Most people get entangled try to understand what is reliability and what is integrity. It is pretty simple if we can visualized it as our car. Yes, that vehicle that we drive everyday to go to work. Integrity refer to the car in its running conditions. Is the car still have the doors, engine, seat belt, steering and others essentials equipment for it to be driven and maneuver? If you car is still intact than the integrity of the car is in good level. Reliability refer to the car condition after some minor collision or you just miss your 5000 KM or 10,000 KM inspection and service at nearby workshop. If the car still running despite of having dented front bumper and not yet being service, than the car reliability level is pretty good!!

Integrity and reliability somehow related in structural engineering world. Since most of offshore structures are at sea, inspection scheme can be really costly and sometimes invites other risk like boat impact and diver's safety. This is the part that we can utilized reliability and integrity engineering to optimize cost but still maintain the risk to be as low as possible. Intact platform (without losing members) with good inspections plan  usually have good integrity but not necessary have good reliability. Reliability also depend on type of braces whether it is X, K or Y brace. Additional loading and changing environmental condition also effect reliability of offshore structures.

This definition however might varies throughout companies and universities around the world, but this is how I understand it.  I always remember that we inspect to take care the integrity so the structure will always fit for purpose. We strengthen the structure to increase its reliability against future load uncertainties or addition, so we will always have safe structure. :)