Scatter Plot Analysis, how to raise an alarm.....

[dinosaur_uk]

HI there,

I need a method od detecting a change in levels in a system. I have made a confidence test to find the upper and lower limits of the unit. The X-Axis is time and the y axis is deviation from the mean. Basically i want a test to determine if it has shifted away from this limit. However, with this limit, a certain amount of data points will be out of these limits. Can anyone suggest a good mathematical solution to this?

I am running this test online, so it needs to collect data and process it.

I am using a normal distribution to determine upper and lower limits, should i use another ?

Image 1 is of a typical normal behaviour
Image 2 is a failure of the unit.

How do i spot it mathematically?

[Rassis]

However, with this limit, a certain amount of data points will be out of these limits.

You mean that you want to keep tracking of data lying outside limits?

I am using a normal distribution to determine upper and lower limits, should i use another ?

A fit of data to the normal distribution or any other has first to be checked. You can use any of the statistical methods available for this purpose, such as the “chi-square” method, and compute “trial and error” by hand or with the aid of a spreadsheet. Or you can use software, such as BestFit (Palisade in USA) for the same purpose being far faster. Then you decide how far from the mean you allow the variable under control to deviate. Typically one decides based on a number of magnitude (1, 1.5, 2, etc.) times the standard deviation.

[dinosaur_uk]

No...I dont want to keep tracking the outer points...

Basically the situation is as follows, as time goes by the unit should be within a certain band, and if the general trend starts to dip down (decrease) then i want to raise an alarm. So currently, i am using last month's data to create a confidence limit, so let say 0% to 1.6%, so this unit should be around this limit, and if on a certain day it steps outside of this limit say (50 times) then i should raise the alarm...

Do you know what i mean?

[Rassis]

If I understood your problem right, you have the solution in the attached EXCEL spreadsheet. If not, please let me know and I will try once more.

The spreadsheet is a simulation model of the behaviour over time of any type of signal which you want to control and predict which value it will probably attain within a certain number of periods ahead. The spreadsheet allows you to enter data (blue cells in column C up to 2000 periods), the number of periods ahead whose signal value you wish to forecast (blue cell I16) and the number of past periods (up to 100) on which the trend analysis is based (blue cell I17).

The data field is currently filled with random values sampled from a normal probability distribution with mean 100 and standard deviation 20. You can of course change the parameters (just to see what happens!) or just delete the contents and enter your raw data.

I set both control limits as 2 times the standard deviation. Once more, you can change this value (just to see what happens!).

The trend is evaluated based on the number of periods entered in cell I17 and the parameters of the line that fits the best these points are computed in cells I20 and I21.

Cell I22 tells you whether your data presents a trend such that within (n periods from now – the value entered in cell I16) the signal will likely fall outside limits (turning red if above and green if under). It will stay yellow otherwise.

The change in colour of cell I22 (from yellow to red or green) or the change in text in cell I23 allows you to transform the state of the “proximity of out of control” into any kind of outside warning signal.

Please notice that blue cells are for data to be entered, green cells are programmed and show intermediate calculus and yellow cells are also programmed and show final results.

Please tell me if this satisfies you and be happy.

[dinosaur_uk]

Hi Rassis

It is great....however, i do not want to predict future values, i just want it to alarm if it steps outside the limits for a longer time.

I kinda know what i have to do...

CHEERS !

[Rassis]

Hi Dinosaur,

I am glad because it seems that you found a way to solve your problem. Nevertheless, no matter what alarm criteria you come to choose, let me add a few more words:

I missed saying that to start with, you must choose a certain number (say n = 50 to 100) of observations (data points) to initialize the control process. These data points have to be considered good data (it is up to you to decide what good data means).
Second, you compute the mean, the standard deviation and both the control limits.
Third, you freeze these results (parameters) to be used all along the control process for as long as you wish. No new data points will change the parameters unless you wish to. To accomplish this, you select these n data points in the spreadsheet and make “copy, paste special, value”.
Fourth, change the range in formulas resident in cells H6 to H9 in order to account only for this set of initializing data points.
Fifth, any further data entered after the n base data points have been set, will only then be subject to control.

You surely will find ways to go even further. Have fun.

[dinosaur_uk]

Yeah ...

that is kinda what i am trying to do ...

I am also using Accumulative Summation to detect step change in the values...