Due to the long-run accumulation and the complex and changeable external environment

the performance level of a system is uncertain. Accurate quantitative description may cause the interval estimation of the system performance level to be too narrow

which already cannot fulfill the engineering calculation in practice. Meanwhile

failure-correlation is another important factor affecting the reliability of the system. Ignoring failure-correlation can lead to the overestimation of the system reliability

which affects the distribution of maintenance force and the storage of spare components

and is not conducive to the long-term stable operation of the system. Therefore

taking the parallel repairable system of main and auxiliary units composed of multi-state components as research object

the failure transfer rate

repair transfer rate

and state performance level of the components were regarded as fuzzy numbers

and the failure-correlation of the system components was investigated. The reliability analysis of two typical kinds of main and auxiliary parallel systems were carried out. The model for fuzzy multi-state main and auxiliary repairable parallel system with failure-correlation and the fuzzy state transfer differential equations were established

and the fuzzy state probability of the system was obtained. By using the α-level truncation set and the Zadeh-expansion principle

the truncated set interval of the fuzzy state probability and the steady state availability of the system was determined. The steady measures of the system were obtained

and the influence of the fuzzy degree of component parameters on the steady measures was given by numeral application

which provides reference for the study on the failure-correlation of multi-state systems under complex conditions

and is conducive to the optimization of maintenance support in engineering design.