The multivariate control chart with variable dimension for monitoring both location and dispersion

Abstract

When p related variables in a multivariate process need to be controlled, p₁ variables are easy to measure and inexpensive, while the rest of p₂ variables are difficult to measure and expensive. Therefore, controlling the whole set of p variables may be difficult and expensive. In order to reduce sampling costs of the multivariate control chart in detecting shifts in the process mean vector and the process covariance matrix of a multivariate normally distributed process, a new multivariate control chart with variable dimension (VD) is proposed, which uses two different dimensions, two different control limits and one warming limit. The VD multivariate control chart uses genetic algorithm to optimize the parameters and Markov chain model to calculate the performance measures. The performance of the proposed optimized VD chart is compared with the standard chart for which all p₁ and p variables are measured. Numerical results show that the VD chart surpasses the standard chart in detecting process mean vector and the process covariance matrix, while also reducing sampling costs.

Keywords:

• ARL
• Markov chain
• Mean
• Variance covariance matrix
• Variable dimension