DocumentCode :
1514323
Title :
State Distributions of Multi-State Consecutive- 
Systems
Author :
Xian Zhao ; Yu Xu ; Fangyu Liu
Author_Institution :
Sch. of Manage. & Econ., Beijing Inst. of Technol., Beijing, China
Volume :
61
Issue :
2
fYear :
2012
fDate :
6/1/2012 12:00:00 AM
Firstpage :
274
Lastpage :
281
Abstract :
As a flexible, accurate tool for representing practical industrial and military systems, multi-state systems have been paid great attention to in both academic and engineering fields. Multi-state consecutive-k systems are extensions of binary consecutive-k systems. In this paper, by using the finite Markov chain imbedding approach, we present a unified formula with the product of matrices for evaluating state distributions of two kinds of multi-state consecutive-k systems. Moreover, the analytic expressions are given for the expectation, the probability mass function, and the distribution of the waiting time for the appearance of a state of multi-state consecutive- k systems. The formulas obtained in this paper will be useful for start-up demonstration tests, quality control, and so on. Finally, numeral examples are given, which show the flexibility and effectiveness of our model.
Keywords :
Markov processes; consecutive system reliability; matrix algebra; probability; binary consecutive-k systems; finite Markov chain embedding approach; matrices product; multistate consecutive-k systems; probability mass function; quality control; start-up demonstration tests; state distributions; Equations; Finite element methods; Indexes; Markov processes; Optimization; Reliability; Vectors; Consecutive- $k$ ; finite Markov chain imbedding approach; multi-state systems; system state distribution;
fLanguage :
English
Journal_Title :
Reliability, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9529
Type :
jour
DOI :
10.1109/TR.2012.2194194
Filename :
6198320
Link To Document :
