Abstract
ABSTRACTThe Weibull distribution is very effective in modelling many different failure mechanisms given its intrinsic flexibility to represent different hazard functions via suitable selections of the shape and scale parameters. Given that the shape parameter of the distribution directly controls the hazard rate, we discuss a Shiryaev–Roberts (SR)–type scheme for monitoring the shape parameter with a fixed scale parameter when using Type II right‐censored Weibull lifetime data. A comparative analysis with existing schemes from the literature is provided by the average run length (ARL), along with the standard deviation of run length (SDRL) and some run‐length percentiles. The average extra quadratic loss (AEQL), the relative mean index (RMI) and the performance comparison index (PCI) are also considered to assess the overall performance. Our simulation results display certain advantages of the SR‐type scheme compared to those of traditional charts in detecting changes in censored lifetime data. An example based on the breaking strengths of the carbon fibre is also presented to demonstrate the proposed method's effectiveness in real situations.
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