Hotelling's T2 control charts with fixed and variable sample sizes for monitoring short production runs

Short production runs are common in enterprises that require a high degree of flexibility and variety in manufacturing processes. To date, past research on short production runs has little focus on the multivariate control charts. In view of this, fixed sample size (FSS) and variable sample size (VSS) Hotelling's T² charts are designed to monitor the process mean when the production horizon is finite. Optimal parameters to minimize the out‐of‐control (1) truncated average run length (TARL) and (2) expected TARL (ETARL) are provided such that the in‐control TARL is equal to the number of inspections (say I). The numerical study considers the run length performances of the FSS and VSS T² short‐run charts for both known and unknown shift sizes. The VSS T² short‐run chart performs well in swiftly detecting various mean shifts in comparison with the FSS T² short‐run chart. Additionally, the VSS T² short‐run chart is superior to the FSS T² short‐run chart, in terms of the truncated standard deviation of the run length, expected truncated standard deviation of the run length, probability that the chart signals an alarm within the I inspections, ie, P(I) and expected P(I). A case study on the impurity profile of a crystalline drug substance illustrates the implementation of the VSS T² short‐run chart.