Modeling of Material Wastage by Ornstein-Uhlenbeck Process

Abstract

Consider the problem of modeling the proportion wastage arising out of trimming the edges of paper and metal sheets to give these a regular shape. It is observed that curved edges in such cases may follow the sample path of a Ornstein- Uhlenbeck process. The production characteristic can then be expressed in terms of the parameters of the process which are estimable from the observed shape of the edge. Sample edge trajectories of two production processes are analysed and the production efficiency is interpreted in terms of proportion wastage.

On the distribution of burr with applications

“…In some operations metal-sheets are given a finer thickness by pressing these through a series of rollers and then the sheets are given a regular shape by trimming the edges; see Dasgupta (2006) where efficiencies of production processes in terms of minimizing wastage due to trimming are compared by this stochastic process. Ornstein-Uhlenbeck process satisfies the following differential equation.…”

Rate of Convergence in Invariance Principle for Random Partial Sums with Applications

“…One may like to compare production processes when the numbers of observations taken are not fixed but random. Figures 2(b) and 2(c) of Dasgupta (2006) refer to the trimmed portion of two iron sheets arising out of two processes. We would like to compare two processes in terms of wastage.…”

“…It is worth mentioning that Csorgo et al (2003) obtained an invariance principle for self-normalized partial sums processes of independent random variables. In Dasgupta (2006), an Ornstein-Uhlenbeck model is proposed for the deviations of the edge curve from the central line of mean expansion. Related to the proposed procedure of comparison are CUSUM charts.…”