When S2 is the sample variance of a normal random sample, (n - 1)S2/2 has a chi-squared distribution with n - 1 df, so from

When S2 is the sample variance of a normal random sample, (n - 1)S2/σ2 has a chi-squared distribution with n - 1 df, so

from which

This suggests that an alternative chart for controlling process variation involves plotting the sample variances and using the control limits

Construct the corresponding chart for the data of Exercise 11.

1(nS2 = .998 001-1 2 LCL = s%99m-1/(n-1) UCL = shola-1/(n-1 )