Learn Russian: Жёсткий контроль гарантирует отсутствие дефектов. - Strict control guarantees the absence of defects.

You would say наижесточайший контроль. The prefix наи- is attached to the synthetic superlative form of an adjective to express the absolute highest degree. The superlative of жёсткий is жесточайший, making the absolute superlative наижесточайший.

I learned that жёсткий means physically hard. Is it common to use it for 'strict'?

Yes, while its literal meaning is hard or rigid, жёсткий is the standard word for strict, tough, or uncompromising when talking about rules, measures, or systems. You will frequently see phrases like жёсткие меры (tough measures) alongside жёсткий контроль.

The verb гарантирует comes from гарантировать. Is this imperfective or perfective here?

Гарантировать is a biaspectual verb, meaning the exact same dictionary form serves as both the imperfective and perfective aspect depending on context. Because this sentence states a general, ongoing fact, it functions as an imperfective verb here in the present tense.

Why is дефектов in the genitive case?

The direct object of the verb is отсутствие (absence), which takes the accusative case. Дефектов is in the genitive plural because it modifies that noun. Just as English uses 'of' in 'absence of defects', Russian uses the genitive case to link these two nouns.