Daniel Duret

Weighted Inertial Tolerancing

The objective of tolerancing methods is to limit the variations of a characteristic while trying to minimize the cost of realization. Traditionally expressed in the form of an interval (min, max), it can also be expressed in a different form as in the case of inertial tolerancing. The principle of inertial tolerancing consists of tolerancing the mean square deviation in relationship to the target. This new tolerancing method has many properties that the property of additivity of the mean square deviation offers. However, when several characteristics are added to give a resulting characteristic, it leads to a significant tightening of the variations around the target in the case of a process with a small dispersion. Our proposal consists of defining a new alternative of inertial tolerancing: weighted inertial tolerancing. Its goal is to obtain the best possible compromise between statistical tolerancing and worst-case tolerancing method. One will be able to use it when it is not useful to guarantee an inertia on the resulting characteristic, but simply to limit the variations compared with the target.

Process adjustment by a Bayesian approach

Abstract 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.