IEEE TRANSACTIONS ON EDUCATION, JULY 1970

was made by both the Awards Group and the AbstractsGroup with all recommendations being within one quin-tile of each other.

7) There was little use for the newer courses inmodern mathematics such as group theory, Lie algebras,multilinear algebra, mathematical logic, game theory,and geometric algebra. Therefore, these courses shouldbe given low priority. The data also showed an aware-ness by those in the lowest age group of the use of realvariables and functional analysis.

8) The combination group recommended more math-ematics than the applied group.

9) There was little difference in recommendations

between the administrative group and the nonadmin-istrative group, but there was a slightly greater empha-sis on mathematics by the nonadministrative group.

10) The academic group and the business or industrygroup agreed in most recommendations.

11) In general, the Ph.D. group made use of moremathematics than the B.S.-M.S. group.

12) Additional work needs to be done to obtain moredetails on the precise content of each of the recom-mended mathematics courses for the electrical engineer.This information can be determined by personal inter-viewing and by working in cooperation with the majorprofessional electrical engineering organizations.

Short Papers and Classroom Notes.

Reliability EducationMARTIN L. SHOOMAN, MEMBER, IEEE

Abstract-The lack of sufficient formal education in the field ofreliability is an accepted fact by both the engineering educator andreliability manager. This paper describes this problem in some detailand contrasts the state of reliability education with other moreestablished disciplines. Some of the previous ambitious attempts toremedy this situation are discussed and some more limited and per-haps more feasible suggestions are presented.

INTRODUCTION

Reliability as an engineering discipline began in the late 1940's,and now after two decades of rapid development is entering a periQdof slower growth and maturation. The field can no longer claim to bein its infancy. Since reliability education is a recurrent theme through-out industry and professional organizations, it is appropriate that welook at the current state of affairs.

Almost any reliability manager will complain openly of the diffi-culty in finding qualified reliability engineers and may comment pri-vately on the shortcomings in training of many members of his staff.After some study it becomnes clear that these are not the ordinarycomments of an engineering manager who really wants all his peopleto be simultaneously young and creative, have 20 years experience,and have a Ph.D.The reliability problem is somewhat special. Whilethe average engineering manager is striving for better talent, he isbasically satisfied that a proper job is being done with his presentstaff. The reliability manager in many instances will feel that hisgroup is performing inadequately due to a lack of talent.

In this discussion it was assumed that we were discussing a spe-

cialized reliability group that operates as a staff group. It is alsoimportant that a large portion of systems engineers know somethingabout reliability so that they can make simple decisions regardingequipment reliability without consulting a staff reliability man. Also,when a staff reliability man is called in on a more elaborate reliabilityproblem, the system engineer will have to understand his outputsand integrate them into the system design. It is fair to say that onlythe surface has been scratched in educating the systems engineer inthe reliability area.

GROWTH OF THE RELIABILITY FIELD

It is somewhat difficult to document the birth and growth of anew engineering discipline, however, there is enough perspectiveafter about two decades to draw at least a rough picture. The fieldof reliability engineering began in the late 1940's. The Institute ofRadio Engineers1 formed a technical group in reliability on July 12,1949. This perhaps represents the first formal professional reliabilityorganization. Electrical engineers of course represent only one com-ponent of reliability engineers in industry. Large portions of the re-liability engineering population come from industrial engineering,mechanical engineering, aeronautical engineering, and mathematics.The membership in the IEEE reliability group can, however, be usedto predict the growth rate. In Fig. 1 the growth of the IEEE reli-ability group is compared with the growth of the automatic controlgroup. Of course, the field of automatic control has existed for 1 2 or 2decades longer than reliability, but is also a field that cuts acrosstraditional engineering lines. To place the group membership figuresin further perspective we note that the IEEE membership totals150 000. Also, some members join several technical groups, whereasothers join no technical groups. Overall we can say that the reliabilitygroup is joined by 1.7 percent of the members and the control groupby 4.5 percent. Thus, automatic control is about 2' times as large asreliability and has 3j times the growth rate.

