Online monitoring of the Weibull distributed process based on progressive Type II censoring scheme

Designing more efficient control charts is critical to enhance product lifetime management and improve product stability in many research fields and industrial productions. To overcome the limitation that censored data frequently appears in lifetime experiments, we propose three monitoring schemes to detect the Weibull scale parameter under progressive Type II censored data based on the likelihood ratio test, maximum likelihood estimation and a novel weighted likelihood ratio test, respectively. Furthermore, the proposed schemes enable extension to joint monitor both the scale parameter and shape parameter of the Weibull distributed process. These control charts are improved with the corresponding self-starting schemes when there are not adequate in-control datasets in Phase I. Numerous simulation experiments and a real dataset on the breaking strength of carbon fibers are applied to illustrate the excellent performance and practical application of our methods separately.