On estimating control limits of X ̄ chart when the number of subgroups is small

When the process parameters are not known, we present an approach for establishing X̄ control limits that enables the practitioner to begin monitoring the process means at an earlier stage other than the usual approach. The proposed control limits can be constructed easily through student’s t-distribution and are close to any specific percentile of run length distribution of the true limits, even when only a few initial subgroups are available. Performances of the proposed approach are studied by Monte Carlo simulation. The simulation results show that the proposed control limits perform similarly to the true limits even when the limits are estimated from a small number of initial subgroups .