Empirical Likelihood Based Control Charts

The success of the implementation of control chart depends upon the assumptions made on the distribution of the quality characteristics. If the distributional assumption deviates too much from the true one or if it is misspecified, the performance of the control chart is seriously affected and one may make wrong conclusions about the process. To avoid such situations, we propose a new class of control chart based on the empirical likelihood (EL). We propose to monitor the EL ratio statistic for mean and use resampling method to arrive at its empirical distribution which is inverted to obtain the control limits. Our simulation results clearly indicated that EL control charts have a comparable performance with Shewhart control chart, when the distribution of the quality characteristic follows a normal distribution. When the distribution of quality characteristics are misspecified, the EL control chart shows a better performance with all competing control charts. Finally, our proposed method is illustrated by a real example.