A process control method based on five-parameter generalized lambda distribution

Abstract

The use of control charts in statistical quality control, which are statistical measures of quality limits, is based on several assumptions. For instance, the process output distribution is assumed to follow a specified probability distribution (normal for continuous measurements and binomial or Poisson for attribute data) and the process supposed to be for large production runs. These assumptions are not always fulfilled in practice. This paper focuses on the problem when the process monitored has an output which has unknown distribution, or/and when the production run is short. The five-parameter generalized lambda distributions (GLD) which are subject to estimating data distributions, as a very flexible family of statistical distributions is presented and proposed as the base of control parameters estimation. The proposed chart is of the Shewhart type and simple equations are proposed for calculating the lower and upper control limits (LCL and UCL) for unknown distribution type of data. When the underlying distribution cannot be modeled sufficiently accurately, the presented control chart comes into the picture. We develop a computationally efficient method for accurate calculations of the control limits. As the vital measure of performance of SPC methods, we compute ARL’s and compare them to show the explicit excellence of the proposed method.