I prefer 'total number of'

http://www.proz.com/kudoz/japanese_to_english/linguistics/23...
Japans 353 flashcards | Quizlet
nobeshūrōnissū (延べ[就労]日数), the total number of man-days. nobe (野辺), fields. nobe no okuri o suru (野辺の送りをする), to bury a person's remains. nobebarai (延べ払い), deferred payment, deferred account. nobebō (延棒), [金の] a ...
quizlet.com/168053/japans-353-flash-cards/ - キャッシュ
Toastmasters District 76 Fall Conference 2009 in Yokohama ...
延べ参加人数が200人を超えました! / The total number of participants exceeded 200 ! おかげさまで、1日でかなりの申し込みがあり、10月17日現在、27クラブ・208人の申し込みがありました！ ワークショップ抽選の関係上、お早目の申し込みを歓迎して ...
blog.toastmasters-yokohama-fallconf09.org/article/130555954.html

Let me explain that「のべ/延べ」is not just a regular total.
A ja-ja dictionary (sanseido.net) explains it as
重複していても，それぞれひとつとして数える数え方
'A way of counting in which each is counted as an individual, even if duplicate.'

I learned this concept in elementary school Math in the Japanese curriculum, as "のべ人数":
If a total of 10 people (individuals) have gone to the event but 5 of them went twice and 1 of them went three times, the のべ人数 is 17.
(4 persons * 1 time)+(5 persons * 2 times)+(1 persons * 3 times) = のべ17人
even though the number of individual persons involved is 10.

I don't remember learning this concept in Math in the U.S.A.
This thinking is used in, say, website visitor counters, but I wasn't able to find a term for it.
I would describe it as "non-unique", in contrast to "unique visitors."
I found this idea in a page on the Nobel prize website:
"A small number of individuals and organizations have been honoured more than once, which means that 881 individuals and 23 unique organizations have received the Nobel Prize in total."

So, in applying this definition to your のべ検査時間 and のべ培養時間, it would mean that the sentence is counting each hour of 検査時間 and 培養時間 it took for each sample (or batch or another unit, depending on the context), even if the they were running concurrently so it didn't take as much actual time as if they had run back-to-back.
Example:
1 sample/batch requires 3 hours of test time.
There were 5 samples/batches tested.
The 検査時間 was のべ15時間, whether it actually took 15 hours or subsequent tests started 10 minutes after the previous one so it only took 3h 40m until the last one completed.

I think, in English, though, "a total of 15 test hours" includes the implication that "it's not describing the usual hours," but the best way I can think of describing this explicitly is "non-unique hours."