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On properties of probability‐based multivariate process capability indices
Author(s) -
Khadse Kailas Govinda,
Khadse Aditya Kailas
Publication year - 2020
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2659
Subject(s) - univariate , estimator , multivariate statistics , statistics , process capability , computer science , probability distribution , generalization , process capability index , mathematics , econometrics , engineering , work in process , mathematical analysis , operations management
Abstract Multivariate process capability indices (MPCIs) have been proposed to measure multivariate process capability in real‐world application over the past three decades. For the practitioner's point of view, the intention of this paper is to examine the performances and distributional properties of probability‐based MPCIs. Considering issues of construction of capability indices in multivariate setup and computation with performance, we found that probability‐based MPCIs are a proper generalization of univariate basic process capability indices (PCIs). In the beginning of this decade, computation of probability‐based indices was a difficult and time‐consuming task, but in the computer age statistics, computation of probability‐based MPCIs is simple and quick. Recent work on the performance of MPCI NMC pm and distributional properties of its estimator reasonably recommended this index, for use in practical situations. To study distributional properties of natural estimators of probability‐based MPCIs and recommended index estimator, we conducted simulation study. Though natural estimators of probability‐based indices are negatively biased, they are better with respect to mean, relative bias, mean square error. Probability‐based MPCI MC pm is better as compared with NMC pm with respect to performance and as its estimator quality. Hence, in real‐world practice, we recommend probability‐based MPCIs as a multivariate analogue of basic PCIs.

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