Statistical design of ARL-unbiased exponential chart with runs and scans rules using repetitive sampling

Abstract

Exponential chart is widely used to monitor the high-yield processes, i.e., where the failure rate is too low. The exponential chart with runs and scans rules (RSR) scheme has been suggested in the literature for improved performance, especially, for small to moderate shifts. A single sample is used in such a control chart to determine whether the process is in-control (IC) or out-of-control (OOC). However, real-world scenarios may not always permit such conclusive decisions with a single sample. Repetitive sampling can be considered an alternative to single sampling when there is a dispute about the process based on a single sample. In this article, we proposed the exponential chart with the RSR scheme using repetitive sampling and evaluated its performance in terms of average run length $(\mathrm{ARL})$. It is found that the proposed chart is $\mathrm{ARL}$-biased. Therefore, we present a method for designing an $\mathrm{ARL}$-unbiased exponential chart with the RSR scheme using repetitive sampling. The OOC $\mathrm{ARL}$ for various shift levels has been computed in order to assess the proposed chart’s efficiency. The advantages of the suggested monitoring scheme have been examined and compared with both the existing $\mathrm{ARL}$-unbiased exponential chart using repetitive sampling and the RSR scheme using single sampling. Further, the proposed chart has been compared with the existing control chart using single sampling with roughly matched sample size to the IC average sample size $({\mathrm{ASS}}_0)$ of repetitive sampling and found to be the control chart using repetitive sampling is efficient with smaller $\mathrm{ASS}$ values. Finally, in order to illustrate the designed chart an example has been given.