Control chart for monitoring the Weibull shape parameter under two competing risks

In this paper, we propose a control chart to monitor the Weibull shape parameter where the observations are censored due to competing risks. We assume that the failure occurs due to two competing risks that are independent and follow Weibull distribution with different shape and scale parameters. The control charts are proposed to monitor one or both of the shape parameters of competing risk distributions and established based on the conditional expected values. The proposed control chart for both shape parameters is used in certain situations and allows to monitor both shape parameters in only one chart. The control limits depend on the sample size, number of failures due to each risk and the desired stable average run length (ARL). We also consider the estimation problem of the target parameters when the Phase I sample is incomplete. We assumed that some of the products that fail during the life testing have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the expectation-maximization (EM) algorithm is proposed to estimate the parameters. For both cases, with and without masking, the behaviour of ARLs of charts is studied through the numerical methods. The influence of masking on the performance of proposed charts is also studied through a simulation study. An example illustrates the applicability of the proposed charts.