## MTA Trending: Envelope Trending

The upper and lower envelope on the data are esitimated as follows.

• Extract data using dataseeker. The dataseeker data are 5 min averaged values.
• Check the data range. If a data set contains zero and/or positive values only, check how many are "zero". If more than or equal to 3% of data are non-zero, then all "zero" data points are dropped from the data set. Otherwise, keep all data points.
• For full range data, the data are further averaged out to one hour interval. For the quarterly and weekly data, the 5 min average is used.
• Divide the data into sub data sets. Due to change of environments, the data often have discontinuities. These discontinuities are identified by eye, and recorded in a file for each data set. Using these breaking points, divide the data into sub data sets.
• Find the minimum and maximum data points for a given interval. For the full range data set, one week is the length of the interval, two days for quarterly, and 30 mins for the weekly data set.
• Fit a regression line on the maximum or minimum data points. Although a straight line is good for most data, there are a dozen cases which required a quadratic line fit.
• Using the fitted result, find a standard deviation around the line, then select out data point outside of an estimated value (from the fitted line) plus 0.2 * standard deviation.
• Re-fit a line to the selected data set, and the result is given as an outer envelope.
• Extend the envelope line for the next 10 years, and check whether the envelope will violate upper or lower yellow limits. If so, find an approximate date of the violation. Note that this estimation is done with the full range data; quarterly and weekly data are not used for this purpose.
• For the secondary data sets which are computed from the main data sets (e.g., gradients) or selected with extra criteria (e.g., HRC I/S/OFF), only difference is that the data are obtained from /data/mta4/Deriv/, not from dataseeker. Most data are hour averaged data, and hence lower in resolution, especially for the weekly data.
• Estimations of the envelopes of the full range data are updated once a month, those of the quaterly data are updated weekly, and those of the weekly data are updated daily.

If you like to check all yellow violations, go to MTA Estimated Date of Yellow Limit Violations page.

If you like to check the break points of the plots, go to Break Point Table.

## MTA Secondary Data Trend

Web Site Last Update: May 01, 2009
If you have questions, contact T. Isobe (isobe@head.cfa.harvard.edu)