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Unbiased Weibull capabilities indices using multiple linear regression
Author(s) -
PiñaMonarrez Manuel R.,
BaroTijerina Manuel,
OrtizYañez Jesús F.
Publication year - 2017
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.2155
Subject(s) - weibull distribution , statistics , mathematics , function (biology) , value (mathematics) , standard deviation , measure (data warehouse) , linear regression , computer science , data mining , evolutionary biology , biology
Although the recently proposed Weibull process capability indices (PCIs) actually measure the times that the standard deviation ( σ x ) is within the tolerance specifications, because they not accurately estimate neither the log‐mean ( μ x ) nor the σ x values, then the actual PCIs are biased. This actually because μ x and σ x are both estimated without considering the effect that the sample size ( n ) has over their values. Hence, μ x is subestimated and σ x is overestimated. As a response to this issue, in this paper, μ x and σ x are estimated in function of n . In particular, the PCIs' efficiency is based on the following facts: (1) the derived n value is unique and it completely determines η , (2) the μ x value completely determines the η value, and (3) the σ x value completely determines the β value. Thus, now, since μ x and σ x are in function of n and they completely determine β and η , then the proposed PCIs are unbiased, and they completely represent the analyzed process also. Finally, a step by step numerical application is given.