Bootstrap‐Based Control Chart for Percentiles of the Generalized Lognormal Distribution With Reliability Applications

ABSTRACT The generalized lognormal (GLN) distribution, which extends the lognormal distribution by incorporating the Box–Cox transformation, is commonly used for modeling datasets that exhibit right‐skewed behavior. However, statistical control charts related to GLN percentiles, which are essential indicators of product quality for certain products, have not been explored in the existing literature. Additionally, the Shewhart‐type control chart may not be suitable for monitoring GLN percentiles, as the sampling distributions of percentile estimators are often unknown or not bell‐shaped, particularly when dealing with relatively small sample sizes. In this paper, we propose a bootstrap‐based control chart to monitor GLN percentiles and also establish the Shewhart‐type control chart using normality approximations. We conduct extensive Monte Carlo simulations to compare the finite‐sample performance of the two proposed control charts. Numerical results show that the proposed bootstrap control chart generally outperforms the Shewhart‐type control chart in terms of the average run length and the standard deviation of run length. A real‐data application is also provided for illustrative purposes.