Practical Application example: figure 2 shows data from a seriously improved micro capillary laboratory GC instrument, figure 3 shows data from a micro capillary GC process instrument.
In case we measured 14 times the concentration of methane in wet natural gas the one step forwarding calculation of s with sets of four consecutive methane concentrations resulted in 11 “sf4” values. In case we made a series repetition of 30 consecutively methane quantitations, we got 30 minus 3 = 27 “sf4” values.
This series of time correlated data is calculated and seen graphically as sf4 - values on the Y-axis over the number of the repeated N runs on the X-axis. It is obvious, that the X-axis represents a time axis - see the figures below.
Normally the analyst who took 30 consecutively repeated runs would calculate one mean value and one standard deviation value. Whilst the mean is a quality control number for the single values, s is a quality control number for the mean. There is no quality control number available for the total s under these conditions. But one understands that the “sf4” values are quality control numbers for the one total standard deviation value based on the total of N repetitions. An instrument or a method would get a quality certification based on these many 30 runs, its mean and its total s-value. But nothing is seen about systematic errors which may be time correlated. If however 30 - 3 = 27 sf4-values show what is seen in figure 3 below, the producer, user, regulator or certifier would very probably change his mind and would return to development and quality control procedures. This might be the only “bad” effect of “sf4”. As this is such a new mode of method/instrument/sampling/sample-stability quality control and as even statistically well trained experts have problems with “sf4”, it should be stressed, why “sf4” is so informative:
Reason A: ONE single “s” value is a number. Independent of the amount of work invested based on a large N one single “s” value has NO any own information about its own quality. The mean value however has a quality control number: This is the total s based on N. X+-7% is a poor X; X+-0.02% is good X.
Reason B: a consecutive series of three or many more correlated “sf4” values show TIME dependence. They have TIME related information. Most of systematic errors in chromatography are time correlated as already mentioned elsewhere in this site. N repeated analytical runs need N times the single runtime. Thus if anything changes with time it will change. If those changes - like the amount of non volatile or non solvable “dirt” in a sample inlet system growing towards a critical limit - it will affect the sample composition. This MUST result in changed and now falsified qualitative and or quantitative analytical results. Thus the analytical result does no longer represent the real sample composition. But this is not the only effect. Not all chromatography modes have this problem. In case of PLC or HPTLC it does not exist because in PLC any next sample starts chromatography at a (hopefully) clean new stationary phase. Any GC or HPLC column is no longer untouched after already the very first run.
These are the real main effects detected by “sf4”:
- Temperature - pressure - flow may change with time and then will change the mobile phase action in
GC, HPLC, PLC
- Polarity changes, density changes, film thickness changes of the stationary phase are time correlated
in all chromatography modes.
- Changes of the sample composition qualitatively and/or quantitatively from run to run are nearly always source of systematic errors because of the fundamental chromatography effect on any solid (or liquid) surface and because of very often existing “dead volumes” causing long lasting sample remixing effects. Thus it may look like a constant stable situation after a sample has been given three times, but the “sf4” data are very sensitively detecting even smallest composition changes and may tell, that even after twenty repetitions “sf4” data change - which means something invisible by other modes of data quality checks exists and should be found. Now what about the goodness of only one or two runs at all ?
“sf4” found immediately systematic errors in capillary GC, in micro gas capillary process instruments, in HPTLC scanners, in differing sampling procedures, in the use of pressure regulators or large volume needle valves, in too long or too wide or too chemically active sample lines and those with non constant temperature.
The whole procedure is simple and fast when using table calculation programs with graphics display. The latter is necessary for a correct evaluation - see two examples below.
Repeated WARNING: older EXCEL software (Microsoft Excel 2003), the corresponding table calculation software on MAC under MacOS 9 and higher (AppleWorks 7) and under LINUX (OpenOffice.org.1.1) - all three - calculate “s” data without any warning seriously wrong if other delimiters are used than the COLON. Differing other delimiters reduce the series of to be taken data in the table without warning.