Approaches for measurement system analysis considering randomness and fuzziness

For some quality inspection practices, subjective judgements based on the inspectors’ experience and knowledge, such as visual inspection, may be required for some particular quality characteristics. This kind of measurement system, including its associated randomness and fuzziness, should be assessed by Measurement system analysis (MSA) before its application. For such purpose, this article represents observations with randomness and fuzziness from MSAs as fuzzy random variables, and then two pairs of descriptive parameters, i.e., expected value and variance, are derived. Then, the relationship of the total sum of squares of factors is proven to hold, so that fuzzy analysis of variance (FANOVA) in terms of gauge repeatability and reproducibility can be developed. The proposed approach has the advantage that FANOVA is developed based on the relationship of the total sum of squares of factors, considering randomness and fuzziness. A real case in the semiconductor packaging industry is used to demonstrate the applicability of the proposed approaches to MSA.