Unbiased Weibull capabilities indices using multiple linear regression |
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| Authors: | Manuel R. Piña‐Monarrez Manuel Baro‐Tijerina Jesús F. Ortiz‐Yañez |
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| Affiliation: | 1. Manufacturing and Industrial Engineering Department of the Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Cd. Juárez Chih, Mexico;2. Doctoral Student of the Technological Doctoral Program at the Engineering and Technological Institute, Universidad Autónoma de Ciudad Juárez, Cd. Juárez, Chih, Mexico;3. Validation Laboratory Department, Ted de México S.A de C.V., Cd. Juárez, Chih, Mexico |
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| Abstract: | Although the recently proposed Weibull process capability indices (PCIs) actually measure the times that the standard deviation (σx) is within the tolerance specifications, because they not accurately estimate neither the log‐mean (μx) nor the σx values, then the actual PCIs are biased. This actually because μx and σx are both estimated without considering the effect that the sample size (n) has over their values. Hence, μx is subestimated and σx is overestimated. As a response to this issue, in this paper, μx and σx 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 μx value completely determines the η value, and (3) the σx value completely determines the β value. Thus, now, since μx and σx 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. |
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| Keywords: | multiple linear regression process capability indices sample size Weibull distribution |
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