Part count and design of robust systems

Part Count and Design ofRobust Systems*Daniel Frey,1, † Joseph Palladino,2 John Sullivan,3 and Malvern Atherton4

1Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139

2General Electric Aircraft Engines (retired), 1000 Western Avenue, Lynn, MA 01910

3Pratt & Whitney, 400 Main Street, East Hartford, CT 06108

4Rolls-Royce International, Ltd., 65 Buckingham Gate, London, United Kingdom

PART COUNT AND DESIGN OF ROBUST SYSTEMS

Received 24 April 2006; Revised 10 December 2006; Accepted 16 February 2007, after one or more revisionsPublished online in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/sys.20071

ABSTRACT

Systems engineering frequently includes efforts to reduce part count with the goal of cuttingcosts, enhancing performance, or improving reliability. This paper examines the engineeringpractices related to part count, applying three different theories—Theory of Inventive Prob-lem Solving, Axiomatic Design, and Highly Optimized Tolerance. Case studies from the jetengine industry are used to illustrate the complicated tradesoffs involved in real-world partcount reduction efforts. The principal conclusions are that: (1) Part consolidation at thecomponent level has generally been accomplished as technological advancements enablethem which is consistent with the “law of ideality” in the Theory of Inventive Problem Solving;(2) part count reduction frequently increases coupling among functional requirements, designparameters, and processing variables while also delivering higher reliability which conflictswith the theory of Axiomatic Design; and (3) at the overall system level, jet engine part counthas generally increased in response to escalating demands for system robustness as sug-gested by the theory of Highly Optimized Tolerance. © 2007 Wiley Periodicals, Inc. Syst Eng10: 203–221, 2007

Key words: robust design; Theory of Inventive Problem Solving; Axiomatic Design; HighlyOptimized Tolerance

Regular Paper

*This paper was presented at the 16th Annual International Symposium of the International Council on Systems Engineering (INCOSE), July9–14, 2006, Orlando, FL.†Author to whom all correspondence should be addressed (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

Systems Engineering, Vol. 10, No. 3, 2007© 2007 Wiley Periodicals, Inc.

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1. INTRODUCTION

The purpose of this paper is to study the role of partcount in systems engineering, particularly in the long-term evolution of technologically advanced electrome-chanical systems. In particular, this paper will exploreand contrast the implications of three different theoriesof systems engineering as they are related to part count.Also, this paper will examine the technological evolu-tion of jet engines in an effort to test the predictions ofthe theories.

Part count is defined, for the purposes of this paper,as the total number of physically separate parts in anengineering system. By this definition, a complex partwith many features will count as only one part as longas it is made without first creating many smaller partsthat are later assembled. Part count is useful to track instudying an engineering system because it is related tothe challenges of initially launching a system (e.g., tomanufacturability) and to the challenges of keeping asystem in service (e.g., to reliability). Part count can beviewed as a surrogate for more directly useful systemproperties, but it must be acknowledged that it can,under some circumstances, be a misleading indicator(as will be discussed in subsequent sections).

Unique part count is defined, for the purposes of thispaper, as the total number of parts with a separateidentity as typically indicated by a part number on anengineering bill of materials or parts catalog. By thisdefinition, an array of identical parts may contributegreatly to part count, yet contribute only a little tounique part count. On the other hand, even parts madeby an identical manufacturing process may take on aseparate identity such as when parts are inspected andthen binned according to the tolerances held. Uniquepart count is important in systems engineering becauseit creates demands on inter-functional coordination(e.g., all drawings must be signed off) and in logisticsand supply chain management (e.g., unique parts mustoften be kept at maintenance and repair facilities).

Systems engineering efforts are frequently made toreduce part count and/or unique part count while main-taining or improving system functionality, reliability,and robustness. Under the rubric of “Design for Manu-facturablity and Assembly” (or DFMA), some greatstrides have been made that reduce cost and improvereliability. These DFMA efforts frequently, but notalways, result in part count reductions because they arelikely to:

• Consolidate multiple parts into one, more com-plex part,

• Eliminate a part and force other parts to take overits functions, and/or

• Dramatically reconceptualize the system designto reallocate functions across the subsystems andcomponents.

Technological advances frequently enable part countreduction by some combination of the means listedabove. For example, integrated circuits replaced myriadseparate resistors, transistors, and diodes with a singlewafer and injection molding technologies enabledscores of bosses, holes, snaps, and other functionalfeatures to be incorporated into a single part. Despitesuch broad trends toward part consolidation, it must beemphasized that not every reduction in part count is astep in the right direction. The systems engineeringdecisions regarding part count must balance issuesthroughout the system life cycle including technologymaturity, time to market, cost (both fixed and variable),reliability, serviceability, supportability, and recycling[Miles, 1961]. In particular, reliability is in direct con-flict with part count when parallel redundancy is beingconsidered. Systems Engineers therefore seek guidancein these decisions. Design handbooks articulate simpleheuristics for part count reduction. For example, Ander-son (1990) defines three questions to be asked duringredesign:

• When the product is in operation, do adjacentparts move with respect to each other?

