A Study of a Complex Engineering System under Human Failure

Bhagawati Prasad Joshi1 and Mukesh Pandey2

1Department of Applied Sciences

Seemant Institute of Technology, Pithoragarh, Uttarakhand, India

2Department of Computer Science

Seemant Institute of Technology, Pithoragarh, Uttarakhand, India

Email: , ;

Abstract

This paper studies the analysis of a complex system having two types of failures namely partial and human. The failure and repair follow exponential and general distributions respectively. Supplementary variable techniques have been employed to obtain various probability states. The steady state behaviour, special cases and numerical examples are also studied.

Introduction

Several authors including [1-4] considered system under various repair discipline. But in all these studies no thought was given to priority repair under human errors. [5] have analysed this system under head of line repair policy but no thought was given for preemptive repair policy. Keeping this in view in this paper a mathematical model is considered having two independent repairable subsystems A and B in 1-out-of 2: G and 1-out-of n: F arrangement respectively. Subsystem A consists of two independent and identically distributed mini systems ,out of which one is operating and other is in cold standby, i.e. fails unless in operation with sensor and switching over device. This device observes the failed mini system and switches to its standby to take over the load. Subsystem A fails when both minisystem fail. Subsystem B consists of n non-identical and repairable components connected in series and can have two types of failure viz. Partial and Catastrophic. The partial failure reduces the efficiency of the subsystem and hence the system, whereas catastrophic failure either stops the operation or is stopped to avoid the further risk of the major damages. Further the entire system can fail due to human error, which is an important aspect in practical life considerations. It has been assumed that catastrophic failure can occur in fully operational as well as partially operational state whereas human failure can occur only in fully operational state.

The repair of catastrophic failure and human failure in B is assumed to be opportunistic i.e.it is undertaken immediately, and failure in A and partial failure in B if any, would be taken care along with the repair of a catastrophic/human failure. The failure and repair times for both the subsystem follow exponential and general distributions respectively. The repair is undertaken according to preemptive-repeat repair discipline.

We analyse the following characteristics of the systems using supplementary variable technique

(1) Transition probabilities

(2) Evaluation of operational availability and ergodic behavior of the system.

(3) Some special cases, numerical computation and interpretation of result.

The transition diagram representing the various probability states of the system is given in fig.1. The following state specifications and notations with their definitions have been taken to formulate the mathematical model:

p/h  Partial Failure/Human failure

 Normally operating states

 Degraded state

to  Failed state

2. Modelling of ComplexEngineering System

Figure 1. Transition diagram

3. Evaluation of Operational Availibility

The L.T. of the probability that the system is available and not available for operation at time t is given by

4. Special Case

When catastrophic failure rate in B is zero. i.e.=0.For this the L.T. of various time dependent probabilities are given as under:

Where

5. Numerical Computation

The time independent operational availability of the system has been computed to study the behavior of partial and catastrophic failures. The various values of the parameter used are given below:

.Also let the repair rates of subsystem follow exponential time distributions.

Figure2.effect of partial failure for =.082 / Figure3.effect of catastrophic failure for =.062

Then setting,

And taking

And plotting the results in the graph, one can get the figure 2 and taking. One can get the figure 3.

6. Conclusions

(1)A careful examination of Figure 2 implies that for increasing partial failure rate:

(a)P0, P1 i.e. the probability of normal availability decreases as time passes away.

(b)P2, P3 i.e. the probability of reduced efficiency state increases.

(c)The overall operational availability of the system does not effect much.

(2)Further from Figure 3 one may conclude easily that for increasing catastrophic failure rate

(a)The normal availability of the system decreases

(b)The reduced efficiency state of the system decreases.

(c)The total operational availability of the system decreases considerably.

(3) The study shows preemptive repeat repair policy gives better availability than the Head of line repair policy.

References

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