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2015•Journal of Qiqihar UniversityRequires access

Process capability analysis in non-normality based on Box-Cox transformation and Johnson transformation

LI Chang-jian

Open publisher page 6 citations

Abstract

The Box-Cox transformation and Johnson transformation methods are studied, their calculation performance for PCIs are compared. The simulation results show that the Box-Cox transformation and Johnson transformation can both convert common probability distributions to normal distribution, with success rate over 97%, while Johnson transformation conversion ability is stronger, with success rate more than 99.5%. In terms of the effectiveness of the PCIs calculation, the performance difference between Box-Cox transformation and Johnson transformation is not big, the substandard products rate calculated form PCIs is compared to theoretical substandard products rate and the relative error is within 2%.

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What this paper is about

The Box-Cox transformation and Johnson transformation methods are studied, their calculation performance for PCIs are compared. The simulation results show that the Box-Cox transformation and Johnson transformation can both convert common probability distributions to normal distribution, with success rate over 97%, while Johnson transformation conversion ability is stronger, with success rate more than 99.5%. In terms of the effectiveness of the PCIs calculation, the performance difference between Box-Cox transformation and Johnson transformation is not big, the substandard products rate calculated form PCIs is compared to theoretical substandard products rate and the relative error is within 2%.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The Box-Cox transformation and Johnson transformation methods are studied, their calculation performance for PCIs are compared. The simulation results show that the Box-Cox transformation and Johnson transformation can both convert common probability distributions to normal distribution, with success rate over 97%, while Johnson transformation conversion ability is stronger, with success rate more than 99.5%. In terms of the effectiveness of the PCIs calculation, the performance difference between Box-Cox transformation and Johnson transformation is not big, the substandard products rate calculated form PCIs is compared to theoretical substandard products rate and the relative error is within 2%.

Key concepts: Power transform, Transformation (genetics), Normality, Mathematics, Process (computing), Statistics, Normal distribution, Data transformation

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Process capability analysis in non-normality based on Box-Cox transformation and Johnson transformation — Research Paper | ScholarLens