Variable Limits and Control Charts Based on the Half Normal Distribution

Abstract

The well-known variable control charts for mean and range of sub-groups for the half normal distribution were constructed by three different approaches. One from the first principles of using percentiles of the sampling distribution of the sample mean and sample range, the second from Shewhart control limits, and the third approach was a skewness correction procedure depending on the skewness coefficient. The coverage probabilities of the three different approaches were computed through simulation and compared.

Ultra-fine transformation of data for normality

“…Many authors claim that the normal distribution is the most important probability distribution in statistics [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. This is due to three reasons: 1) Many phenomena in nature are distributed naturally [ 18 ]; 2) Many statistical analyses require the application of normally distributed data; and 3) Lastly, many statistical applications, such as statistical quality control, need normally distributed data to be applied.…”