Online control using integrated moving average model for manufacturing errors

Abstract

We propose a protocol for online control using an Integrated Moving Average (IMA) model for manufacturing errors. This model is suitable for manufacturing processes that are mildly to moderately non-stationary. The protocol is similar to that of the Shewhart X-bar chart. After some number N of the units of product have been manufactured, the ( N + 1)th unit is sampled and its error relative to the target value is checked and recorded. At each check, the observed absolute error is compared against a benchmark, called the correction limit denoted by D to assess the state of errors. When errors are excessive, the system is stopped for correction. Our objective is to determine the ideal settings for N and D from engineering economic and statistical viewpoints. We use root expected mean square error (REMSE) as a measure of the dispersion of errors subject to online control. We use the IMA model to approximate REMSE as a simple function of N and D . Next, we use the approximate REMSE to define a loss function due to manufacturing error. We then determine explicit expressions for N and D that minimize the loss function. The expressions for N and D are simple functions of the engineering economic parameters (manufacturer's cost per unit of product due to errors, cost of checking, cost of correction, and product tolerance) and the two statistical parameters of IMA. We discuss estimation of these parameters and propose how this approach may be used for multiple product characteristics.