IJPAM: Volume 106, No. 1 (2016)

STOCHASTIC ANALYSIS OF PRINTED CIRCUIT BOARDS
MANUFACTURING SYSTEM CONSIDERING REPAIRS BY
INTERNAL/EXTERNAL ENGINEERS AND ARBITRARY
ARRIVAL TIME OF EXTERNAL ENGINEERS

Shefali Batra$^1$, Rajeev Kumar$^2$
$^1$Department of Mathematics
Chitkara University
Solan, Himachal Pradesh, INDIA
$^2$Department of Mathematics
Maharishi Dayanand University
Rohtak, Haryana, INDIA


Abstract. In the present paper, a stochastic model for the system involved in the printed circuit boards(PCBs) manufacturing process is developed. The manufacturing process, based on Surface Mount Technology (SMT), is carried out in three stages viz. printing, placing and soldering through a hardware-software system. During the process, inspections, maintenances and repairs on occurrence of faults of the system are done by internal/external engineers. The internal engineers inspect the system and every manufactured PCB. The system's software faults as well as faults in the PCBs are repaired by the internal engineers whereas system's hardware faults are repaired only by the external engineers. In the model, possibilities of different kinds of faults, online PCB's repairs and arbitrary arrival time of the external engineers, are also incorporated. The expressions for various measures of system performance have been derived using Markov process and regenerative techniques. In the last, numerical computation and graphical analysis have been given for a particular case to show the effect of various parameters on the system performance and cost-benefit.

Received: August 7, 2015

AMS Subject Classification: 60K15, 90B25, 60K10, 60J27

Key Words and Phrases: printed circuit board (PCB), mean time to system failure (MTSF), availability, cost function, markov process and regenerative techniques

Download paper from here.




DOI: 10.12732/ijpam.v106i1.5 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 59 - 74


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).