Autocorrelated Data by Donald J. Wheeler

[New to statistics]

Hello
From the article Autocorrelated Data by Donald J. Wheeler Quality Digest 07/07/2017 ( chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.spcpress.com/pdf/DJW319.Aug.17.Autocorrelated%20Data.pdf )

Positive autocorrelation:
Why he take these pairs of points? what's the reason?
Figure 5 In positive autocorrelation is not supposed to values to go up in spc?

Negative autocorrelation:
Page 6 how this equation made?

 

[John Predmore]

Why he take these pairs of points? what's the reason?

The paragraphs and figures are from the Autocorrelated Data article you reference. One popular form of SPC chart is the Individuals and Moving Range (ImR) in figure 1. Rather than plot averages and ranges of subgroups, the individual values and difference between consecutive values are plotted (thus, a pair is a subgroup of two).

Figure 5 In positive autocorrelation is not supposed to values to go up in spc?

The whole purpose of the article is to demonstrate how autocorrelated data might appear in SPC charts. The second paragraph after figure 2 explains that the first example {distillation) process experiences a process change, beginning in period 11. That is why the SPC charts show an increasing downward trend. In the paragraph below figure 5, Dr. Wheeler explains that "we cannot have a large positive autocorrelation without also having a process that is moving around." After period 11, there is change in the process which is no longer stable.

Page 6 how this equation made?

Starting on page 6, the article uses data from a different process (thickness of ball-joints), to illustrate how negative autocorrelation might appear. Unlike the first example, the data in the second example are generated in pairs at each data collection point, from Cavity 1 and Cavity 2. Figure 9 uses the more classical X-bar/R chart. The X-bar values are the average of subgroups of two. Dr. Wheeler goes on to explain in the Summary that irrational subgrouping "mixes apples and oranges", and violates of the principle of rational subgrouping necessary for a meaningful Shewhart chart.

 

[NotMe]

Positive autocorrelation:
Why he take these pairs of points? what's the reason?

We are interested in the "lag 1" autocorrelation. Thus, we plot on the x axis the data-point, and on the y axis the previous data point, or vice versa. As the first data point does not have a previous data pointe start with the second data point.

Figure 5 In positive autocorrelation is not supposed to values to go up in spc?

No. A positive correlation does not indicate that the values are increasing, nor does it indicate that they are decreasing. Instead a passive correlation tells us that both points lie on the same side with respect to the average value.

Negative autocorrelation:
Page 6 how this equation made?

Could not find an equation on page 6.