We are so far apart on this discussion it is hard to know where to start.
The PF interval needs to be assessed on an experiential basis. It can be done in fracture mechanics and some other applicatoins but in most cases no one calculates it in reality. The problem with lack of data means we can not use mathematical models (in the majority of cases)- we need to use empirical information. In the practical world we assess orders of magnitude, hours, shifts, days, weeks etc. From this basis we determine inspection intervals that intervene within the PF interval, hourly inspections, inspections each shift, each day etc etc.
If the inspection is not robust then it should not be used. Mathematically though, if the inspection is 80% effective, then doing it twice increases the chances of detection. This is a mathematical fact but in reality, maintainers are far better of improving the detection method hence there is no value in the formula that increases inspection interval because of poor inspection methods.
If you are aware of the formula for probability of detection when an inspection has less than 100% success, it factors in cost.... hence the assessment of the consequences comes into being. then and only then is the consequence a consideration in setting the interval of inspection.