Controlling the Velocity and Kinetic Energy of an Ideal Gas: An EWMA Control Chart and Its Average Run Length

Yupaporn  AREEPONG; Rapin  SUNTHORNWAT

doi:10.48048/wjst.2021.9586

Authors

Yupaporn AREEPONG Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Rapin SUNTHORNWAT Industrial Technology Program, Faculty of Science and Technology, Pathumwan Institute of Technology, Bangkok 10330, Thailand https://orcid.org/0000-0001-8981-5107

DOI:

https://doi.org/10.48048/wjst.2021.9586

Keywords:

Maxwell-Boltzmann distribution, Average run length, Integral equation, Ideal gas, Molecular velocity, Kinetic energy

Abstract

An ideal gas is a gas in the form of a particle or molecule. Its velocity and kinetic energy are interesting topics in several studies in physical chemistry. This research aims to evaluate the average run length based on the exponentially weighted moving average statistic for its molecular velocity and kinetic energy of Maxwell-Boltzmann distribution. Derivation of the integral equation, which is equal to the average run length and numerical method of the integral equation, was applied to evaluate the average run length of a gas molecule’s molecular velocity and kinetic energy. The Trapezoidal rule as numerical method and its error was analyzed for approximation of average run length. The findings showed that the average run length of molecular velocity decreased in the higher temperature with the given mass of the molecule. Moreover, there was a decrease in the average run length of molecular kinetic energy in the higher temperature.

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