A multivariate non-parametric control chart based on run test

Abstract

Multivariate control charts have a wide range of applications in the field of quality management. This paper proposes a new multivariate non-parametric control chart based on run test. First, the shortest Hamiltonian path of the observations is determined by means of Kruskal algorithm. Then an EWMA control chart with sliding window based on the number of runs of the shortest Hamiltonian path is proposed. The selection of the design parameters and the determination of control limit are discussed in detail. The effect of different dimensions, shift magnitude, reference data size and the underlying distribution are investigated via Monte Carlo simulation. Compared with three recent non-parametric multivariate control charts, the newly proposed chart has superior performance when mean shift magnitude is large and the underlying distribution is non-normal. Also, the chart proposed is more suitable for monitoring in high-dimensional situations. A real case study is also presented to show the implementation procedures of the chart.