BACKGROUND OF RELIABILITY ENGINEERS

Much of the early work in reliability was done by mathematicianswith training in probability and statistics, but with inadequate appre-ciation for the engineering aspects of the problem; or by experiencedengineers with an intuitive appreciation for the problem but tooweak a background in probability to do much quantitative work.Fortunately, in recent years, more people with adequate back-grounds in both engineering and mathematics are entering the re-liability field.

Unfortunately, reliability was viewed as an easy problem in theearly days. I remember a personal industrial experience in 1957 whenafter nine months of productive work on a series of memos on re-liability modeling no new funds were appropriated because a seniorengineer had convinced management that all reliability problemswere solved. He went on to state that one could always use a series

Manuscript received July 19, 1969The author is with the Polytechnic Institute of Brooklyn, Brooklyn, N. Y.

24

I The IRE and the AIEF, merged into the IEEE in 1963.

SHORT PAPERS AND CLASSROOM NOTES

Membership

7

4

2.

7,000 6,777.

;,000 _

o000o AutomaticControl Group

;,000 _

3,000 _____

',000 Re liabilityGroup

1,000 _

048 50 52 4 56 58 60 62 64 68 70

Reliability Automatic YEARGroup ControlFormed Group Formed

Fig. 1. Growth of the IEEE Reliability and Automatic Control Groups.

reliability structure, add the constant failure rates, and use an ex-

ponential reliability function. Such thinking explained why manage-ment assigned component engineers, standard engineers, and non-

mathematically inclined quality control engineers to reliabilitygroups.

To better appreciate the need for reliability training, let us takea close look at the background of a leading manufacturer of militaryequipment and one of his reliability groups. Within the companythere are several reliability groups. However, we will focus on thelargest and most talented. After many years of effort the manager

feels that his group is much improved and on a par with some of thebest in the industry. He has 50 engineers, 35 of whom have collegedegrees. Of the 35, five have 2-year associate degrees, 25 B.S. de-grees, and 5 masters degrees. About 15 have had at least one formalcourse in reliability or probability. Thus, out of the 30 people withengineering degrees only about 50 percent have had even one collegecourse which directly prepares them for the work they do. We mightcompare this with an automatic control group in industry. Not onlywould we expect a higher percentage of M.S. degrees but also prob-ably every graduate engineer would have had at least one controlcourse and many would have had several graduate courses in theirarea. This clearly documents the need for reliability education.

COLLEGE AND UNIVERSITY RELIABILITY COURSES

There have been a number of surveys made since 1960 to deter-mine how many universities and colleges throughout the countryoffered reliability courses [1], [2], [5]-[7], [9]. Some of these were

directed at mechanical engineers, others at electrical engineers, etc.Some were surveyed by letter and others by inspection of the schoolbulletins. Two studies [2], [51 were felt complete enough to estimatethe percentage of the 158 engineering schools that offer reliabilitycourses. The data is plotted in Fig. 2. The Battelle study [2] indicatedthat 12 schools were presently offering courses and 7 more were pre-

paring courses. Thus, 12 schools were counted in 1961 and 19 in1962. The study by Hock [5] included Canadian schools and two-year community colleges for 47 positive responses out of 223. (If we

excluded two-year community colleges the percentage would in-crease.) The first conclusion from this rather meager data is thatbefore about 1959 no reliability courses were offered. (The first re-

liability textbook appeared in 1961). Thus, during the first 10 years

of the 20-year span of reliability no formal course work was offered.The projected growth by 1970 predicts that 40 percent of the schoolsoffer reliability today. We can estimate the total number of studentshaving received formal reliability training by finding the area underthe curve (2), and multiplying by the number of schools (158), theaverage class size (20), and the number of courses per year (1). Theresult predicts a cumulate enrollment of 6320 students. If we estimatethat half of these people have gone into the reliability field and thatone-third are members of the IEEE reliability group then 1054members of the IEEE reliability group have had formal reliability

Percentage of SchoolsOffering Reliability Courses

lOOr

80O

60-

40F

20

I I"' I

48 50 52 54 56 58 60 62 64 66 68 70

YEAR

Fig. 2. Percentage of colleges and universitiesoffering reliability courses.

training, about 40 percent. Thus, in addition to a large number ofsystems engineers who require reliability training, perhaps 60 percentor more of the reliability engineers need training.

