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Hi I have collected some process data for 3 years and I want to mimic a EWMA prospective analysis, to see if my set smoothing parameter would have detect all the important changes (without too many false alarms).

It seems like most textbooks and literature that I have looked that use a mean and standard deviation to calculate the Control Limits. This is usually the "in-control" mean and standard deviation from some historical data, or the mean and sd of the population from which the samples are drawn. I don't have either information.

Is there another way to calculate the Control Limits?

Is there a variation of the EWMA chart that does not use mean and standard deviation?

Any creative ideas?

Thank you in advance

user3295481
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  • To make sure I understand this: you could compute the EWMA mean and variance, but you don't have a baseline to compare them to? It sounds to me like you have a supervised technique (which assumes you can define what it "should" look like), but you want an unsupervised technique (which only looks for differences without calling one state "good" and another "bad"). For unsupervised techniques, clustering comes to mind, but it would have to be modified to apply to timeseries. How about Generalized Likelihood Ratio (GLR)? – Jim Pivarski Jun 25 '14 at 02:49
  • If we refer to http://en.wikipedia.org/wiki/EWMA_chart, I can compute the Zi for my given lambda, but when it comes to the control limits, I don't have historical data to compute the T and S. Thank you I will look into GLR and also post on Cross Validated. – user3295481 Jun 25 '14 at 02:54
  • Also, this should probably go to Cross Validated: http://stats.stackexchange.com/ – Jim Pivarski Jun 25 '14 at 02:54
  • Yeah, T and S are the mean and standard deviation of a baseline distribution, which is either given a priori or determined from a training dataset. The training dataset represents what the data "should" look like, hence this is a supervised technique and you want an unsupervised technique. GLR isn't exponentially weighted, but it dynamically finds a break in the data between two different distributions and combines data on each side of the break to get more robust results. It could be what you want. – Jim Pivarski Jun 25 '14 at 03:00

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From a practical/operational perspective, the use of statistical analysis of historical data alone, is rare. Yes, it provides some guidance on how the process (and its control system) are performing, however the most important thing by far is to have a good understanding and knowledge of the "engineering limits".

I refer to the operational limits, which are determined by the specifications and performance characteristics of the various pieces of equipment. This allows one to develop a good understanding of how the process is supposed to behave (in terms of optimal operating point and upper/lower control limits) and where the areas of greatest deviation from optimal are. This has very little to do with statistical analysis of historical data, and a great deal to do with process engineering/metallurgy - depending on the type of process you are dealing with.

The control limits are ultimately determined from what the Process Manager / Process Engineer WANTS, which are usually (but not always) within the nameplate capacity of the equipment.

If you are working within the operational limits, and you are in the realm of process optimisation, then yes, statistical analysis is more widely used and can offer good insight. Depending upon the variability of your process, how well your control system is set up, and the homogeneity of your feed product, the upper/lower control limits that are selected will vary. A good starting point is the optimal operating point (e.g. 100 m3/hr), then use a sensible amount of historical data to calculate a standard deviation, and make your upper limit 100 + 1 standard dev, and your lower limit 100 - 1 standard dev. This is by no means a "hard and fast" rule, but it is a sensible starting point.

Stracky
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