• Must adjacent parts be made of different materi-als?

• Must adjacent parts be able to separate for assem-bly or service?

Such rules help the novice engineer avoid mistakes,but they fall short of what is needed in advanced sys-tems engineering. Such simple rules admit many excep-tions such as when relative motion is afforded withoutseparate parts through elastic deformation. They alsofrequently fail to provide adequate guidance when dif-ferent system attributes are in tension. Theories of sys-tem design might assist engineers by offering a morecoherent and consistent view. The next section reviewsthree currently existing theories and their relationshipto part count reduction.

2. PART COUNT REDUCTION IN THEORY

This section reviews three different theories related tosystems engineering with a selective focus on theirimplications regarding part count. The three theoriesare: 1) Theory of Inventive Problem Solving, 2) Axi-omatic Design, and 3) Highly Optimized Tolerance.This set of theories is not intended to be comprehensive,

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Systems Engineering DOI 10.1002/sys

rather it is a sample of three particularly prominenttheories, widely cited in the literature, that also havespecific implications regarding part count.

2.1. Theory of Inventive Problem Solving

Altshuller proposed that engineering creativity could bemade an exact science. His algorithmic approach isknown as the Theory of Inventive Problem Solving,frequently referred to by the Russian acronym TRIZ oralternately referred to as TIPS. Starting in 1946, Alt-shuller and his collaborators studied hundreds of thou-sands of patents seeking patterns of innovation thatwould lay the basis of this theory. Since Altschuller’sinitial publications, there has been considerable addi-tional development. A complete description of TRIZand all its full state of current development wouldrequire volumes covering SuField analysis [Fey, Rivin,and Vertkin, 1994], the algorithm for inventive problemsolving [Arciszewski, 1988], and technology forecast-ing [Fey and Rivin, 1999; Clarke, 2000; Mann, 2003a,2003b]. As TRIZ has developed, there have been manydifferent texts developed [e.g., Terninko, Zusman, andZlotkin, 1998; Fey and Rivin, 1999] and there also beensubstantial divergence in the methodology. By one ac-count, there are 15 distinct versions of the developmentlaws [Cavallucci, 2001]. Due to these factors, a com-prehensive review of the entire TRIZ literature is out-side the scope of this paper. The goal of this section israther more limited. This section presents the mainideas of TRIZ and a few details and recent develop-ments related to part count reduction.

In the view of the authors, TRIZ was strongly influ-enced by the ideas that dominated the Soviet Union inthe mid-20th century when Altshuller developed histheory. The Soviet perspective on history and socialorganization was based on an evolution of Hegeliandialectic (Hegel, 1812) called dialectical materialism,which asserts that historical and social developmentsare explained by clashing of theses and antitheses,resulting in synthesis. Lenin wrote in the CommunistManifesto that repeated cycles of these conflicts wouldeventually lead to a perfect system of social organiza-tion wherein no government was needed. Altshullerappears to have adopted this philosophical frameworkas the basis of TRIZ stating that “development of tech-nical systems, like all other systems is subject to thegeneral law of dialectics” [Altshuller, 1984, p. 32].

A major organizing concept of TRIZ is the “law ofideality.” Just as the Soviets viewed history as a pro-gression toward an ideal state with no need for govern-ment, Alschuller proposed that technical systems tendtoward an ideal final result which requires no “sub-stance” and “no expenditure of energy and time” [Alt-

shuller, 1984, p. 83]. Altshuller’s “law of ideality” isfrequently interpreted as governing a ratio of usefulfunctionality to a sum of harmful effects and/or costs[Cavallucci, 2001; Clausing and Fey, 2004]. Thus,TRIZ allows for part count increase if the additionalparts adequately compensate for their presence bymeans of greater function or reduced harmful effects.Salamatov [1999] noted that technical systems fre-quently exhibit an “expansion period” (in which func-tion expands ad the expense of simplicity) followed bya “convolution period” (which superficially appears tobe simplification but in reality retains useful functionswhile better respecting constraints on physical, eco-nomic, and ecological complication. Mann [2000a] hy-pothesized that part count should reach an apex at thetime marked by an inflection in the technology “S-curve.”

To accelerate the progression toward ideality, TRIZincludes a great deal of supporting detail. Consistentwith the framework of dialectics, in TRIZ, inventionsare classified according to how they resolve underlyingconflicts or contradictions. For example, one majorclass of conflicts involves a tool acting usefully on anobject, but such action is accompanied by a harmfulaction as well. Three major tactics for resolving thisconflict are listed below and depicted in Figure 1:

1. Eliminate the object so that the tool is not neededanymore.

2. Eliminate the tool and assign the useful action tothe object.

3. Eliminate the tool and assign the useful action tothe environment.

These three major tactics are all consistent with partcount reduction, but the next levels of supporting detailare mixed in this regard. Altshuller proposed 40 inven-

Figure 1. Tactics for resolving system conflicts [adapted fromClausing and Fey, 2004].