Let us examine in more detail the enrollment in a few of the re-

liability courses that are taught. We shall compare Northeastern,Long Island University (C. W. Post College), Polytechnic Instituteof Brooklyn, and University of California at Los Angeles. All thesecourses are graduate level with a high percentage of part-time stu-dents. At Northeastern, which runs a trimester system, 43 studentsregistered for reliability last year. Class size was limited to 30, 23continued into the second term, and 17 remained in the third term.The instructor attributed most of the dropouts to poor mathematicalbackground on the part of the student. There is a probability pre-quisite for this course. At Brooklyn Polytechnic, Reliability I is taughtin the fall and spring semesters and carries a well-enforced prob-ability prerequisite. Fall registration averages 25 and spring term15. About 20 percent of the students withdraw by the final exam.

(An average or a little above average attrition rate.) Reliability IIoffered for the first time in spring, 1969, at Brooklyn Polytechnic hada class size of 10. At C. W. Post the reliability course has a prob-ability prerequisite, an average enrollment of 15, and an attritionrate of 20 percent. The U.C.L.A. reliability course is reported to havean enrollment of 25 students.

The pattern is clear (at least in the instances cited). With sucha pool of untrained people in industry one would expect large vigor-ous enrollments in reliability classes. Such is not the case. Actualenrollments are small, below the average graduate class size. Com-pare this with a really "hot" area of student interest, computers,where at Brooklyn Polytechnic we run 3 or 4 sections of 35-40 stu-dents simultaneously.

We now turn our attention to special reliability programs. Theseare usually an entire day in duration with all-day lectures. These are

generally sponsored by universities, professional organizations, or

private enterprise. These courses may include 30 hours of lectureconcentrated within one week compared with 30-45 lecture hours ina standard graduate course. Because of the time scale, even thoughthe hours are roughly commensurate, the goals of a concentratedcourse and a regular university course must differ. In the concen-

trated course the rate of presentation is such that the student willretain only a small portion of the material unless the course is fol-lowed up by subsequent study at home and on the job. Such a course

probably best fits the needs of a systems engineer who needs to as-

similate rapidly some techniques and philosophy in the reliabilityarea. Also they serve the needs of a reliability engineer who lives inan area where no regular graduate reliability courses are offered or

who needs an immediate injection of some ideas that will be followedby a regular course at a later date. The cost of special courses is rela-tively high, $600-$400 per course (plus travel and living expenses inmany cases), which is many times the cost of a regular graduate course.

Most universities that run these courses have found that regis-tration is modest and they just break even or lose money on thecourse. Although no detailed information is available, it seems thatthe private organizations that have offered these courses have beenmarginally successful or unsuccessful. The courses sponsored byprofessional societies probably have had larger attendance. The costsare one-half to one-third of the university courses, which is probably

' ' ' ' r '

25

IEEE TRANSACTIONS ON EDUCATION, JULY 1970

the biggest attraction. Often the instructors and administratorsdonate their services in part or in full or the organization funds pay

for any deficit incurred. In part the low attendance is due to theunwillingness of the reliability manager in paying for tuition costs,loss of a week's pay, and living costs for very many of his personnel.However, the total sum may reach $500-$1000 per man, which issizable and perhaps 5-10 times the cost of a regular graduate course.Also, the regular graduate course tuition may come out of a com-pany-sponsored tuition refund program, whereas, the special coursemoney may come directly from his budget. Some people feel that thepresent predominance of fixed-fee contracts as opposed to the pre-vious popularity of cost plus fixed-fee contracts may also have astrong influence on special course enrollment. Often such educationalexpenses could be charged as costs.

One counter example should be cited before we write off the effec-tiveness of special courses. During the summer of 1968, BrooklynPolytechnic's office of special programs offered a special one-weekreliability course for Picatinny Arsenal in Dover, N.J. A circular wassent by the training office at the arsenal inviting all qualified engi-neers to take the course. Those applicants who were approved bytheir management were released for the week to take the course whichwas held at a nearby motel. Seventy engineers registered for thecourse, necessitating two 35-man sessions-one at the beginning andone at the end of the summer. In 1969 this course was repeated withthree sections of 25 students each. The registration figures for 1970are not yet available.

