Page 217 - Six Sigma Demystified

Part 3 s i x s i g m a to o l s 197

for m = 2, 3, 4, . . . , n/4, where n is the number of observations, and X is the
average of the observations.

Partial Autocorrelation Function
The partial autocorrelation function (PACF) is estimated at the given lag (m)
as follows:
m ∑
r − n − m Φ r
Φ = j =1 m −1, j m −1
mm 1 − ∑ m −1 Φ
r
j=1 m −1, j j
where r is the autocorrelation function.
m
Significance limit. The significance limit for the ACF (and the PACF) are
calculated at the stated significance level, if the true population ACF (or PACF)
is zero. ACFs (or PACFs) exceeding this value should be investigated and
assumed to be nonzero:

 k 
r,Φ = ±   n  

where k is the ordinate of the normal distribution at the stated significance
level (determined using Appendix 1), and n is the number of observations in-
cluded in the analysis.

Autocorrelation Chart

Minitab

Use Stat\Time Series\Autocorrelation.
Use the “Select” button to enter the data column label into the Series field.

Excel

Using Gree Belt XL Add-On
Use New Chart\Autocorrelation Chart.
Enter the data’s cell references (e.g., $A$2:$A$102) into the Data Range (step
2) dialog box.