The reliability of products can be affected by the quality errors which may occur during the production process. Product reliability decreases when the rate of manufactured products with quality errors increases. Detecting the quality errors and monitoring their rate can be essential in monitoring the reliability of products. In this research, a Beta distribution is utilized to model the random variable of quality error rates. A competing risk model is then used for the reliability of products that may be manufactured with quality errors. Also, a procedure for estimating the assembly error rate according to the products’ failure times is proposed. Finally, a novel process capability Beta control chart is developed for the monitoring of quality errors. The proposed reliability model and control chart are validated through an illustrative example and simulation experiments.