Multivariate process adjustment by boundary contraction and taking the cost of each setting parameter into account
- PDF / 1,490,801 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 39 Downloads / 230 Views
ORIGINAL ARTICLE
Multivariate process adjustment by boundary contraction and taking the cost of each setting parameter into account Éric Pairel 1 Received: 17 April 2020 / Accepted: 17 August 2020 / Published online: 6 October 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The adjustment problem of a process, which creates a scatter and a drift on the characteristics of its products, is extremely common in industry. Although old, it still has no satisfactory solution. To solve it, this problem is first formulated on a direct variational model, which it is always possible to establish for such a process. Control limits and a target are to be chosen for each of the product’s quality characteristics. An adjustment is sought if, at least, one characteristic of the last product is outside its limits. It is calculated by optimizing a problem of contracting the limits containing the characteristics towards their targets. Applied to a simulated production of one hundred and fifty workpieces, the “boundary contraction adjustment” results in two times less adjustments than the method of “minimum mean squared error” and, especially, makes it possible to control, automatically, the quality of all the characteristics. Keywords Statistical process control (SPC) . Statistical process adjustment (SPA) . Minimum mean squared error (MMSE) . Setting . Boundary contraction adjustment (BCA)
1 Introduction The addressed issue in this paper is the adjustment of the manufacturing processes creating a drift and a scatter of the characteristics of their products. This is obviously a problem that is extremely common in industries and not yet satisfactorily solved from a practical point of view and even from a scientific point of view for the processes we are considering. These processes have the following fairly frequent properties: & &
&
They have no dynamics, that is to say, a modification of their setting immediately changes the characteristics of their products. They create a gradual drift of the characteristics. This is particularly the case for machining processes whose tools wear out during production and therefore drift the dimensions. They are adjusted according to the characteristics measured on their products.
* Éric Pairel [email protected] 1
Univ. Savoie Mont Blanc, SYMME, F-74000 Annecy, France
&
The characteristics all have an instantaneous random scatter created by the manufacturing process but also by the measurement process so that we do not know precisely their central tendencies that must be corrected.
Currently, in companies, these processes are mostly adjusted by adjusters based solely on their experience. They are sometimes a little helped by the implementation of SPC control charts that allow them to know when to set up the process. The most commonly used charts are the Shewhart control chart [1] and the acceptance control chart [2]. The Shewhart control chart uses limits symmetrically set around the target, below which Deming [3] has shown that one should not seek to correct t
Data Loading...
