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I'm having some trouble trending turbofan jet engines exhaust gas temperatures (EGT). Data collected shown that EGT measured in the test cell versus EGT measured on-wing while flying is different.

EGT measured in the test cell is normalised to standard day conditions by correcting for temperature, humidity, test cell correlations etc, to give EGT hot day (EGTHD). These correction factors are fixed by the OEM. After the engines are run in the test cell, they are installed on the aircraft and their EGT measured, and then normalised to standard day condition (EGTHD) using a different set of correction factors, as a basis of comparison.

So what was observed is that EGTHD calculated in the test cell versus on aircraft is different; this difference is normally distributed with mean 0 and std dev 8. The std dev is a little high as 8 deg C is roughly 10% of EGT, and with a 3 s.d, it reaches 30%.

I have a little hypothesis on the difference: Model errors could be introduced in the normalising process. Since the multifactor regressions would result in some residuals, and assuming that these residuals are random, then the normal distribution observed should be logical as it follows central limit theorem. OEM has also mentioned that for a certain correction factor, the error is observed to be larger at extreme ends i.e residuals at the extremes are greater than in the middle part.

Now I am curious as to whether this distribution of difference is acceptable (clearly my bosses do not think so), and whether the test cell correlation has shifted out of limits. Right now I am attributing the variation to the errors introduced in the normalisation process. Is there any statistical parameter that I should ask the OEM regarding their normalising process to get a better analysis? i.e standard error, std dev of residuals etc.

Thanks in advance!

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I'm not sure that I completely understand your question. It seems that particular tests give different results on the test cells and on the aircraft, but the mean difference is 0. That means that the measures are consistent. They just seem to be rather noisy -- presumably because test conditions and aircraft differ.

As to whether the noise is too great, that depends on how much precision you need. A large variance means that, while the test conditions are not biased for flight conditions, accurate prediction is difficult. So basically, this is not a statistical question but a "real world" question: how much accuracy do you need? Your bosses are probably right if they think the test cells are not performing correctly.

I assume that these measurements are taken on a regular basis, over time. I think you want to plot your data and see if there is a trend, possibly using a control chart. A Bland-Altman plot is also a good way to see if two measurements that purport to measure the same thing are actually doing so.

Anyway, I can't say much more without seeing your data and knowing what you use it for. Are these tests used to make a decision of some kind?

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  • $\begingroup$ Hi Placidia, thank you for the response. Really appreciate it. The thing is that the two measures are calculated parameters, normalised with their models, which would introduce model errors and noise I guess. The issue here is comparing two methods that have uncertainty, and then determining whether the distribution of the difference reflects whether one method has become less accurate. Could I just confirm if the CLT hypothesis with regards to model residuals summing up to represent a normal distribution correct? Thanks! $\endgroup$ – silentscope Feb 18 '16 at 0:20

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