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Non‐normal Capability Indices for the Weibull and Lognormal Distributions
Author(s) -
PiñaMonarrez Manuel R.,
OrtizYañez Jesús F.,
RodríguezBorbón Manuel I.
Publication year - 2016
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.1832
Subject(s) - weibull distribution , log normal distribution , gumbel distribution , standard deviation , statistics , mathematics , extreme value theory , normal distribution , generalized extreme value distribution
Because the normal process capability indices (PCIs) C p , C pu , C pl , and C pk represent the times that the process standard deviation is within the specification limits; then, based on and by using the direct relations among the parameters of the Weibull, Gumbel (minimum extreme value type I) and lognormal distributions, the Weibull and lognormal PCIs are derived in this paper. On the other hand, because the proposed PCIs P p , P pu , P pl , and P pk were derived as a function of the mean and standard deviation of the analyzed process, they have the same practical meaning with those of the normal distribution. Results show that the proposed PCIs could be used as the standard C p , C pu , C pl , and C pk if a short‐term variance is analyzed. An application to a set of simulated data is presented. Copyright © 2015 John Wiley & Sons, Ltd.