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Stochastic modeling and cost-benefit analysis of computing device with fault detection subject to expert repair facility

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Abstract

In the present study, two stochastic models of a computing device are studied using the concept of imperfect fault detection in the presence of regular and expert repairman. The computing device is a combination of hardware and software components which works together but fails independently. In both models, the unit is under observation for fault detection by the regular repairman. In first model, if the unit is seriously damaged then it undergoes for replacement by regular repairman otherwise it is sent back to operation after maintenance. In second model, if the unit is seriously damaged then it undergoes for repair by expert repairman otherwise it is sent back to operation after maintenance. Various reliability measures for both the system models are obtained using semi-Markov process and regenerative point technique. Finally to highlight the importance of the study empirical results have been obtained with respect to fault detection rate.

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Abbreviations

ɛ ij :

Transition probability from state S i to state S j

pη 1 :

Indicates the system’s hardware failure rate

qη 2 :

Indicates the system’s software failure rate

a, b:

Indicates the probability of fault detection or not in hardware component

c, d:

Indicates the probability of fault detection or not in software component

g(t) = αe −αt :

Denotes the random variable related to fault detection rate of hardware component

h(t) = βe −t :

Denotes the random variable related to fault detection rate of software component

f(t) = λe −λt :

Indicates hardware replacement rate by regular repairman

f 1(t) = γe −γt :

Indicates software up-gradation rate by regular repairman

\(X\left( t \right) = \lambda_{1} e^{{ - \lambda_{1} t}}\) :

Indicates hardware repair rate by expert repairman

\(Y\left( t \right) = \gamma_{1} e^{{ - \gamma_{1} t}}\) :

Indicates software up-gradation rate by expert repairman

R i (t):

C.d.f. of first passage time from operative state to another operative/failed state

τ i (t):

Indicates the probability that system is available for use at time t in state S i

∏ i (t):

Indicates the busy period of repairman at time t in state S i

ℑ i (t):

Indicates the expected number of visits by repairman

CBA:

Cost-benefit analysis

SSA:

Steady state availability

BPR:

Busy period analysis of repairman

ENVR:

Expected number of visits by repairman

μ i :

Mean sojourn time at ith regenerative state

S i :

Represent ith state

o/Cs :

Operative/cold standby unit

HFi/SFi :

Hardware/software component under fault detection

HFurp/SFup/HFur/SFI :

Failed hardware component under replacement by regular repairman/failed software component under up-gradation/failed hardware component under repair by expert repairman/software component under fault detection continuously from previous state

WHFi/HFI/WSFi/SFUP :

Hardware component waiting for fault detection/hardware component under fault detection continuously from previous state/software component waiting for fault detection/software component under up-gradation continuously from previous state

HFURP/WHFI/HFUR :

Failed hardware component under replacement by regular repairman continuously from previous state/hardware component waiting for fault detection continuously from previous state/failed hardware component under repair by expert repairman continuously from previous state

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India

    Ashish Kumar & Monika Saini

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  1. Ashish Kumar
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  2. Monika Saini
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Correspondence to Ashish Kumar.

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Kumar, A., Saini, M. Stochastic modeling and cost-benefit analysis of computing device with fault detection subject to expert repair facility. Int. j. inf. tecnol. 10, 391–401 (2018). https://doi.org/10.1007/s41870-018-0082-7

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