Statistical process control for a limited amount of data

Abstract

Some production systems control many quality characteristics with a restricted amount of data, not allowing a convenient estimation of the process parameters (mean and variance), thereby creating a difficulty in implementing the traditional Statistical Process Control (SPC). In order to address this question, the approach suggested is to adopt the developments proposed by by Charles Quesenberry, which consists in the statistics sample transformation at time i. This transformation is based on a parameter estimation at time (i – 1). This paper addresses two situations, the univariate and multivariate SPC, with the use of Q dimensionless statistics. Both univariate (Q) and multivariate (MQ) statistics are distributed according to standard Normal distribution. It is also suggested the application of new capability indices QL and QU to study the univariate process capability, which are represented in the mean Q control chart to evaluate in real time the performance of the various processes and predict the possibility of production of nonconforming product, which will increase customer satisfaction. The methodology is applicable to different production systems, both for industry and services. Based on a methodology developed, a case study is presented and discussed.