PART COUNT AND DESIGN OF ROBUST SYSTEMS 205


tive principles for conflict elimination. Some of theseprinciples are consistent with part count reduction. Forexample, the principle of joining suggests “joining ho-mogeneous objects or those destined for contiguousoperations.” However, many of the conflict resolution“principles” in TRIZ involve increased part count. Forexample, the “principle of fragmentation” includes “di-viding the object into independent parts” [Altschuller,1984, p. 151]. Similarly, the principle of the “previouslyplaced cushion” states that one may “compensate forthe relatively low reliability of an object by accidentmeasures placed in advance” [Altschuller, 1984, p.155]. By one account, the inventive principles thatincrease part count outnumber those that reduce partcount [Mann, 2000b]. Nevertheless, when a product issufficiently mature, it is generally held that TRIZ pro-vides a useful set of tools to aid in part count reduction,especially when used in concert with analysis strategiessuch as Design for Manufacture and Assembly [Luc-chetta, Bariani, and Knight, 2005].

As discussed in this section, relating TRIZ to partcount is challenging. As Cavallucci (2001) noted, theoriginal texts on the subject are vague and the views ofthe theory are manifold. In addition, the supportingdetails of TRIZ are mixed with regard to part count.However, the “law of ideality” strongly supports partcount reduction, at least over the long term. In the nearterm, part count increases can be consistent with TRIZif performance or side effects are improved enough towarrant the additional parts. But if a technology be-comes mature so that increments in performance arenecessarily small, then the additional improvements inthe ratio of functionality to harmful effects and costswould seem to require part count reduction. More spe-cifically, Mann used TRIZ to surmise that part count injet engines should have begun to decrease around 1975and published his analysis in the TRIZ Journal [Mann,2000a]. One of the goals of this paper is to examine thisclaim regarding historical trends in jet engine part countand to suggest adjustments to the Theory of InventiveProblem Solving (TRIZ) on the basis of the analysis.

2.2. Axiomatic Design

Axiomatic Design (AD) is a theory of design proposedby Suh [1990]. Just as TRIZ seeks a scientific founda-tion for creativity, AD seeks a scientific basis for engi-neering design but on an axiomatic rather than analgorithmic basis. An algorithmic approach, such asTRIZ, defines step-by-step procedures for a designer tofollow. By contrast, an axiomatic approach identifiesprimitive propositions and seeks to develop theoremsfrom the primitive propositions by deduction.

Axiomatic Design posits the existence of four do-mains [Suh, 1990]—the customer domain, the func-tional domain, the physical domain, and the processdomain. Design is viewed as mapping between pairs ofdomains where (in Fig. 2) the domain on the left is“what we want to achieve” and the domain on the rightis “how we propose to achieve it.” For example, thefunctional requirements (FRs) are the minimum set ofindependent requirements that characterize the designgoals. The design parameters (DPs) are the key vari-ables that characterize the physical entity created by thedesign process to fulfill the FRs. Therefore, the designof a product is the mapping from FRs to DPs. Similarly,the design of the manufacturing system involves select-ing process variables (PVs) to satisfy the DPs.

According to Suh, the mapping from the functionaldomain to the physical domain can be represented bythe design equation {FR} = [A]{DP}. The elements ofthe design matrix are defined as the partial derivativesof the functional requirements with respect to the designparameters Ai,j = ∂FRi/∂DPj.

Suh defines an uncoupled design as a design whoseA matrix can be arranged as a diagonal matrix by anappropriate ordering of the rows and columns. He de-fines a decoupled design as a design whose A matrixcan be arranged as a triangular matrix. He defines acoupled design as a design whose A matrix cannot bearranged as a triangular or diagonal matrix. Based onthe structure of this design matrix, A, Suh defines whathe calls the “independence axiom.” He states that anuncoupled design satisfies the independence axiom,that a decoupled design satisfies the independence ax-iom as long as changes in the DPs are performed in theappropriate order, and that a coupled design does notsatisfy the independence axiom.

In addition to the “independence axiom,” Suh [1990]proposes the “information axiom” embodied by theimperative to “minimize information content.” This

Figure 2. The four domains in Axiomatic Design.

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axiom is frequently misinterpreted as governing de-scriptive complexity of the design, but, in fact, it hasquite different implications. The information axiomdepends on Suh’s definition of the information contentof a design. Within Axiomatic Design, the probabilitythat a product can satisfy all of its FRs is called theprobability of success (ps). Based on the notion ofprobability of success, information content I is definedas I = log2(1/ps). Given the definition of informationcontent, the theory of axiomatic design includes thefollowing “theorem”: “The sum of information for a setof events is also information, provided that the properconditional probabilities are used when the events arenot statistically independent” [Suh, 1990, p. 394].

