PetroStreet

We have a situation where welding construction flaws are getting surfaced and resulting in leaks.
What sort of quality inspection program should be put in place to address this issue?
Random inspection? What else can help us ensuring that the welds which are now in-service are all healthy?

Yes. If you are already seeing in-service leaks attributable to construction/welding flaws, I would not treat this simply as a routine inspection issue. It suggests a potential systemic fabrication-quality problem, and the response should have two parallel tracks:
1.Find and control the population of defective welds already in service.
2. Strengthen the construction QA/QC system so new defects do not enter the plant.
Random inspection alone is not sufficient for the first objective.

Before deciding on an inspection percentage, perform a weld failure/defect trend analysis.

For every leak or weld defect, capture:
Line number / piping class
Weld number
Weld type — butt, socket, branch, fillet, nozzle, attachment, etc.
Welder ID
Welding procedure
Welding consumable
Material/P-number
Thickness and diameter
Service and operating conditions
Construction contractor
Construction period
NDE originally performed
NDE method — RT, UT, PT, MT
Original NDE result
Defect type discovered
Exact defect location
Failure mechanism
Whether the defect was fabrication-related or service-induced
(though you may not find all these inputs easily from construction records!)

Then look for common denominators.
For example, if 70% of the leaks involve welds made by 3 particular welders, one contractor, one construction campaign, one WPS, or one particular piping class, you have a very different problem from random isolated weld failures.

Don't really know about the real situation you are in but the basic question here which you must ask is:
What weld population could reasonably contain the same defect, and what examination extent gives us sufficient confidence that the population is fit for continued service?
Answer would be coming from the actual data you have with you and definitely would provide some pointers.

The actual issue is the coverage and allocation of extra resources.
Then not everything could be picked up when the piping circuits are all online.
mechcolor has provided some very good pointers to narrow down where exactly we might be having the issue but this all data, I hope we find that all.

A plan is required to be made for such a scenario. These are all those necessary QC checks which were not rightly implemented and now people at site have to face them all.
Better you get extra resources assign for this particular inspection call.
And the call itself is required to be based upon two of the major factors in my opinion. One is that what is critical for you (should not leak as flammable or toxic) + history of failures (locations etc.). Plot these two factors, risk rate them and perform inspections. Keep monitoring the results and keep minimizing the risk till you can say, "No what may leak carries an overall LOW risk". You cannot keep investing finding low risk flaws which upon surfacing would not cause any notable damages.