Process capability vector for multivariate nonlinear profiles

Abstract

We present a two-phase methodology based on the concept of depth to measure the capability of processes characterized by the functional relationship of multivariate nonlinear profile data, treated as multivariate functional observations. In the first phase, the modified tolerance region is estimated using a historical data set, while in the second, a current process is assessed using the proposed three-component vector, where the first component measures the volume ratio between the current process region and the modified tolerance region; the second measures the probability that the median of the current process is within the modified tolerance region, and the third measures the probability that the current process region is inside the modified tolerance region. To facilitate interpretation, a single index is derived from this capability vector. A simulation study is carried out to assess the performance of the proposed method. An real example illustrates the applicability of this approach.

Keywords:

• Multivariate functional data
• multivariate nonlinear profiles
• process capability indices

Disclosure statement

No potential conflict of interest was reported by the author(s).