COMPANY RELIABILITY COURSES

In addition to the regular graduate and special courses, there arenumerous company reliability courses. These vary greatly in levelfrom the few that are equivalent to a regular university graduatecourse to the larger number that are better described as orientationseminars. These comments are not meant to depreciate company-sponsored courses. The company course generally serves a valuablebut far different role than the university-sponsored courses. If acompany course is held after working hours it competes directly witha university reliability course. The advantages are of course con-venience, lack of formal admission and registration procedure, andabsence of tuition. (The latter is generally no real advantage sincemost companies now reimburse part of all the tuition expenses oftheir engineers who are enrolled in a part-time college program.) Thedisadvantages are the lack of a qualified teacher (unless the companybrings in a professor as a consultant or has a man with teaching ex-perience within their own organization), the fact that students can-not use the course for graduate credit, and the fact that there is no

penalty for withdrawal. (In a university course the student is onlyreimbursed upon successful completion of the course, and withdrawalmeans loss of some or all the tuition fee). Graduate education is hardwork for well-prepared student and even harder for the student witha weak background. In addition, part-time education requires astudent to do two jobs at once. Only a course sound in scholarly con-tent, pedagogically strong, with well-motivated students will succeedunder such circumstances.

RECOMMENDATIONS AND CONCLUSIONS

I believe that a clear case has been presented for the need forimproving reliability education. Let us examine some of the pastattempts in this area. Obviously, industry has played a major rolein the establishment of university reliability courses. The reliabilitycourse at Brooklyn Polytechnic was established in 1961 after theDean of the Graduate School received several requests for a reli-ability course. More of this encouragment should continue at uni-versities that now offer no reliability courses but serve an industrialcommunity that needs this training. Of course, there must be suffi-cient continuing interest to assure minimum enrollment figures aremet. For areas that cannot supply sufficient students to populate aregular course, the IEEE is exploring the possibility of a movie orvideo-tape version of a reliability course.

Several organizations and individuals have proposed that a B.S.or M.S. degree in reliability be given at many universities throughout

the country [3], [41, [8S. Presently the Air Force Institute of Tech-nology and the University of Arizona have M.S. degree programs inreliability. Although it is commendable that some universities offerdegree programs in reliability, it is neither necessary nor desirablethat a large number of universities offer such degrees. Few schoolsoffer B.S. or M.S. degrees in the area of control systems, however, itis plainly clear that there is an ample supply of qualified engineers inthe control area at the B.S., M.S., Ph.D. levels. This is because thereis a good varied supply of control courses that are offered as seniorelectives and graduate courses. Also most modern curricula in elec-trical, mechanical, aeronautical, and chemical engineering actuallyinclude some required control material in the undergraduate program.

There are some positive proposals that can be made in which bothindustry and the university can cooperate in order to improve thelevel of competence in the profession.

1) Universities should work toward strengthening existing courses

and making students aware of the importance of reliability in en-

gineering work.2) Universities should attempt to integrate some reliability ma-

terial into their required undergraduate program.

3) Reliability managers should set some unofficial standards for

engineers in their group: perhaps a minimum of one probabilitycourse for all engineers, and a minimum of one probability course,

one statistics course, and one reliability course for their top analysts.4) Since many present and perspective personnel will not have

the backgrounds suggested in 3), each reliability manager shouldapportion from his budget perhaps 10 percent as an educational fund.These monies would be used tofinance a program that would grad-ually raise the competence level of the group to meet the standardsoutlined in 3).

Regarding the first proposal, obviously all university courses are

periodically reviewed so that the content can keep up with new de-velopments in the field. Industries can offer seminar speakers to

nearby universities. In choosing speakers industry should take care

to send their best. An interesting and well-presented talk in thejunior year could mean two or three bright recruits in the Senior year.

Industrial reliability managers should not overlook better cooperation

with reliability educators via consulting, industrial seminars, andsummer employment. Universities can also popularize reliability

somewhat by advertising their courses to the student body to in-crease enrollment.

