A distribution-free adaptive CUSUM-sign chart for monitoring shifts in the location of unknown industrial process

Abstract

In most of the manufacturing industry, the distributional assumption of the online working processes is customarily unknown or hard to meet. In such situations, parametric charting mechanisms generally designed under normality assumptions of the model yield more false alarms and invalid out-of-control (OOC) comparisons. The nonparametric (distribution-free) charts are a better choice for practitioners in such cases as their in-control (IC) run length (RL) profiles remain the same. The study intends to develop a new distribution-free adaptive CUSUM sign (NPACUSUM-SN; named hereafter) chart for monitoring the process location. The proposed NPACUSUM-SN chart estimates the unknown process mean shift using an unbiased function and updates adaptively the reference parameter of the CUSUM statistic. The IC robustness of the conventional adaptive CUSUM and the proposed NPACUSUM-SN charts under the symmetric, skewed, and contaminated normal (CN) distributions have been computed using Monte Carlo simulations. The OOC RL profiles of the proposed study have been assessed for the initial state and the shift delay (steady state) in the processes. The proposed NPACUSUM-SN chart shows more resistance against non-normality and effective behaviour as compared to its conventional competitor. The proposed NPACUSUM-SN chart provides uniformly efficient RL characteristics as compared to its counterparts. Implementation of the proposal is made by using a manufacturing industry dataset along with an artificial dataset.