Microelectron. Reliab., Vol. 26, No. 5, pp. 841-846, 1986. 0026-2714/8653.00 + .00 Printed in Great Britain. Pergamon Journals Ltd. COST ANALYSIS OF A 2-UNIT STANDBY REDUNDANT ELECTRONIC SYSTEM WITH CRITICAL HUMAN ERRORS P. P. GUPTA,R. K. GUPTAand R. K. SHARMA Reliability Group, Mathematics Department, M.M. (P.G.) College, Modinagar (U.P.), India (Receivedfor publication 17 December 1985) Abstract--In this paper, investigations have been carried out for the evaluation of availability and expected profit during the operable stage of a standby redundant, electronic system, incorporating the concept of human failure. The system can be in any of the three states: good, degraded and failed. One repair facility is available for the repair of a unit in failed or degraded state. The system cannot be repaired when it fails due to critical human errors. The repair of the system in any state follows general distribution. To make the system more applicable to practical lifeproblems, time dependent probabilities have been evaluated so as to forecast the expected profit and the operational availability of the system at any time. INTRODUCTION Many authors [1, 2] have evaluated the cost analysis of various complex systems, but so far, very few re- searchers have attempted the problem of evaluating the availability and the cost analysis of a 2-unit standby redundant system under critical human errors. According to Meister [3], 20-30% of system failures are due to human errors which may be due to (a) misinterpretation of the system, (b) wrong action and (c) maintenance errors. Recently Dhillon I-4] con- sidered the reliability of a system with critical human errors, under the assumption that repair rate follows exponential distribution. However, in practical life models repair need not always follow exponential distribution. Keeping the above facts in mind, the authors in this paper have, therefore, considered a 2-unit standby redundant electronic system which may be in any of three states: good, degraded and failed. The failure of the system due to human errors is also considered in two good states of the system. ASSUMPTIONS (1) The system has two identical units connected in standby redundancy. (2) (2) Initially the system is in good state. (3) A unit of the system can fail partially or completely. The system is said to be in degraded state if it works with a partially failed unit. (4) The system has three states: good, degraded and (3) failed. (a) The system is in good state when it operates with a good unit, the other standby unit may be good or failed. (4) (b) The system is in degraded state when it oper- ates with a degraded unit, the other standby unit may be good or failed. (c) (i) The system can fail due to critical human errors in any of the two good states of the system or 841 (ii) the system is in failed state when both units fail completely. (5) At an instant, only one change can take place in the state of the system. (6) A unit can fail in the degraded state too, with different failure rate than that in the good state of the system. (7) The system has one repair facility which cannot be availed in the degraded state D2. (8) The system cannot be repaired when it has failed due to critical human errors. (9) Repairs are to be like new and never damages anything. (10) The failure and repair times for the system follow exponential and general distributions, respectively. (1) G1, G 2 G1 DI,D 2 D1 2, 2D, 2'D 2 2D NOTATION good states of the system system operating with one unit which is good, the standby unit is also good G2 system operating with the standby unit which is good, the other unit has failed and is under repair degraded states of the system system operating with a unit which is degraded, the other unit is good D2 system operating with a standby unit which is degraded, the other unit is failed and is under repair F, F1 failed states of the system F failed state of the system due to critical human error in good state G1 or G2 F 1 failed state of the system when both units (main and standby) fail constant failure rates of a unit failure rate of a good unit to failed state failure rate of a good unit to degraded state 2'D failure rate of a degraded unit to failed state