Proportionate Hazards Model Cost Function

Just a post to see if anyone on here is familiar with Andrew Jardine's work on hazard, risk and cost correlations within the PHM.

A few questions when looking at the cost function, here is the literature I am following:


Is Q(d) simply the CDF? If not how is it different to F(t)? (the CDF)
How to determine the function W(d)?

I think I am missing some fundamental point with this problem as I have been looking at it for days. The notation in the literature is not the easiest to follow either. When I enter values in the cost function using the normal CDF as a function of time I get a minimum at t = 0 which can't be right.

Any help would be very much appreciated, thank-you, and apologies for how vague this post is, I wasn't sure the best way to write it.