We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical multiplicative process for non-stationary and non-ergodic dynamics. Resetting is sudden interruption process, which consecutively renews its show that, although renders GBM stationary, resulting remains non-ergodic. Quite surprisingly, effect pivotal in manifesting behavior. In particular, we observe th...

In the conditions of high-speed processing parts complex configuration, with a large end and longitudinal length, from hard-to-work steels alloys, it is difficult to ensure wear resistance cutting tool in aisles one technological passage. To appropriate quality indicators surface layer, impossible replace worn-out tool. connection above, problem ensuring operability (wear resistance) acute. The...

Recently, statistical process control (SPC) methodologies have been developed to accommodate autocorrelated data. To construct control charts for stationary process data, the process variance needs to be estimated. For an independently identically distributed sequence of a random variable, the variance is usually estimated by the sample variance. For a weakly stationary process, different estim...

Methods such as wavelets and M-stationary process have been developed to analyze the time-frequency properties of a process where frequency changes with time. In certain circumstances, when the frequencies of a process change systematically either monotonically increasing or monotonically decreasing across time, another approach is to apply an appropriate Box-Cox transformation to the time axis...

Accurate characterization of spatial variation is essential for statistical performance analysis and modeling, post-silicon tuning, and yield analysis. Existing approaches for spatial modeling either assume that: (i) non-stationarities exist due to a smoothly varying trend component or that (ii) the process is stationary within regions associated with a predefined grid. While such assumptions m...