The independence axiom and the information axiomare interrelated. For example, Suh [1990, p. 393] statesthat the “information content of an uncoupled design isindependent of the sequence by which the DPs arechanged to satisfy the given set of FRs.” An evenstronger claim relating the independence and the infor-mation axioms is “when the state of FRs is changedfrom one state to another in the functional domain, theinformation required for the change is greater for acoupled process than for an uncoupled process” [Suh,1990, p. 394].

There has been an effort to relate Axiomatic Designand TRIZ. Mann [1999a, 1999b] explored the compati-bility between the two theories concluding that: (1)Axiomatic Design offers TRIZ practitioners a meansfor problem definition and the handling of multi-lay-ered problems; and (2) TRIZ offers practitioners ofAxiomatic Design a means to develop candidate DPsonce FRs are defined. Along similar lines of reasoning,a hybrid methodology has been proposed merging Axi-omatic Design with TRIZ and also with robust designand Reliability Centered Maintenance [Sarno, Kumar,and Li, 2005]. In this hybrid, once again, TRIZ isprimarily employed as a tool for developing solutionswithin a process structured via Axiomatic Design.

The theory of Axiomatic Design has specific impli-cations for part count reduction. It is clear that anydesign having fewer DPs than FRs must be coupled andhence unacceptable according to the theory. However,the theory does not hold that each DP requires a separatepart. This is made more explicit in Suh’s [1990] “Cor-ollary 3 (Integration of Physical Parts)” which calls forintegrating design parameters into a single physicalprocess, device, or system, but only when the Inde-pendence Axiom can be satisfied. In other words, partcount reduction can and should proceed by consolidat-ing multiple DPs into a single part but only if theresulting design matrix has the required structure.Therefore, Axiomatic Design makes a specific predic-tion about part count reduction and system reliability—

that part count reduction will reduce system reliabilityif it brings about coupling of the design.

2.3. Highly Optimized Tolerance

Carlson and Doyle [2000, p. 2529] have offered a visionof technological evolution based on Highly OptimizedTolerance (HOT)—a term “intended to reflect systemsdesigned for high performance in an uncertain environ-ment….” This conception of HOT systems stands incontrast to other contemporary complex systems theo-ries which generally emphasize “self organized critical-ity”—the idea that complex behavior emerges from aset of simple components. By contrast, HOT empha-sizes configurations due to deliberate design or biologi-cal evolution rather than emergence from physicalprocesses only. Although the theory of HOT is in con-trast to most complex systems theory today, it is notwithout precedent. Ashby’s [1958] Law of RequisiteVariety states that in order to achieve control, the varietyof actions a control system is able to execute must be atleast as great as the variety of environmental perturba-tions that need to be compensated. These ideas werebuilt upon by the cybernetics community, for example,by Heylighen [1991, 1996].

The theory of HOT has significant implications forpart count reduction. Carlson and Doyle [2000, p. 2529]note that modern engineered systems are characterizedby tremendous complexity. For example, comparing acar manufactured today and a car manufactured 30years ago with a similar list of additional features suchas radios, most would agree that the newer automobilehas substantially more parts and a greater variety ofparts. At the highest level of abstraction, the function ofthe car has not changed: It still must apply power to thewheels, enable the driver to steer and brake, and handlethe bumps in the road. This raises the question of whatthis increasing complexity serves to achieve. Compar-ing the earlier systems with low part count to the newersystems, Carlson and Doyle [2000, p. 2529] observe,“[W]hat is lost in these simpler systems is not their basicfunctionality, but their robustness.” Most people whohave recently driven an older car will agree that they arefar less robust than their modern counterparts. Forexample, they may start easily enough on a warm day,but are generally hard to start in cold weather. In otherwords, the function of starting in an older vehicle designis not as robust to ambient temperature as in a moremodern vehicle design. Others have come to a similarconclusion regarding complexity and robustness [e.g.,Heylighen, 1996].

With the theory of HOT, Carlson and Doyle [2000]challenge notions from TRIZ. While TRIZ predicts thattechnological evolution leads to simplification in the



long term (at least after the inflection in the “S-curve,”according to Mann [2000a]), Carlson and Doyle [2000,p. 2544] take an opposite stance: “[W]hile it has becomecliché that greater complexity creates unreliability, theactual story is more complicated…. The essence of thisrobustness, and hence of complexity, is the elaborationof highly structured communication, computing, andcontrol networks that also create barriers to cascadingfailure events.”

As an example of such barriers to cascading failure,consider the introduction of airbags in passenger cars.Figure 3 depicts the state space of the vehicle and theairbag. A set of cascading failure events begins with achange from a normal driving condition to a dangerousone. If the actions of the driver are inadequate, thisresults in a crash. Without an airbag, the driver’s headis likely to contact the car leading to trauma, but theairbag senses the crash and deploys. This leads to thedriver’s head contacting the airbag rather than the car.

