Process adjustment by a Bayesian approach

In a production or measure situation, operators are required to make corrections to a process using the measurement of a sample. In both cases, it is always difficult to suggest a correction from a deviation. The correction is the result of two different deviations: one in set-up and the second in production. The latter is considered as noise. The objective of this paper is to propose an original approach to calculate the best correction using a Bayesian approach. A correction formula is given with three assumptions as regards adjusting the distribution: uniform, triangular and normal distribution. This paper gives a graphical interpretation of these different assumptions and a discussion of the results. Based on these results, the paper proposes a practical rule for calculating the most likely maladjustment in the case of a normal distribution. This practical rule gives the best adjustment using a simple relation (Adjustment = K*sample mean) where K depends on the sample size, the ratio between the maladjustment and the short-term variability and a Type I risk of large maladjustment