Unbiased Weibull capabilities indices using multiple linear regression

摘要

Although the recently proposed Weibull process capability indices (PCIs) actually measure the times that the standard deviation (sigma(x)) is within the tolerance specifications, because they not accurately estimate neither the log-mean (mu(x)) nor the sigma(x) values, then the actual PCIs are biased. This actually because mu(x) and sigma(x) are both estimated without considering the effect that the sample size (eta) has over their values. Hence, mu(x) is subestimated and sx is overestimated. As a response to this issue, in this paper, mu(x) and sigma(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 eta, (2) the mu(x) value completely determines the n value, and (3) the sigma(x) value completely determines the beta value. Thus, now, since mu(x) and sigma(x) are in function of eta and they completely determine beta and eta, then the proposed PCIs are unbiased, and they completely represent the analyzed process also. Finally, a step by step numerical application is given.