Stochastic analysis of a non-identical three units repairable system with operational priority to simultaneously working of identical units

Abstract

PurposeThe purpose of present study is to carry out stochastic analysis of some important reliability measures of a three-unit system where there are two types of units called type-I and type-II. In type-II, two identical units work simultaneously to meet the system requirements while in type-I, a single unit is kept in spare and can be used to work whenever required at the failure of either of the units of type-II. The system starts its operation with type-II units and thus priority is given to the operation of type-II units. The type II units are different to type-I unit but can perform the same task. There is a single server who handles repair activities of both type of units and the units are assumed to be in pristine condition after every repair. Failures of both types of units are independent and constant. The system can fail at the failure of either of the type-II units and type-I unit.Design/methodology/approachSemi-Markov process and regenerative point technique are used to study the behaviour of different reliability measures of the system.FindingsIn this paper, a three-unit non-identical repairable system is analysed stochastically and its reliability characteristics such as transition probabilities (TP), mean sojourn time (MST), MTSF, steady state availability, expected number of repairs of units, expected number of visits of the repairman and expected busy period of repairman are derived to carry out profit analysis.Research limitations/implicationsThe direct application of the present study can be seen is case of a power distribution system where solar panels may be considered as type-II units and transformer as the type-I unit. Here, the case study is carried out by using approximate data from some old studies; however, a study with accurate data would be more preferable.Originality/valueThis paper is one of the few reliability studies conducted on a system with simultaneous working units. Also, the comparative study of the profit of the present system model has been done with that of the model Kadyan et al. (2020a).