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 P2

.999,n1  (



n 

2 1)S2

 2

.001,n1
.998 from which P  S2  
.998 This suggests that an alternative chart for controlling process variation involves plotting the sample variances and using the control limits LCL
s2 2

.999,n1

/(n  1)

UCL
s2 2

.001,n1

/(n  1)

Construct the corresponding chart for the data of Exercise 9.

[Hint: The lower- and upper-tailed chi-squared critical values for 5 df are .210 and 20.515, respectively.]