Personally, I wouldn't consider the miss other than as a routine operational event which one is expecting to be a high probability when commencing many approaches ... but, regardless of definitions ... what are you intending to do IF the noise stops on one below minimums ?
Me .. I'd be having some pertinent corporate risk discussions with the chief pilot and senior ops engineering folk .... all sounds a bit like blind man's buff to me ... or else take out more personal insurance so that your family can pay the damages awarded and/or live better after the accident ....