Suggestion 2) is aimed at incorporation of reliability ideas into theundergraduate engineering curriculum. This would of course be donein a different manner in each undergraduate department. For an

electrical engineering department, I will offer some concrete sugges-

tions. About three lecture hours are needed to present the principlesof catastrophic reliability. Since most electrical engineering depart-ments require undergraduates to take probability, the material couldbe integrated into this course. Alternately it could be given in a fol-lowing control or circuits or electronics course. The three hours mightfocus on the concepts of simple series and parallel reliability graphs;relationships between hazard function, density function, and reli-

ability functions; and constant, linearly increasing, and Weibullhazard models. In addition, another three hours on marginal failures

could be included in a control or electronics course. Topics such as

worst case analysis, approximate techniques for change of randomvariables, and sensitivity analysis might be included. If the circuitor electronics course included any computer-aided circuit analysis,the worst case and sensitivity features of the ECAP computer-aidedcircuit analysis program could be utilized.

The third proposal seems obvious, however, I wonder how many

reliability engineers would not meet these minimum standards. Cer-

tainly any reliability engineer who has not had a probability course

owes it to himself to see that this deficiency is remedied promptly.Some engineers who have been in practice for many years may need

a mathematics refresher course first to review basic calculus andelementary differential equations. I remember a reliability manager

who was in my reliahility class several years ago who had not used

calculus for 20 years and had forgotten how to integrate and differen-tiate an exponential function. With some hard work on his part this

bright person managed to refresh his background mathematics and

26

SHORT PAPERS AND CLASSROOM NOTES

did well by the end of the semester. This is one area in which a com-pany course could excel.

A two-term two hour per week course beginning with a review ofcalculus, continuing on to basic probability in detail, and ending upwith introducing reliability, would be of great value. Such a courseshould have a professional teacher, graded homework, and exams toaccomplish its objective. A university would be unlikely to give sucha course because the subject matter covers the span from the fresh-man year to first year graduate school material. In order to encourageattendance at such a course the engineering manager might considerholding it during working hours or at the end of the work day withthe first hour on company time and the second hour on personneltime.

Suggestion 4) calls for the appropriations necessary to carry outthe good resolutions of the other suggestions. Many managers maybalk at this as being too large a sum to appropriate for education. Ifthey do then they also must reject the fact that the average reliabilityengineer is perhaps 10 percent or more, less qualified for his job thenis the case in other engineering specialties. To measure the proposi-tion by other standards we might ask, would a manager rather hire areliability man with experience in reliability work but no practicalcourse training for $12 000 per year, or a man with similar experienceplus formal training in probability and reliability for $13 200. WhatI am suggesting is that the latter man may not be available or thatone might want to upgrade a man without formal training already onthe staff, by spending up to $1200 a year for a few years on this man'straining. It is envisioned that summer courses, convention expenses,professional society dues, cost of released time for courses duringworking hours, etc. all be charged against this fund.

In summary, reliability although 20 years old is still a relativelynew profession aind is experiencing many growing pains. One of theseis lack of sufficient well-trained personnel. To remedy this, industrymust help educate the engineering colleges to the need and cooperatein sponsoring new programs. In addition, some informal minimumstandards must be set and a concentrated effort undertaken to worktoward these goals. To implement these programs industry shouldset aside a portion of each man's salary as an educational fund.Rapid implementation of these suggestions is urged since not onlythe productive capacity but the professional stature of the reliabilityengineering profession is at stake.

REFERENCES11] C. A. Krohn, "Survey of reliability in the engineering curricula," IRE Trans'

Reliability and Quality Control, vol. RQC-9, pp. 42-45, September 1960.[2] "Status of survey of current educational activities in reliability,' Battelle

Memorial Institute, December 28, 1961, unpublished memo.[3] H. C. Jones, "A proposed curriculum for reliability engineering," presented at

the 9th Natl. Symp. Reliability Quality Control, January 22, 1963.[4] T. L. Regulinski, "Systems reliability engineering graduate curricula," Air Force

Institute of Technology, Wright-Patterson Air Force Base, Ohio, 1963.[5] C. D. Hock, "Reliability engineering education at colleges and universities,"

M.S. thesis, George Washington University, Washington, D. C., 1965; also,DDC AD-491708.

