Control charts for monitoring relative risk rate in the presence of Weibull competing risks with censored and masked data

ABSTRACT

Competing risks data frequently appear in real-world operations like quality inspections, survival analysis, reliability tests, and clinical trials. From the quality point of view, relative risk rate can be considered an interesting quality indicator in analyzing the competing risks data for statistical process monitoring purposes. The relative risk rate measures the proportion of failures caused by the primary risk among a set of competing risks. This paper introduces two Shewhart-type control charts for monitoring the relative risk rate when the lifetimes of competing risks are independent Weibull random variables. The former chart is constructed based on the maximum likelihood estimation method, while the latter is developed based on the Bayesian approach. The proposed control charts can be applied in Phase II. The calculation of the Bayesian control charts and the evaluation of both process monitoring techniques have been done based on Monte Carlo simulations. The performance of the proposed control charts has been examined based on the average run length metric. The illustrative example is also discussed in detail to demonstrate the applicability of the proposed methods.

KEYWORDS:

• Shewhart-type control chart
• competing risks
• Weibull distribution
• masked data
• censored data

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Adel Ahmadi Nadi

Adel Ahmadi Nadi is currently a postdoctoral fellow of Statistics at the University of Waterloo (U of W) in the Department of Statistics and Actuarial Science, Canada. He finished his Ph.D. in Statistics in 2021 at the Ferdowsi University of Mashhad, Iran. His research mainly focuses on developing statistical techniques in the Statical Quality Control and Measurement Systems Analysis. His current project at U of W is developing statistical methodologies to assess the agreement between Measurement Systems as well as introducing monitoring techniques for complex streaming data in the context of fitness trackers and hospital performance.

Robab Afshari

Robab Afshari is currently an assistant professor in the department of Statistics at the University of Zanjan, Iran. She finished her Ph.D. in Statistics in 2018 at the Ferdowsi University of Mashhad, Iran. She mainly does research on developing fuzzy-based Statical Quality Control techniques.

Bahram Sadeghpour Gildeh

Bahram Sadeghpour Gildeh is a professor of Statistics at the Ferdowsi University of Mashhad, Iran. He received his MSc in Mathematical Statistics at the Ferdowsi University of Mashhad (Iran) and Ph.D. in Informatics at the Blaise Pascal University, France. His research interests include statistical quality control, process capability analysis, and fuzzy statistics.