Cite this article:
Gupta and Bhardwaj (2014). A Discrete Parametric Markov-Chain Model of a Two Non-identical Unit Cold Standby System with Repair, Inspection and Post Repair. Journal of Ravishankar University (Part-B: Science), 27(1), pp. 82-91.
Journal
of Ravishankar University Vol. 27 No. B (Science) 2014 PP 82-91
ISSN 0970-5910
A Discrete Parametric
Markov-Chain Model of a Two Non-identical Unit Cold
Standby System
with Repair, Inspection and Post Repair
Rakesh Gupta* and Parul
Bhardwaj
Department of Statistics,
Chaudhary Charan Singh University, Meerut- 250004, Uttar Pradesh, India
corresponding author:prgheadstats@yahoo.in
(Received 18 January 2014; revised version received
2 April 2014; accepted 10 April 2014)
Abstract. This paper deals with the
reliability, MTSF and profit analysis of a two non-identical units (unit-I and unit
2) cold standby
system model assuming two modes- normal and total failure of each unit. Unit-I goes for inspection after th.e repair
to decide whether the repair done is perfect or not. If
the repair is
found to be perfect then the repaired unit becomes operative, otherwise it is sent for post repair. A
single repair
facility is available with the system to repair both
types of;
failed units as
well as inspection and post repair of unit-I. AU the random variables denoting failure
and repair times of both units, time to inspection and post repair of unit-I
are independent
of discrete nature and follow geometric distributions with different
parameters. The various measures of system effectiveness are obtained by using
regenerative point technique.
Keywords: Transition probability;
mean sojourn time; regenerative point; reliability; MTSF; availability of
system; busy period of repairman.
NOTE:
Full version of this manuscript is available in PDF.