It is important in this context to draw a distinctionbetween adding a new function and making an existingfunction more robust. The example of air bags is usefulfor illustrating our position on this. One may argue thatthe function of seat belts is to enable the driver toexperience a collision without injury. Seatbelts canenable this function fully under the right conditions.However, as the range of conditions is expanded toinclude more angles of impact, locations of impact,seating positions of the driver, etc., the seatbelt alonefrequently appears inadequate. Adding front and sideairbags enables the basic function previously providedby seatbelts to be delivered across a larger range ofuncertain or variable factors. According to the defini-tions proposed by Clausing and Frey [2005], the oper-ating window of the system has been expanded and, ifit holds the previous operating window as a subset, thesystem robustness has surely improved. This is theinterpretation we propose here regarding the theory ofHOT. As long as the previous design can carry out thebasic function under consideration, at least under idealconditions, and the design changes proposed only serve

to enable the function over a larger operating windowof uncertain or variable conditions, then we proposethat this design change was driven by robustness asconceptualized in HOT.

Perhaps making a function more robust by additionalnetworks and barriers can also be accounted for underTRIZ by allowing some rise in the numerator in the “lawof ideality” to offset the rise in the denominator. How-ever, in its current form, the concept of “ideality” as astate that “requires no material to be built, consumes noenergy, and does not need space and time to operate”seems to be clearly at odds with the predictions of HOT.Further, there is a specific conflict with the predictionof Mann [2000a, 2000b] that part count will reach anapex at the inflection point in the technology “S-curve”whereas HOT suggests complexity continues to risewithout ever reaching an apex.

The theory of HOT also challenges notions fromAxiomatic Design. Axiomatic Design holds that infor-mation content of a system is summative. Thus it fol-lows that probability of success must decline withaddition of Design Parameters to a design that meets the“independence axiom” unless that addition not onlyadds columns to the design matrix but also alters thestructure of the current design matrix elements. In ap-parent contrast, Carlson and Doyle [2000, p. 2545]argue that “advanced technologies and organisms, attheir best, use complicated architectures with sloppyparts to create systems so robust as to create the illusionof very simple, reliable, and consistent behavior appar-ently unperturbed by the environment.” This idea goesback at least as far as John von Neumann’s 1952 lectureson “Probabilistic Logics and the Synthesis of ReliableOrgans from Unreliable Components” [von Neumann,1952]. In this work, von Neumann proved that multi-plexed “bundles” of basic organs can be arranged so thatthe system error rate decreases monotonically with thenumber of parts as long as the component reliabilitiesare better than 1/6. These results are not consistent witha procedure of summing information content defined asit was by Suh [1990], but they were shown by vonNeumann to be consistent with information as definedby Shannon [1948].

According to von Neumann’s theorems, the numberof “basic organs” needed, although large (~20,000) isremarkably insensitive to the escalation in system re-quirements [von Neumann, 1952]. The theory of HOTbuilds upon this idea, but says something different too.While von Neumann analyzed parallel structures oforgans of the same kinds, the theory of HOT holds thatsystems will evolve to become more heterogeneous(parts should generally not all be the same) and beformed of complex architectures (not merely parallelstructures). Therefore, the theory of HOT suggests that

Figure 3. The use of airbags to interrupt a cascading failure(adapted from Doyle [2004]).

208 FREY ET AL.


not only part count rises, but the number of unique partswill also frequently rise in order to accomplish robust-ness. Perhaps the heterogeneity also enables the totalpart count increases to be less than the huge increasesdescribed under von Neumann’s schema.

To illustrate how HOT is related to a rise in uniquepart count, again consider Figure 3. The automotiveairbag, while adding unique parts, reduces the severityof one cascading failure. At the same time, the new partscreate another possible cascading failure event in whichthe airbag deploys under normal driving conditions,leading to a crash and trauma. However, good design ofthe sensing and deployment systems can make thiscascading failure highly improbable. A car with anairbag is both more complex and more robust than a carwithout an airbag, which is why insurance companiesoffer financial incentives for drivers to purchase vehi-cles with airbags. However, this is accomplished not bymassive parallelism of identical “sloppy” parts as oftenobserved in biological systems, but by judicious addi-tion of a modest number of highly engineered, uniqueparts.

As observed by Carlson and Doyle [2000], partcount reduction is not the rule in technological evolu-tion. Even if baseline system performance becomesstable, escalating demands for robustness will fre-quently drive higher system complexity both in partcount and in unique part count. Due to these trends, itseems that a full theoretical understanding of part countchanges in systems engineering must include consid-erations of system robustness.

