Y=F(X): How to Define Y Without the Customer?

I’ve been reading this excellent article: Y=f(X) Roadmap: Telling the DMAIC Story Using Xs and Ys. It argues that each DMAIC phase can be described by how it contributes to identifying which few process and input variables mainly influence the process output measures:

• Define: Understand the project Y and how to measure it.
• Measure: Prioritize potential Xs and measure Xs and Y.
• Analyze: Test X-Y relationships and verify/quantify important Xs.
• Improve: Implement solutions to improve Y and address important Xs.
• Control: Monitor important Xs and the Y over time.

However, I’ve a question:

During the Define stage of a Six Sigma project it is important to get a clear understanding of the project Y. Here you would define Y as a measurable process metric that tells how well the process is performing today (the baseline) and how performance should be after process improvement (the goal). Y (sometimes called CTQs) is a result of the drivers (Xs) within processes. To reach a clear definition of the Y, the voice of the customer (VOC) is normally used.

My question is what if the customer never sees the failure mode in question and the problem is purely experienced and captured internally? The problem is the customer will not know what the CTQ factors are which we have to improve and control to prevent or eliminate the failure? The failure mode in question here is a pass/fail at final inspection.

How would you identify these CTQ factors and verify these?

I’ve also posted the same question here and here.