Assessment of reliability and availability of a system by using a bivariate stochastic model

In the present age of industrial revolution where the smart manufacturing and smart production are being used in the developed countries, the production systems are still vulnerable to disruptions and outages that affect the reliability and availability of the systems. Certain scientific and probabilistic approaches are required to study the inter‐failure times and repair times and find the possible solutions for maximum production and minimum losses. In this article, we propose a bivariate Power Pareto distribution to model the inter‐failure times and repair times of a system along with some of its characteristics. The model parameters are estimated by employing the maximum likelihood estimation, Bayesian estimation and ant colony optimization algorithm. A simulation study is conducted for different sample sizes to assess the stability of the model parameters. Moreover, we derive the distribution of convolution from our proposed bivariate stochastic distribution and compute its quantiles that help to determine the total time of availability and recovery of a certain system. To demonstrate the efficacy of our model, we use real data set of inter‐failure times and repair times of a certain system.