3. CASE STUDIES: PART COUNT AND GASTURBINE ENGINES

This section is comprised of case studies intended toillustrate the benefits and pitfalls of part count reduc-tion. All the case studies are from a single industry, gasturbine engines. This strategy was employed so that ateam of experienced, engineers could be assembledwith deep working knowledge of the subject includingexperiences at all three major manufacturers—GeneralElectric, Pratt & Whitney, and Rolls Royce. Althoughthe cases all concern gas turbine engines, they areintended to span a wide range of systems engineeringconsiderations.

A brief introduction may be in order for those unfa-miliar with jet engines. Figure 4 is a simplified sche-matic of a turbofan engine. Air enters from the left andflows into the inlet where it is compressed and acceler-ated by the fan. The air often splits so that a portionflows into the core of the engine and a portion bypassesthe core enabling a larger total mass flow. The core of

the engine is comprised of the compressor, combustor,and turbine. The function of the compressor is to in-crease the air pressure. The combustor adds fuel to theflow where it is burned, greatly raising its temperature.The turbine then extracts some of the energy from theflow, lowering its pressure and driving the compressorthrough a shaft connecting the two. A nozzle thenaccelerates the flow.

The remainder of this section is a set of discussionsof major part count reduction efforts in gas turbineengines and their relationships to the three system de-sign theories introduced in Section 2.

3.1. Separate Blades and Rotors Versus anIntegral Design

Conventionally, axial flow compressors have had sepa-rate blades and rotors, most often with “fir tree” con-nections such as those depicted in Figure 5. However,there has recently been a trend toward consolidationinto a single part. This technical innovation is knownvariously as a “blisk” at General Electric or an “inte-grally bladed rotor” at Pratt & Whitney.

The consolidation of blades and disks in a single partis not new. Centrifugal flow compressors have conven-tionally been cut out of a single block of material. Butaxial flow compressors require a large number of

Figure 4. Schematic of a jet engine showing its major com-ponents.

Figure 5. The blade–disk interface is often shaped like a firtree.



closely spaced blades with complex, tightly tolerancedgeometry and extreme strength due to high centrifugalloading. The TRIZ principle of local quality suggeststhat making the blades separate affords some advan-tages. Separate blades can be forged, machined, andinspected separately and also can be replaced individu-ally if they are damaged in service. Therefore, we seethat initial trends in compressor design (resulting in partcount increase) are consistent with TRIZ.

Despite the advantages of separate blades, there ismotivation to consolidate blades and disks into a singlepart, and this has been accomplished in many designs.In one specific example, a mid-stage compressor bladeddisk employed 75 airfoils, a corresponding number offront and rear seals, and blade locks, in addition to thedisk, resulting in over 230 parts for the one disk alone,all of which were consolidated into a single part leadingto the following advantages:

1. Lower lifecycle cost. The cost associated withdelivery, inspection, handling, and inventoryholding for all 230 parts was enormous. Despitehigher initial cost of the integrated part, thelifecycle costs decreased dramatically with partconsolidation.

2. Reduced weight. The need for attachment fea-tures adds significant mass to the outboard regionof the disk. In modern compressors, the overallweight penalty as compared with an integratedpart is 5–10%. This percentage savings is verylarge by aerospace industry standards.

3. Lessened leakage flow. The radial gap betweenthe airfoil root and the root of the disk slot pro-vides a path for leakage from high pressure re-gions to low pressure regions. This leakagereduces compressor efficiency, cuts stall margin,and increases disk rim temperatures. Essentiallyall of the leakage associated with attachmentfeatures was eliminated by part consolidationenabling improved performance and robustnessto inlet flow disturbances.

4. Improved reliability and simplified mainte-nance. The blade/disk interface is a major sourceof stress concentration and also a locus for fret-ting and cracking. As a consequence, blade at-tachments are a likely region for failure and mustbe inspected periodically. These reliability andmaintenance issues were greatly mitigated withpart consolidation.

While the consolidation of blades and disks into asingle part has provided significant advantages, it hasalso created daunting design challenges at both thecomponent level and at the system level.

First, consider the manufacturing issues. Attainingtight spacing of the blades has pushed manufacturerstoward flank milling in which the side of the cutter is incontact with the work rather than the tip (Fig. 6). Butflank milling restricts the geometries one can producewhich might compromise aerodynamic performance.Adequate solutions could only be found by multipleiterations of aerodynamic design and manufacturingprocess design [Wu, 1995]. This is clear evidence thatpart count reduction caused aerodynamic design andmanufacturing to become coupled. From the perspec-tive of Axiomatic Design, this fact would be evidencedby a nontriangular matrix AB representing the productof the matrix A mapping from aerodynamic FRs toblade geometry DPs and the matrix B mapping fromblade geometry DPs to tool path/tool shape PVs. Thechallenge of executing this coupled design has been metthrough new CAD tools capable of modeling the flankmilling process and tying together milling simulationsand computational fluid dynamics. By this means, thedesign iterations required to execute the flank milledblades were greatly accelerated, and so despite thecoupling, which creates a need for iteration, good de-signs could be developed quickly [Wu, 1995]. Thecoupling of design and manufacturing, which was evi-dent in the case of flank milled blisks, is specificallyprecluded by Theorem 9 in Axiomatic Design whichholds that the manufacturing process parameters shouldbe arranged so that they can be decided in a singleiteration once the best ordering is determined. Despite

Figure 6. Flank milling of complex compressor blades(adapted from Wu [1995]).

