Bayesian and Classical Estimation of Reliability Measures in a Two‐Unit System With Geometric Failure‐Repair Time Distributions

ABSTRACT

The aim of this research is to examine two non‐identical unit system model with geometric failure and repair time distributions. The investigation of reliability features and parameter estimation in the classical and Bayesian paradigms are the primary areas of attention. The units in the system are named as A and B. Unit A undergoes two different types of failure that is, type 1 failure (minor failure) and type 2 failure (major failure), and unit B undergoes normal failure. Atleast one of the units A or B must be operational for the system to function properly. When a unit fails, it will be right away taken to the repair facility for its repair. Any type of failure or malfunction found with any unit can be handled by a single repair facility. Each unit's failure and repair times are assumed to be follow geometric distributions with different parameters. Various measures of effectiveness are studied using the regenerative point technique. The study has derived MLE and Bayes estimates for the different failure and repair parameters. Additionally, a simulation study has been conducted to demonstrate how the derived characteristics behave in both classical and Bayesian setups, and a comparison is then made. The density estimation of MTSF and profit function has been attempted using various kernel functions. The tables and graphs produced for various performance indicators for different values of repair and failure parameters have led to a number of findings. After obtaining all the dependability characteristics, the system's profit has been calculated and graphically examined.