You don't state your industry or which standard(s) you are registered to, so first your Customer(s) may have specific expectations for validating the removal of in-process tests.
In general there are several things you can do:
- Since these are in-process tests, I assume that yoru final acceptance testing would catch any defects that might occur. In which case, you could 'justify' the elimination of these tests by a long history of no defects, a low severity of the effect of the defect and the liklihood that your final acceptance testing would catch them. In other words you are willing to take the cost and delivery hit should the defects occur
- Secondly one can justify the removal based on preventive controls at your supplier or in-process systems. these typically should be validated as effective.
The bottom line (unless you have specific Customer requirements) inspections are risk based: how likely is it that the defect will occur? What is the effect of the defect should it occur? What is your ability to detect it (downstream of the eliminated inspection) should it occur? This is really your decision - what risk are you willing to tolerate?