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design/manufacturing coupling, the jet engine industryhas succeeded in implementing flank milled integratedblades with excellent results. This verifiable, observ-able phenomenon is not consistent with Axiomatic De-sign; it is a counterexample to the theory.

While the manufacturing issues serve to illustrate thecomponent-level design challenges, Foreign ObjectDamage (FOD) nicely illustrates the system-level con-siderations. In a bladed disk design, the blades can oftenbe repaired on-wing. By contrast, once an integratedblade is damaged beyond repair limits, the engine mustbe removed. Because an engine removal is both disrup-tive and costly, either separate blades are needed or elsecountermeasures against FOD must be adopted. Onecountermeasure to FOD is increased blade leading edgethickness, but this is detrimental to compression systemperformance whose effects can only be fully evaluatedthrough engine-level trade studies. Another option is to“hide” the core flow path from the fan and/or design thefan to act like a centrifuge to force FOD outward andaway from the high pressure system. These designdecisions usually involve performance, weight, andcost trades. Increased repair limits will likewise bedetrimental to compression system performance andwill result in increased fuel burn and a reduction intemperature margin, which could result in early engineremoval. Repair technology improvements are beingdeveloped such as welding technologies to repair dam-age on-wing. Even if this problem is solved, integratedblades and rotors must be carried as spares inventory,and this cost is much greater than the inventory cost ofindividual blades.

Part count reduction at the component level viaintegration of blades and disks into a single part hasbeen accomplished and successfully fielded. The resulthas been dramatically improved thrust to weight ratioand improved reliability. This evolution toward fewerparts and better performance is broadly consistent withthe TRIZ “law of ideality.” But these benefits wereattained at the cost of greatly increased coupling ofdesign and manufacturing, in apparent contradiction ofAxiomatic Design (especially Theorem 9). Aerody-namic design and blade milling became inexorablyintertwined demanding iterative solutions made practi-cable by specially tailored computerized design tools.Even though the industry has overcome the coupling inthe design process, other challenges still remain. Aswith many other innovations, new system-level factorsneed to be considered such as repair and supply chainlogistics. The detailed tradeoffs involved in these sys-tem-level design challenges seem to defy explanationby any simple theory and create a demand for experi-enced professionals whose judgment is needed to createcommercially competitive systems.

3.2. Blade Count Reduction in CompressorDesign

Improved aerodynamic technology, especially com-puter aided engineering, has resulted in three trends inthe design of compressors and turbines each of whichhas contributed to part count reduction:

1. Fewer blades per stage2. Fewer stages to achieve the desired overall per-

formance3. Counter-rotating turbines which allow the elimi-

nation of stationary stages (nozzles) betweenstages.

These three strategies have all been employedwidely in design of turbo-machinery, but are usually notall found in a single design. Choices among thesestrategies involve tradeoffs and systems-level studies todetermine the optimum design for a given set of enginerequirements. Details of each approach are discussed inturn below.

Improvements in Computation Fluid Dynamics(CFD) have enabled design of 3D airfoil shapes withincreased loading per blade, with the result that fewerblades per stage are required to achieve the desiredpressure rise. However, these shapes have greatly in-creased the challenges of compressor design. The 3Dairfoil shapes tend to be more sensitive at the tip sec-tions to vibratory forces because the blade tip chord isusually greater than that of a conventional airfoil in-creasing the tip vibratory stresses caused by aerody-namic forces and blade-to-casing rubbing. Tipvibratory stresses require a better understanding ofvibration modes, aerodynamic forcing functions, andimproved means of measuring blade tip stresses. Fur-ther, to produce these complex shapes, new manufac-turing technologies have been required such aselectro-chemical machining and electric discharge ma-chining. Implementation of these technologies requirescapital investment for new equipment and, in somecases, consideration must be given to hazardous wasteproducts. There is also a new “learning curve” forproduction of the airfoils including training of opera-tors, inspection techniques, and rework procedures toavoid scrapping of expensive parts. The benefits offewer parts, lower weight, and the resulting reductionin operating and maintenance cost must be evaluatedagainst the increased cost per blade and new vibratoryfailure modes which occur because of the 3D shapes.

