Abstract
Most often, minimal repair is defined as a replacement of a failed item by an operable item that has the same distribution of the remaining lifetime as the failed one just prior a failure. This is the so-called statistical minimal repair extensively explored in the literature. Another well-known type of minimal repair takes into account the state of a system prior to a failure (the information-based minimal repair). In this paper, we suggest the new type of minimal repair to be called conditional statistical minimal repair. Our approach goes further and deals with the corresponding minimal repair processes for systems operating in a random environment. Moreover, we also consider heterogeneous populations of items, which makes the model more realistic. Both of these aspects that affect the failure mechanism of items are studied. Environment is modeled by the nonhomogeneous Poisson shock process. Two models for the failure mechanism defined by the extreme shock model and the cumulative shock model, respectively, are considered. Some examples illustrating our findings are presented.
| Original language | English |
|---|---|
| Pages (from-to) | 522-536 |
| Number of pages | 15 |
| Journal | Applied Stochastic Models in Business and Industry |
| Volume | 35 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 May 2019 |
Bibliographical note
Funding Information:Priority Research Centers Program; National Research Foundation of Korea (NRF); Ministry of Education, Science and Technology, Grant/Award Number: 2009-0093827; Korea government (MSIP), Grant/Award Number: 2016R1A2B2014211; National Research Foundation (NRF) of South Africa, Grant/Award Number: 103613
Funding Information:
The authors would like to thank the reviewers for helpful comments and suggestions. The work of the first author was supported by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). The work of the first author was also supported by the National Research Foundation of Korea (NRF) through grant funded by the Korean government (MSIP) (Grant 2016R1A2B2014211). The work of the second author was supported by the National Research Foundation (NRF) of South Africa (Grant 103613).
Publisher Copyright:
© 2018 John Wiley & Sons, Ltd.
Keywords
- cumulative shock model
- extreme shock model
- information-based minimal repair
- nonhomogeneous poisson process
- random environment
- statistical minimal repair