[6] M. Joseph, J. Medford, and N. Mellis, "Report on reliability education offeredby colleges and universities," January 1966 (unpublished).

[71 C. D. Hock, "Reliability engineering education at colleges and universities,in Annals of Reliability and Maintainability (5th Reliability and MaintaintabilityConf.), vol. 5, July 1966.

[8] "Model curriculum for a degree of master of science in reliability engineering,"Education Committee, IEEE Group on Reliability, October 1967 (unpublished).

[9] C. Birnie, Jr., "Status of the incorporation of reliability techniques into mechani-cal engineering education," Pennsylvania State University, State Park, Pa., 1968(unpublished).

graduates. Basic operation of the amplifier, the significance of the"common-mode rejection ratio," the maximum allowable inputsignal level, and the use of "balancing resistors" in the emitter cir-cui'ts are the principal topics covered. In addition, a practical differ-ence amplifier using balancing collector-coupled transistors isanalyzed.

INTRODUCTION

The difference amplifier is a basic building block in most inte-grated-circuit linear amplifiers. With the advent of improved produc-tion methods, such amplifiers are becoming more and more economi-cal to use It is therefore important that the theory of operatioa ofsuch circuits be presented in a meaningful way in undergraduateelectronics courses

A. Basic Concept

The basic circuit of a "difference amplifier" is shown in Fig. 1.We assume initially, in order to simplify our discussion, that eachhalf of the difference amplifier is identical. Thus T1 is identical to T2,both collector resistors are identical and both base resistors are iden-tical. In practice, of course, this condition is only realized approxi-mately.

The utility of the difference amplifier lies in the fact that it yieldsan output current that is proportional to the difference between theinput voltages v, and v2. To show this, we draw the small-signalequivalent of Fig. 1 as shown in Fig. 2. This circuit is obtained by"reflecting" [1 ] the input voltages v1 and V2 and the base resistorsRb into the emitter circuit. The circuit of Fig. 2 can be analyzed in astraightforward manner for isl and i2. However, it is more instructiveto use a procedure that brings the difference and common-modesignals into the analysis.

To employ this procedure we note that vi(t) and v2(t) can be repre-sented by their average value vo(t) and their "distance" from the aver-age [Av(t) ]/2. This is illustrated in Fig. 3(a), where

vst) = 2Vl(t)+V2(t)2

(la)

and

AV(t) = V2(t) - Vl(t). (lb)Thus,

V2(t)= V O(t) + 2 (Ic)

and

v1(t) = vo(t) - () (1d)

Av(t) is known as the difference-mode signal and vo(t) as the com-mon-mode signal.

If we now replace v1 and V2 in Fig. 2 by their equivalents from(1c) and (Id) and use superposition, Fig. 3(b) and (c) result. In Fig3(b), vi(t)=v2(t)=vo(t), the common-mode voltage. From the sym-metry of the circuit we see by inspection that

(2a)ielc = ie2c= v-)2R, +hib+R-

hfe

The Difference Amplifier-An Explanation forthe Undergraduate

C. BELOVE, MEMBER, IEEE, I. M. METH, SENIORMEMBER, IEEE, AND D. L. SCHILLING,

SENIOR MEMBER, IEEE

Abstract-An elementary analysis of the difference amplifier ispresented in this paper in a form that is easily understood by under-

Manuscript received April 5, 1969; revised January 25, 1970.C. Belove is with the New York Institute of Technology, Old Westbury. N. Y.

11568.I. M. Meth and D. L. Schilling are with the City College of New York, New

York, N. Y. 10031.

where the subscript c refers to the common mode.In Fig. 3(c) vi(t) and v2(t) are replaced by the difference voltage,

T [zAv(t) ]/2. Again, taking advantage of the symmetry of the circuitwe find ied=-ield where the subscript d refers to the differencemode. Thus, the voltage drop across Re is zero and

- ~~~At(t)4e2d = - ild

2 [hib + Rb](2b)

Equation (2b) is used to find the differential-mode gain of the am-plifier. If hfb=' 1, then from Fig. 2,

Vc2 Vei R(A V AV 2((hlb + R/ls1f) (

27