An optimal design of multiattribute control charts for processes subject to a multiplicity of assignable causes

We have developed a model for the optimal design of multiattribute control charts (MACCs) for processes subject to multiple assignable causes. The development of the model is based on the J approximation (J.K. Jolayemi, Comput. Stat. Data Anal., 18, 1994, pp 403-417; J.K. Jolayemi and J.N. Berrettoni, Appl. Math. Comput. 32 (1) (1989) pp. 1-16) and on the modification and extension of Gibra's model for the design of attribute control charts (I.N. Gibra, J. Quality Technol. 13 (2) (1981) pp. 93-99). A computational procedure for optimizing the model is presented. Some numerical examples are given to illustrate the model and the computational procedure. The examples show that the MACC and its design parameters are very sensitive to changes in the values of the input parameters. The model does not require any approximation by the matching process (see I.N. Gibra, J. Quality Technol. 13 (2) (1981) pp. 93-99 for an example of the matching process), as an exact solution to it is very easy to obtain. The justifications for applying the J approximation (JA) are illustrated by numerical examples. The numerical examples show that JA is very accurate in determining sample sizes. The examples also show that unlike when used to compute convolution probability values, JA is indifferent to the differences in the values of the proportion defectives when applied for determining sample sizes - whatever the magnitudes of the differences. (C) 2000 Elsevier Science Inc. All rights reserved.