Practitioner advice: Approximation of the cumulative density of left-sided truncated normal distribution using logistic function and its implementation in Microsoft Excel

ABSTRACT

The left-sided truncated normal distribution is especially important in quality engineering where we remove the left side of the distribution, for example, due to estimation of the life of used products. Although the theoretical background of truncated normal distribution is already established, there is very little work on mathematical approximation of the probability density and the cumulative probability density functions. In this article, a high accuracy mathematical approximation of the left-sided truncated normal distribution is proposed. A full analysis of errors and recommendations for implementation using Microsoft Excel are provided at the end of this article.

KEYWORDS:

• cumulative probability function
• distribution
• error function
• errors analysis
• logistic distribution
• logistic function
• mathematical approximation
• normal distribution
• probability function
• truncated normal distribution

Additional information

Notes on contributors

Mohammad M. Hamasha

Mohammad M. Hamasha received his Ph.D. in Industrial and Systems Engineering from the State University of New York at Binghamton, New York, in December 2011. He also received his M.S. in Industrial Engineering and BS in Biosystems Engineering from Jordan University of Science and Technology (JUST) in 2008 and 2005, respectively. He worked for 2 years as a postdoctoral associate with the Center for Autonomous Solar Power in Binghamton, New York doing a research related to smart grid optimization and reliability of solar cell from 2011–2013. Mohammad is currently an assistant professor with the department of engineering management at Prince Sultan University, Riyadh, Saudi Arabia. His research interests are in the areas of simulation, operational research, reliability engineering, design and analysis of production systems, stochastic and simulation optimization, and lean Six Sigma.