Testing hypothesis on stability of expected value and variance

The simple samples are independently taken from normal distribution. The two functions of the sample means and sample variances are considered. The density functions of these two statistics have been derived. These statistics can be applied for verifying the hypothesis on stability of expected value and variance of normal distribution considered, e.g., in statistical process control. The critical values for these statistics have been found using numerical integration. The tables with approximated critical values of these statistics have been presented.