Jerry Fish, JMP Systems Engineer, SAS
Part distributions are easy to measure: parts are built, an operator measures the parts with a gauge, and the results are assembled into a measured part distribution (MPD).
But the resulting distribution is contaminated by errors associated with the measurement system. Random errors, gauge bias, and linearity problems all contribute to inaccuracies in measuring the true part values, so the individual values can never be truly known.
However, if we had a way to estimate the true part distribution (TPD), we could compare it to the MPD and calculate the impact (cost) associated with using the imperfect gauge in terms of Type 1 and Type 2 errors.
It is trivial to estimate the TPD from an MPD if the gauge creates simple normally distributed errors around a normally distributed TPD (i.e., simply subtract variance of gauge from MPD variance to get TPD variance). But what if the gauge has linearity problems? Or what if the TPD has a non-normal shape?
This paper describes a new JSL script for determining an arbitrary (i.e., non-parametric) TPD from an arbitrary MPD and associated gauge performance characteristics. The resulting TPD can then be fed to a second script to determine production costs associated with the imperfect gauge and setting guardbands to optimize economics of the gauge errors. Performance of the estimation routine is evaluated, in terms of shape of TPD, various gauge characteristics, and resolution of distributions.
