IEEE TRANSACTIONS ON RELIABILITY, NOVEMBER 1971 259

to the fourth stage. But this violates the third constraint; Referencestherefore, the fourth stage has n4 = 3 and is eliminated fromfthere csefrat stage has th

3

e highes [11 F. Moskowitz and J.B. McLean, "Some reliability aspects offurther consideration. Now the first stage has the highest systems design," IRE Trans. Rel. Qual. Contr., vol. RQC-8, pp.unreliability. One proceeds as before. The optimum solution is 7-35, Sept. 1956.n is (3, 2, 2, 3, 3). The system reliability is 0.9045. [2] F. Proschan and T.H. Bray, "Optimum redundancy under

multiple constraints," Oper. Res., vol. 13, pp. 800-814, Sept.-Oct. 1965.

[3] J.D. Kettelle, Jr., "Least cost allocation of reliability invest-V. Conclusion ment," Oper. Res., vol. 10, pp. 229-265, Mar.-Apr. 1967.

[41 R.E. Bellman and S.E. Dreyfus, "Dynamic programming and the

This paper provides simple computations for the solutions reliability of multi-component devices," Oper. Res., vol. 6, pp.200-206, Mar.-Apr. 1958.

of redundancy allocation problems. The method is not [5] L.T. Fan, C.S. Wang, F.A. Tillman, and C.L. Hwang, "Optimiza-affected by the kind or number of constraints (except in the tion of systems reliability," IEEE Trans. Rel., vol. R-16, pp.tediousness of calculations). A computer program would be 81-86, Sept. 1967.[61 F.A. Tillman and Liittschwager, "Integer programming formula-simple and computing would be small for many systems. The tion on constrainted reliability problems," Management Sci., vol.simplicity of the method and its suitability for computer 13, pp. 887-899, July 1967.solution make this method highy useful to reliability engi- [7] K. Mizukami, "Optimum redundancy for maximum systemreliability by the method of convex and integer programming,"neers. It has not been rigorously proved that this method is Oper. Res., vol. 16, pp. 392408, Mar.-Apr. 1968.exact, but no faulty solution has yet been found. Even if the [8] Federowicz and Mazumdar, "Use of geometric programming tomethod is not exact, it appears to be very close, maximize reliability achieved by redundancy," Oper. Res., vol.

16, pp. 948-954, Sept. 1968.[9] P. Ghare and R. Taylor, "Optimal redundancy for reliability in

series systems," Oper. Res., vol. 17, pp. 838-847, Sept. 1969.Acknowledgment [101 K.B. Misra, "A method of solving redundancy optimization

problems," IEEE Trans. Rel., vol. R-20, pp. 117-120, Aug. 1971.[111 J. Sharma, "Optimization of reliability function of a system,"

The authors are grateful to Dr. K.B. Misra and to the M.S. degree project, Univ. Roorkee, Roorkee, India, 1971.referees for their helpful comments. Available from the author.

CorrespondenceCorrespondence items are not refereed.

The Digital Computer in Medical Electronics 1) Periodically calibrate the associated instrumentation with respectto gain, zero, and linearity, either fully automatically or under the

H. WILLIAM PERLIS manual control of the operater.2) Guide the medical staff in the proper operation of the

The issues of reliability and maintainability with regard to medical instrumentation via graphical displays.electronic equipment have not, in the past, been given much attention 3) Maintain records of operator errors for subsequent humanby either the users or manufacturers of the equipment. With the factors analysissimultaneous advent of a serious shortage of trained medical personnel, 4) Maintain calibration and maintenance records for guidance in thethe growing demand for high-quality medical care, and the increasing future purchase, modification, or specification of instrumentation.use of digital techniques in a heretofore analog oriented environment, 5) Aid in the trouble-shooting of the existing equipment.the digital computer must be considered as an integral part of a medical 6) Aid in the education of new personnel in proper equipmentelectronic complex rather than the end link in a data gathering and operation and maintenance through the use of "programmed learning"reduction chain. displays.

In reaching a diagnosis or in ascertaining the effects of a course of Many of the procedures and techniques now commonplace in thetreatment, the physician is performing a pattern recognition task aerospace industry could be applied in the medical environment toinvolving many input parameters. The data presented by the electronic increase systems reliability if the system designer is cognizant of thedevices must be sufficiently accurate to aid in this discrimination, special problems inherent in the medical environment.

With the goals of increasing overall system reliability in mind, the Digital computers are being used in greater numbers every year indigital computer can be integrated into a medical electronic system to medical environments to collect and analyze data, to presentperform the following functions. conclusions drawn from this data and even, in some cases, to interact

with the patient in a closed-loop mode in accord with preprogrammed

Manuscript received April 21, 1971; revised August 7, 1971. This algorithms [1]. Therefore it is important to examine the issues ofwork was supported in part by U.S. Public Health Service Contract equipment reliability and maintainability with respect to the currentPH 43-67-144 1. environment of operation and to project to future environments.

