameter leads to a decreasing Gini coefficient not linearly but nonlinearly, whereas the entropy measure is robust over varying solidarity parameters, implying that there is a trade-off between the intermediate party and the high end.

A group of stock markets can be treated as a complex system. We tried to find the financial market crisis by constructing a global 24 stock market network while using detrended cross-correlation analysis. The community structures by the Girvan-Newman method are observed and other network properties, such as the average degree, clustering coefficient, efficiency, and modularity, are quantified. The criterion of correlation between any two markets on the detrended cross-correlation analysis was considered to be 0.7. We used the return (r_t) and volatility (|r_t|) time series for the periods of 1, 4, 10, and 20-year of composite stock price indices during 1997–2016. Europe (France, Germany, Netherland, UK), USA (USA1, USA2, USA3, USA4) and Oceania (Australia1, Australia2) have been confirmed to make a solid community. This approach also detected the signal of financial crisis, such as Asian liquidity crisis in 1997, world-wide dot-com bubble collapse in 2001, the global financial crisis triggered by the USA in 2008, European sovereign debt crisis in 2010, and the Chinese stock price plunge in 2015 by capturing the local maxima of average degree and efficiency.

In this paper, we investigate the robustness of the well-known DCCA (detrended cross-correlation analysis) methodology and give a qualitative analysis result. Due to the non-stationarity inherent in most observational data sets, the results of DCCA and its variants may be spurious. In particular, oceanographic data sets contaminated with measurement errors are subject to unusual records, making it difficult to trust DCCA results. To ensure the validity of the DCCA methodology for the oceanographic time series, we conduct simulation studies based on the ARFIMA process and perform statistical tests using surrogate methods. First, so-called outliers due to measurement error lead to the spurious results of DCCA methods while discontinuities in the time series have been found to have little effect on the results. This means that the cross-correlation structure is robust to the discontinuity of time series. Second, statistical significance of cross-correlation was obtained through a surrogate statistical test for the oceanographic time series.

Failure mode and effect analysis (FMEA) is one of the most widely employed pre-evaluation techniques to avoid risks that may occur during product design and manufacturing phases. However, use of the risk priority number (RPN) in traditional FMEA results in difficulties being encountered with regard to quantification of the degree of risk involved. This study proposes the use of a probabilistic time-dependent FMEA (TD-FMEA) approach to overcome limitations encountered during implementation of traditional FMEA approaches. To this end, the proposed method defines the risk priority metric (RPM) as a priority decision value. RPM corresponds to the product of the expected loss and occurrence rate of the failure-cause. By assuming exponential and case functions for each occurrence and detection time instant, the expected loss corresponding to each failure-cause can be evaluated. Utility of the proposed approach has been described in the light of results obtained via its implementation during an automotive-manufacturing case study performed for the purpose of illustration.

In this paper, a mathematical and physical interpretation of the length and angle of the catenary curve made by anchor chains was implemented, and the safety of an anchored vessel was reviewed. So far, the holding force has usually been calculated when the angle of the catenary curve of the anchor chain to the seafloor is $0°$. In this study, the holding force equation was strictly and explicitly derived considering the length of the chain and the depth of the sea. In addition, equations for the angle and length of the catenary curve were mathematically derived when anchor dragging occurs. The holding force equations derived in this paper are expected to help provide guidelines for vessel design or increase the safety of anchoring.

Failure mode and effect analysis (FMEA) is a structured technique for identifying risks that may occur during a given stage of a system’s life cycle. However, the use of the risk priority number (RPN) in traditional FMEA results in difficulties with regard to quantification of the degree of risk in the hierarchical failure structure. This study proposes the use of a hierarchical time-dependent FMEA approach to overcome the limitations encountered during the implementation of traditional FMEA approaches. In place of the RPN, a probabilistic loss model is developed under a hierarchical structure considering the elapsed time from the failure-cause (FC) to the system failure. By assuming exponential and case functions for each occurrence and detection time instant, the expected loss corresponding to each FC can be evaluated. As a result of the practical application of the time-dependent probabilistic model through the numerical example, we could reasonably evaluate the risk from the cause of failure in the hierarchical structure in terms of economic loss.