Hmn…. If you need to translate those words, not only to find their differences, how about the followings? Inspection is to decide whether something passed or failed by comparing with criteria. Analysis is to find an actual reason why something happened.
@hashimoton2020 yes I understand your explanation, thanks. I'm working in a medical laboratory in andrology. So, analysis for us is to quantify the concentration of a molecule or the rate of cells present in a sample. when I search the translation of blood test (for example), I find 血液検査 and not 血液分析。 But when I would say that the analysis are made only in the morning, I find 分析は午前中にのみ行われます。 That was the reason of my question.