Autocorrelation
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July 16, 2007 at 8:51 am #47571
Dear All,
I have a few questions related to Autocorrelation and Autocorrelated data set.What is the practical meaning when one says that the data are Autocorrelated. How does it/does not impact my tests on the data viz. capability calculations, hypothesis testings, GRR?
If it impacts the analysis how does one need to use the data/do stratifications and intrepet the statistical analysis?
In case Autocorrelated data cannot be used for a particular analysis/statistical tests, how does one deal with it?
Forums inputs solicitated
Regards
DD0July 16, 2007 at 2:39 pm #158697Autocorrelated data means that a datapoint is somehow dependent on the previous point. You can determine this by doing simple linear regression on X versus X1. (Considered “lag 1”)
GRR, Ttests depend on normality and independence, so these become invalid.
In the SPC case, you could establish a model based on the autocorrelation function, and control chart the residuals. I have only seen autocorrelation in a GRR study once, and that was for CD SEM measurements on a photoresist feature. A charge builds up as you measure, and it influences the next measurement. We opted to characterize the measurement system using etched oxide features instead of photoresist. This was a more practical choice than getting creative with the data.
Sorry this is so brief, but I am on vacation and the family is waiting!0July 16, 2007 at 4:50 pm #158710What is the practical meaning when one says that the data are Autocorrelated. How does it/does not impact my tests on the data viz. capability calculations, hypothesis testings, GRR?
It occurs when you have unknown influences (ie lurking variables) at work during data collection. The result is a timebased effect on your data. For example, tool wear or operator fatigue will cause a gradual erosion in the integrity of your data set, with the value of each measure sharing some degree of association or relationship with the previous one. This lack of independence is the effect of A.C.
It is bad. Many tests are robust to other NIDD violations such as normality or equal variance, but the majority are significantly affected by a signicanicant lack of indepence (ie correlation).
It will generally result in under estimating process capability (i think…need to confirm that one) and put the effects of your parametric hypothesis testing in question.
If it impacts the analysis how does one need to use the data/do stratifications and intrepet the statistical analysis?Stratification isnt useful against autocorrelation.
In case Autocorrelated data cannot be used for a particular analysis/statistical tests, how does one deal with itAs to its detection, plotting the residuals and looking for nonrandom distribution will indicate its presence as will other basic tests for correlation.
The easiest thing to do is plan to prevent it. Control all you can, block where you feel part of the experimental material is more homogeneous than the aggregate, and randomize everything else. The last point is the most critical in terms of preventing autocorrelation. Remember, it is a timebased phenomenom, so ramdomly assigning orders:The run order in a DOE
The order of operators in your GR&R
The order of parts in your GR&R
Assignment of treatment levels in a DOE or ANOVA
Sampling of parts in data collection
Etcinsures its influence is homogeneously distributed across your data, thus nuetralizing its effects.
As to what to do once you have it…dont know if it can be resolved at that point….I believe you will have to go back to your experimental design or data collection procedures, instill randomization techniques, blocking, etc and rerun the testing. But check that one.
Good luck.
0July 16, 2007 at 5:13 pm #158713Thanks for all your responses. they have really been infomative and useful.
0July 17, 2007 at 11:24 am #158759Dear Forumites
Anyone else would like to give his thoughts on AC?0July 26, 2007 at 3:13 pm #159114Practical Meaning
Autocorrelation is often seen in time series data. This usually occurs became your sampling frequency is too large. For example if your process varies over a 10 minute time period and you sample every 30 seconds your data will be highly correlated over that 10 minute time frame or 20 data points. The solution is simple sample less frequently or only use about every 20th data point at the original sampling frequency. This problem has become more prevalent with the use of automated data collection systems which allow one to capture large amounts of data with little effort. Minitab has a nice tool in its time series section that lets you check for autocorrelations without having to calculate all of the lags.0 
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