Optimal designs of variable sample size control chart for monitoring the multivariate coefficient of variation in short production runs

Abstract

Short production runs are common in industries that require high flexibility and variety in manufacturing. Only a limited amount of researches on multivariate control charts in short production runs exists in the literature. This article proposes two one-sided adaptive charts for monitoring the multivariate coefficient of variation (MCV) in short production runs by varying the sample size (called the VSS MCV SPR charts). The two one-sided adaptive charts are the upper-sided and lower-sided VSS MCV SPR charts for monitoring increasing and decreasing shifts, respectively, in the process MCV. The optimal parameters of the VSS MCV SPR charts in minimizing the out-of-control truncated average run length (TARL) value, for various shift sizes, are presented. The proposed VSS MCV SPR charts outperform their non-adaptive short production runs Shewhart MCV counterparts (called the SH MCV SPR charts), as the former have smaller out-of-control TARL value than the latter, for the same shift size. The sensitivity of the VSS MCV SPR charts, in terms of the probability of signaling an alarm within I inspections is also studied, where the VSS MCV SPR charts surpass their corresponding SH MCV SPR charts. An example for implementing the VSS MCV SPR charts is provided.