Control charts for the shape of Gompertz distribution

On one hand, Gompertz distribution is a notable continuous lifetime model, which plays a vital role in many disciplines, especially industrial engineering. On the other hand, control charts have a significant place in industrial engineering, particularly quality control. Monitoring the product lifetimes arising from this model is the main goal of the present study. Considering the crucial performances of the shape parameter in the Gompertz distribution, we are going to provide control charts that monitor, whether the shape parameter changes. These charts are provided for three sampling schemes including one sample, right censoring case and competing risks data. In addition, the same charts are available, in the presence of missing values in every sampling plan. In this regard, we also assess the case of masked causes in competing risk data. To this end, a suitable statistic is given and the prediction problems due to both missing values and masked causes of failures have been investigated. Finally, utilizing the same statistic, the sample size is also monitored and some corresponding concepts are also presented.