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Conditional Weibull Control Charts Using Multiple Linear Regression
Author(s) -
PiñaMonarrez Manuel R.
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.2056
Subject(s) - weibull distribution , statistics , mathematics , control limits , reliability (semiconductor) , control chart , standard deviation , shape parameter , computer science , process (computing) , physics , power (physics) , quantum mechanics , operating system
Because in Weibull analysis, the key variable to be monitored is the lower reliability index ( R ( t )), and because the R ( t ) index is completely determined by both the lower scale parameter ( η ) and the lower shape parameter ( β ), then based on the direct relationships between η and β with the log‐mean ( μ x ) and the log‐standard deviation ( σ x ) of the analyzed lifetime data, a pair of control charts to monitor a Weibull process is proposed. Moreover, because the fact that in Weibull analysis, right censored data is common, and because it gives uncertainty to the estimated Weibull parameters, then in the proposed charts, μ x and σ x are estimated of the conditional expected times of the related Weibull family. After that both, μ x and σ x are used to monitor the Weibull process. In particular, μ x was set as the lower control limit to monitor η , and σ x was set as the upper control limit to monitor β. Numerical applications are used to show how the charts work. Copyright © 2016 John Wiley & Sons, Ltd.