By using the expectation–maximization technique, this paper tackles the crucial issue of estimating unknown parameters in competing risks models. In a framework with latent failure periods following exponential and Weibull distributions, we develop Bayesian estimates under linear-exponential and squared-error loss functions, in addition to standard maximum likelihood estimates. The accuracy of the suggested estimators is evaluated in a thorough simulation exercise using a range of parameter values. Additionally, two real-world datasets in engineering and survival areas illustrate the methodology’s applicability. The outcomes demonstrate that the expectation–maximization method can handle partial cause-of-failure data, making it a flexible tool for reliability and survival research.