Formulation of Measurement Sampling Plan for Small and Medium Batch Products in Supply Chain

The article studies the supply chain of suppliers and manufacturers, considering the overall benefits of the supply chain, the measurement sampling plan is the small batch sampling plan with the smallest amount of sampling and the strongest discriminative ability. If the quality characteristic data is a measurement value, and the inspection workload is large and the inspection cost is high, it is recommended to adopt the measurement sampling plan based on the Laplace distribution. On the premise of ensuring quality, try to reduce the number of inspected samples as much as possible to reduce the workload and cost of inspection.

Wind Speed Analysis of Hurricane Sandy

The database of the HWind project sponsored by the National Oceanic and Atmospheric Administration (NOAA) for hurricanes between 1994 and 2013 is analysed. This is the first objective of the current research. Among these hurricanes, Hurricane Sandy was selected for a detailed study due to the number of files available and its social relevance, with this being the second objective of this study. Robust wind speed statistics showed a sharp increase in wind speed, around 6 m s−1 at the initial stage as Category 1, and a linear progression of its interquartile range, which increased at a rate of 0.54 m s−1 per day. Wind speed distributions were initially right-skewed. However, they evolved to nearly symmetrical or even left-skewed distributions. Robust kurtosis was similar to that of the Gaussian distribution. Due to the noticeable fraction of wind speed intermediate values, the Laplace distribution was used, its scale parameter increasing slightly during the hurricane’s lifecycle. The key features of the current study were the surface and recirculation factor calculation. The surface area with a category equal to, or higher than, a tropical storm was calculated and assumed to be circular. Its radius increased linearly up to 600 km. Finally, parcel trajectories were spirals in the lower atmosphere but loops in the mid-troposphere due to wind translation and rotation. The recirculation factor varied, reaching values close to 0.9 and revealing atmospheric stratification.

Robust LPV models identification approach based on shifted asymmetric Laplace distribution

This paper focuses on the robust parameters estimation algorithm of linear parameters varying (LPV) models. The classical robust identification techniques deal with the polluted training data, for example, outliers in white noise. The paper extends this robustness to both symmetric and asymmetric noise with outliers to achieve stronger robustness. Without the assumption of Gaussian white noise pollution, the paper employs asymmetric Laplace distribution to model broader noise, especially the asymmetrically distributed noise, since it is an asymmetric heavy-tailed distribution. Furthermore, the asymmetric Laplace (AL) distribution is represented as the product of Gaussian distribution and exponential distribution to decompose this complex AL distribution. Then, a shifted parameter is introduced as the regression term to connect the probabilistic models of the noise and the predict output that obeys shifted AL distribution. In this way, the posterior probability distribution of the unobserved variables could be deduced and the robust parameters estimation problem is solved in the general Expectation Maximization algorithm framework. To demonstrate the advantage of the proposed algorithm, a numerical simulation example is employed to identify the parameters of LPV models and to illustrate the convergence.

The Price Dispersion of Consumer Products

Presented is an analytic dynamic model of the price dispersion of consumer products. The theory is based on the idea that sellers offer product units for a profit maximizing price, denoted pm. Product units not sold at pm are called excess units. Based on the conservation equation of offered units, it can be shown that the stationary price distribution of consumer products consists of a Dirac-delta peak at pm surrounded by a fat-tailed Laplace distribution from the excess units. A good quantitative agreement with empirical data can be obtained with a fit of the two free parameters of the theory.