Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails often observed in practical data, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. ...

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models, among which the autoregressive model of order one (AR (1))...

Engineering tolerance plays an important role in the process capability analysis for determining whether a manufacturing process is capable of making good quality products. In contrast with the engineering tolerance region in a multivariate manufacturing process, the multidimensional machining process or the nano-cutting process has a special engineering tolerance called the positional toleranc...