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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. [ABSTRACT FROM AUTHOR]

In this paper, a variable repetitive group sampling (VRGS) plan is proposed based on the exponentially weighted moving average (EWMA) statistic with yield index S p k T for inspection of mutually independent and multivariate normally distributed characteristics. Plan parameters are found optimally based on asymptotic distribution of S p k T using a non linear optimization. A simulation study indicates that the reported parameters can thoroughly warrant determined risks for finite sample sizes. This work also extends application of the proposed plan to the class of correlated characteristics. The obtained findings show that the proposed plan significantly reduces required average sample number compared to the existing modified VRGS plan, single, double, and multiple dependent state sampling plans with yield-based EWMA statistic. Two industrial examples are presented to illustrate the application of the proposed plan in real world. [ABSTRACT FROM AUTHOR]