The author is with the University of Alabama Medical Center, Whereas five to ten years ago an intensive coronary care unit containedBirmingham, Ala. 35233. several beds with their associated electrocardiographic displays watched

260 IEEE TRANSACTIONS ON RELIABILITY, NOVEMBER 1971

by nurses or technicians 24 hours per day, the University of Alabama background areas of the system, the designer has the responsibility toMyocardial Infarction Research Unit (MIRU), contains six beds create a fail-safe design with regard to the data flow and equipmentdedicated to "routine" patient care and research with each bed capable operation. For example, some pieces of equipment may be operated inof generating seven physiological parameters to the computer. In a degraded state, such as a defibrillator which, due to low-line voltageaddition, two "special study" laboratories provide another 28 channels only outputs a maximum of 380 J instead of its rated 400 J; however, aof information to the computer. The computer, in turn, has five pressure transducer which unnoticed, failed to hold its calibrationspecial-purpose output terminals in addition to the usual complement during a cardiac catheterization procedure would introduce seriousof peripheral devices [2]. The increase in complexity and cost errors into the data base collected for that patient and so could lead therepresented by this growth preclude the simple-minded approach to medical staff and/or the computer into an erroneous diagnosis andreliability engineering, i.e., buy two of everything and hope for the treatment. In the case of a degraded performance of the defibrillator,best. the check out system would merely call attention to the drop in

To apply the probabilistic definition of reliability, one needs to output, while in the second case a go-no-go philosophy should beknow: 1) the required time of operation; 2) the environment of adopted. To make intelligent decisions concerning systems design,operation; and 3) what is successful or adequate operation [3]. information regarding failure rates will be required by the user from the

The required timre of operation of an entire coronary care unit is a manufacturers of medical electronic equipment as is now the practiceparameter that does not lend itself to easy quantification. Assume that with regard to aerospace and military equipment. In addition, faultthe entire unit has an indefinite life span, ended only by the elimination analysis must be performed so as to insure the integrity of the rest ofof the medical condition that prompted its conception. During its the system in the event of a subsystem failure.operation the unit should continue to evolve as better techniques are Assuming a continuing growth in medical knowledge, particularly ofdeveloped for dealing with the problems, both medical and electronic, the quantitative kind, and the extension of high-quality medical care towith which it is concerned. Within this indefinite life span, parameters more people, the complexity and amounts of the instrumentation usedfor specific functions can be defined somewhat more rigidly. For must increase to the point where almost all important medical decisionsexample, the defibrillation function for the treatment of cardiac arrest will be assisted in real time by the computer. This increased load willmust be operational 24 hours per day, 7 days per week, for the life of require that the computer be made more "responsible" for the properthe unit. In the normal course of events, the defibrillator is used in the operation of itself and its subsystems.MIRU about every two weeks, but when it is needed it is the onlydevice that will perform its function. The defibrillator requires an Referencesoperational check at least every 24 hours to maintain it in functioning 1] J Macy, Jr., and TN. James, "The value and limitations ofcondition. This is an ideal situation for a computerized checkout ter .t . iprocedure. On the other end of the scale (in the MIRU at least) is the Cardiovascular Disease, to be published.electronic body temperature channel. Body temperature is not 121 H.W. Perlis, S.E. Wixson, and E.M. Strand, "An expanded terminalconsidered a critical parameter in myocardial infarction, the old style design for clinical medical research," presented at the 1970 Proc.mercury thermometer is perfectly adequate and, in addition, it IEEE Int. Comput. Group Conf.promotes contact with the patients by the nurses. Therefore, the [31 H.D. Ross, Jr., "Reliability," in System Engineering Handbook.temperature channel is used infrequently, and only for short periods; New York: McGraw-Hill, 1965, ch. 33.and the mean time between failures can be short. Manual checkout isfeasible and economical.

The physical environment for medical electronic equipmentinevitably leads one to consider digital techniques to increase thereliability of the equipment. While not usually subjected to extremes oftemperature or humidity in day to day operation, the MIRU signalconditioning modules and connectors are subject to extreme Comment on "Psychological Reliability"-Man-Machinemechanical stress due to rough treatment by the medical staff. If it is Systems'not possible to design the equipment to be unbreakable, then it must bedesigned to allow easy determination of the specific fault and to be C.R. BIRDSALLeasily repaired or replaced. Again, standard techniques used in theaerospace industry would allow rapid localization and repair of fault The above-mentioned note by R.L. Cooley and E.A. Pecker isconditions. interesting, especially to a reliability practitioner who has not been

The psychological environment in an intensive care unit with regard directly involved in man-machine systems. I am surprised that theyto the equipment is extremely important, since this equipment is suggest the term "psychological reliability." That suggests to me asupposed to aid the staff in their efforts to help the patient. If the "mystery element." They also say ". . a functional reliability factormedical staff feels that the equipment, rightly or wrongly, does not involved that is not readily amenable to measurement"-anotherhelp them, it will not be used! The use of the digital computer as an mystery? The circumstances are probably not as difficult as theinterface between the human operator and the actual bedside hardware situation we faced several years ago when the failure characteristics ofcan reduce the complexity of initial patient setup, transducer parts, components, and systems were not well known or well defined.calibration, and final checkout by guiding the staff step by step through Definitions were developed, measurements were made, and thethe correct procedure via graphical displays. The use of the computer to methodology evolved in a few years.maintain records of setup restarts, calibration errors, and aborted I suspect that this mysterious aspect of man-machine systems ischeckouts would enable the system designer to refine the system by caused by the circumstance that the available reliability engineeringpinpointing those areas where: 1) the equipment needs change; 2) the technology has not been adequately applied. The treatment of decisionprograms need further refinement; or 3) the personnel need more functions is well developed. Logic models applicable to machinetraining with the equipment. Furthermore, the computer can be used in functions are usually simple. Data or information required to initiatea "teaching-machine" mode to instruct new staff members in theproper operation of the equipment.

The determination of what constitutes proper "foreground" Manuscript received May 12, 1971.functioning of a medical electronics system is made by the medical The author is with the Systems Engineering Division, Lockheedstaff. The system designer can but provide what is asked for with due Missiles and Space Company, Sunnyvale, Calif.regard for the state of the art and the state of the budget. In the ISEEE Trans. Rel. (Corresp.), vol. R-l9, p. 122, Aug. 1970.