The c-Chart with Bootstrap Adjusted Control Limits to Improve Conditional Performance

The integrity of Phase II control charting depends on the accuracy of Phase I estimation. Studies have shown that extremely large sample sizes are needed in Phase I to ensure that performance of control charts with estimated in‐control parameters is comparable with the performance of charts with known parameters. The sample size recommendations can be impractical for attribute control charts. In this article, the in‐control performance of the c‐chart with an estimated in‐control average number of non‐conforming items is assessed. We show that the sampling variability associated with estimation results in a high percentage of control charts with in‐control average run lengths well below that of corresponding control charts with known parameters. This sampling variability can be described as between‐practitioner variability. To overcome the variability in performance, a c‐chart with bootstrapped control limits is recommended. A simulation study reveals that these adjusted bootstrapped control limits improve the conditional average run length performance of the c‐chart by controlling the proportion of charts with in‐control average run length performance below a given value. The out‐of‐control performance of the c‐chart with adjusted limits is also discussed.