How would you calculate this?

[SoaringView]

So let us suppose we have a 3 part assembly as a final product. The first part has 5 dimensions. The capability (z-bench) on the dimensions/specifications are listed below:
Dim 1: 4.5
Dim 2: 2.0
Dim 3: 0.5
Dim 4: 3
Dim 5: 6

Part 2 has 3 dimensions: All have a z-bench of 4.0

Part 3 has 4 dimensions: All have a z-bench of 2.5.

Each part is single step processed and then assembled. Let's suppose, for the sake of simplicity, that there are only two specifications for the stack up of the assembly and that the capability of those stack ups are a results of dimensions Part 1-dim 3, part 2- dim1, and 3-1. The capability for those 2 stack up's turns out to be 5.0 for each.

The assembly undergoes two required tests and the capability of those results are 3 sigma and 4 sigma respectively.

Question: What is the overall process capability of the product?

 

[Miner]

I would use a Monte Carlo simulation using the actual mean and standard deviations for the components to obtain the mean and standard deviation of the assembly.

 

[Bev D]

I would use actual data of the final results over time and plot it against the specification limits and probably calculate the failure rate.
short fo that I would use bootstrapping of the data you have.

...but if this is a homework question then you won’t have any data and you won’t know what the distribution is and...it may be mathematically interesting but has no resemblance to real life. (I haven’t heard the term ‘z-bench’ in over 25 years.

 

[Miner]

(I haven’t heard the term ‘z-bench’ in over 25 years.

It's mostly used in Design for Six Sigma.

 

[Bev D]

It used to mean the Ppk that results when you take into account both tails of the distribution instead of just the worst tail...for both DFSS and DMAIC but it's really an old term