ABSTRACT

As mentioned earlier, the reason for Shewhart to choose the sample range instead of the sample standard deviation for construction of the X chart is probably due to the simplicity of the computation. However, it should be noted that the relative efficiency for using the sample range as an estimator for population standard deviation compared to the minimum variance unbiased estimator is at least 91% for a sample size of less than 7. As a matter of fact, the sample range is more robust than the sample standard deviation for small samples from nonnormal populations.