Where:
x = average or mean of hourly test run data;
t[(n-1),(0.95)] = t score, the one-tailed t value of the Student's t distribution for a specific degree of freedom (n-1) and a confidence level (0.95; 0.99 for Tilden SO2)
s2 = variance of the hourly data set;
n = number of values (e.g. 5,760 if 8 months of valid lbs NOX/MMBTU hourly values)
m = number of values used to calculate the test average (m = 720 as per averaging time)
[RHO] = correlation between data points
t critical = t[(n-2),(0.95)] = t score, the two-tailed t value of the Student's t distribution for a specific degree of freedom (n-2) and a confidence level (0.95)
m = (n + 1) * [ALPHA]
m = the rank of the ordered data point, when data are sorted smallest to largest. The data points are 720-hour averages for establishing NOX limits.
n = number of data points (e.g., 5040 720-hourly averages for eight months of valid NOX lbs/MMBTU values)
[ALPHA] = 0.95, to reflect the 95th percentile
If m is a whole number, then the limit, UPL, shall be computed as:
UPL = Xm
Where:
Xm = value of the mth data point in terms of lbs SO2/hr or lbs NOX/MMBTU, when the data are sorted smallest to largest.
If m is not a whole number, the limit shall be computed by linear interpolation according to the following equation.
UPL = xm = xmi·md = xmi + 0.md (xmi+1- xmi)
Where:
mi = the integer portion of m, i.e.,m truncated at zero decimal places, and
md = the decimal portion of m
40 C.F.R. §52.1183