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I have two questions.

  1. Should I use 'challenges' or 'challenge' in this text?
  2. Should I use article 'the' or 'a' before 'criteria'?

That is why firms attach great importance to the possibility of using integrated system. But the key challenges for people designing solutions for manufacture applications is a complete lack of a criteria and requirements.

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Refine the whole paragraph. It does not look proper. –  Maulik V Apr 24 at 5:04
2  
Not directly related to your question, but in the first sentence, it could be "an/the integrated system" or "integrated systems". Maybe you can tell in context but I can't. Also it should be manufacturing applications*. –  user3169 Apr 24 at 6:11
    
I would rewrite it like this: That is why firms recognize the importance of the possibility of using integrated systems. But the key challenge for people designing solutions for manufacturing applications is the complete lack of criteria and requirements. –  Damkerng T. Apr 24 at 12:19

2 Answers 2

I'm still not fully convinced with the paragraph (many flaws). But, since you asked particularly about those words and the articles, I'm addressing that so that to clarify that in general. Maybe, you take care of this in future then.

In this case, you are talking about the challenge of lacking something (the word lack in your sentence is used as a singular and countable). Thus, it's the challenge and not two or more challenges!

In any case, criteria will not have a, it's plural. The singular will be criterion.

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Re 1:

But the key challenge for people [...] is

Since key and is are singular, their noun, challenge had better be as well.

Re 2:

a complete lack of criteria and requirements.

criteria is plural, so takes no article here.

Additionally, though you didn't ask, manufacture is incorrect, and you probably want manufacturing.

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Like most adjectives, key is unmarked for number. It would be okay with plural challenges: "What are the key challenges you face as a producer?" –  snailboat Apr 24 at 7:27
    
@snailplane, quite right, my mistake! Serves me right for posting after my bedtime. –  Codeswitcher Apr 24 at 17:46

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