Unbiased Weibull capabilities indices using multiple linear regression

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.