schedule an in-service

11:14 Sep 28, 2017 

To me, that pretty much clinches it, then!
This is exactly the sort of way American English tends to abbreviate things (which is perhaps why it sounds a little uncomfortable to my British ears!), and if you have found other context that tends to corroborate this, then I think you have your answer.
To go back to your original question, as to whether or not "programmer une formation continue" is appropriate, the answer is probably still no — although we have the idea of 'formation', 'continue' correctly conveys the notion of training while in post BUT tends to suggest a more long drawn out course of training, whereas here, in the context of training to use one specific piece of equipment, it is reasonable to expect it might be a single training course lasting perhaps, say, one or a few days only.
Hence I wouldn't use 'continue' (really to some extent 'ongoing') for that, but something that better conveys the notion of 'while in post'.

10:52 Sep 28, 2017 

Et je pense qu'il s'agit en fait d'une formation en regardant de plus près la table des matières.

10:21 Sep 28, 2017 

The crux of the matter seems to revolve around the use of 'in-service' as a stand-alone countable noun, where it is more commonly used to qualify e.g. 'training'.
I don't have any problem making the leap of imagination to its being simply a shortened form of that term, as is very typical in the telegraphic kind of language popular in business today, especially in the US! It might help to know where this document originates from? Though the fact that the term is hyphenated might be a sign it is not from the US.
It does seem logical, if the text is saying that this device must only be used by trained personnel, for the next sentence to say "if your personnel are not training, you can request a training course from our sales department".
As a former service engineer myself, I can equally appreciate the idea of this being some kind of service call-out — which was indeed my initial interpretation; BUT there is nothing else in your source text extract to imply it is anything about service, and if it were, it would seem curious to ask the SALES dept. (rather than say, tech support). Is the implication "if it is used by untrained personnel, they may have broken it"?

09:29 Sep 28, 2017 

Je vois qu'en allemand aussi, ce n'est pas clair. Je finis par me demander s'il ne s'agit pas tout simplement de "fixer un calendrier de mise en service", cette dernière ne pouvant naturellement être effectuée que par du personnel dûment formé et habilité ?

09:16 Sep 28, 2017 

J'ai aussi posé la question anglais-allemand puisque je traduis ce manuel dans les deux langues (https://www.proz.com/kudoz/english_to_german/engineering_ind... Les collègues ne comprennent pas non plus.
il s'agit d'une table d'opération universelle.

08:32 Sep 28, 2017 

where (other than "trained personnel") you see the notion of training ?

08:31 Sep 28, 2017 

Juste intervention sans doute. Je pense avoir été influencé par le "sur place" de polyglot45, qui a par ailleurs sans doute raison aussi sur l'idée de seule intervention ? Mais s'agirait-il alors de mise en service ou de maintenance ? Le document dans son ensemble devrait pouvoir indiquer quel est le bon sens.

07:51 Sep 28, 2017 

Whilst I agree with your main points, I can't agree with your last one: 'formation sur site' is NOT the same as 'in-service training'!
'in-service' means training while you are employed, as part of your job — i.e. it is not training to enable you to get a job, for example/ BUT the 'in-service' part doesn't make any implication about HOW or WHERE that training is dispensed: it could equally well be on-line, via a correspondence course, or going away to a training centre; hence 'sur site' amounts to over-interpretation and, potentially, a mis-translation.

07:43 Sep 28, 2017 

La référence n'est sans doute pas complètement fautive et si in-service était complété par education ou training, comme cela se voit souvent, il n'y aurait pas de doute. En revanche, je ne vois pas bien l'idée de continue ici dans la mesure où il est question de former (ponctuellment) à ce device. En interne ou en entreprise se rencontre souvent. Ici je formulerais : organiser une formation sur site, puisqu'aussi bien le tout est "télégraphique"...

19:51 Sep 27, 2017 

We do not have enough of your wider context to work this one out; I would originally have rejected Marielle's suggestion of 'in-service (training)' — but then it is the sort of telegraphic jargon one does find in business; but is your wider context in fact talking about 'training' in any form? The fact that your s:t says "This device is intended for use by trained personnel only" certainly could logically imply that what follows is about getting those personnel trained...?