The evolution toward fewer blades per stage is gen-erally consistent with the TRIZ “law of ideality” sincepart count reduction can be achieved with no change inbasic system functionality. However, a major cost is



paid in the complexity of the design process itself.Where design could previously be handed sequentiallyfrom aerodynamics to structures, today the two do-mains are more strongly coupled. Viewed from theperspective of Axiomatic Design, there are no changesin the functional requirements nor in the high leveldesign parameters, but the mapping between the twodomains has evolved toward tighter coupling demand-ing more design iterations. In general, industry hasfound that the benefits of fewer blades per stage out-weigh the drawback of more coupled design. This trendtherefore generally supports the TRIZ principle of ide-ality and appears to be inconsistent with AxiomaticDesign.

As industry has evolved toward fewer blades perstage, it has also evolved toward fewer stages per engineby a trend toward higher stage loading (see Fig. 7). Asbefore, improved CFD technology has been a keydriver. Improvements on aerodynamic design have ledto typically one or two stages being eliminated with aconstant overall compressor efficiency. Alternatively,CFD can provide one to two points in overall efficiencyfor a constant stage loading. Generally, the industry haschosen to increase stage loading and reduce the numberof stages. Reducing the number of stages gives theadded benefit of reduction in engine length, whichreduces engine weight and assembly time and alsoresults in a stiffer engine making deflection controleasier and reduces sensitivity to rotor imbalance. How-ever, higher stage loading generally demands bettercompressor clearance control. Because of the higherstage loading, there is increased sensitivity to tip clear-ances, which impact both efficiency and surge margin.Even though reduced engine length improves the abilityto control clearances, better 3D heat transfer and deflec-tion technologies are required to understand and setengine clearances over a wide range of operating con-ditions. In addition, there is the need for more complexcontrol functions to ensure sufficient surge margin.These functions may be result in greater hardware com-

plexity (such as variable geometry, bleed valves, and/orclearance control) or additional software (for refinedcontrol of acceleration rates).

The evolution toward fewer stages is generally con-sistent with the TRIZ ideality principle. This trend isparticularly interesting since there has been a clearalternative—to maintain the same part count and im-prove efficiency. Yet faced with the alternative, thebenefits of part count reduction for cost, weight, main-tenance, inventory, etc. are difficult to resist. However,in this case, the evolution toward a simpler compressorhas driven up overall system complexity due to the needfor tip clearance control. This trend is generally consis-tent with HOT theory.

Counter-rotating turbines are a major advance inengine technology providing roughly a “four foldgreater work capacity at a given rotation speed” [Adam-son, Butler, and Wall, 1991]. However, taking advan-tage of this potential benefit requires a betterunderstanding of the exit conditions of the high pressureturbine and, thus, the entrance conditions of the lowpressure turbine. The first generation application of thistechnology has resulted in the elimination of the nozzlebetween the high and low pressure turbines. Elimina-tion of this part and the associated seals and attachmentshas yielded a major reliability improvement since theseparts are subjected to high thermal stresses and are afrequent source of failures. The trend toward adoptionof counter-rotating turbines illustrates how stronglyreliability can serve as a driver of part count reduction.However, the benefits of counter rotating trubines havecome at the expense of much greater design difficulty.Two effects, in particular tend to become intertwined.First, the change in high pressure turbine exit conditionsmust be thoroughly evaluated over the entire operatingrange since the performance benefits of counter rotationcan be lost if the matching of the two turbines is notcorrect. Second, the gyroscopic effects on rotor dynam-ics and engine mechanical loads will be more complex.This is particularly important for engines which havean intershaft bearing which ties the high- and low-pres-sure rotors together mechanically.

Use of counter-rotating turbines, like many otherpart count reduction strategies so far discussed, tends tosupport the TRIZ ideality principle and challenge thetheory of Axiomatic Design. The functions of the noz-zle are taken up by the rotating stages of the turbineleading to part count reduction. However, the mappingamong FRs and DPs becomes increasingly coupledrequiring an iterative design process. According to Axi-omatic Design, the probability of success should havebeen reduced, but in fact the system reliability improvedbecause a high failure rate part was eliminated.

Figure 7. Increase in stage loading as an industry trend(adapted from Wisler [1998]).

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3.3. Engine Control Systems

The control systems of modern gas turbine enginesconsist of a large number of interacting parts. Thehigh-level functions of the control system include start-ing and shutdown control, thrust management, accel-eration and deceleration control, protection fromexceeding engine-operating limits, and communica-tions with aircraft systems including cockpit displaysand pilot commands. The technologies have evolvedfrom purely hydro-mechanical systems, to mixed sys-tems with hydro-mechanical and electronic supervisorycontrollers (analog or digital), leading to full authoritydigital engine controls (FADEC). The evolutionary pathfor Rolls Royce engines is presented in Table I.

Rolls-Royce used hydro-mechanical control sys-tems on the early versions of the RB211-524 and theSpey and Tay engines. These systems contained differ-ent parts for achieving specific functional requirements.Separate components were required for altitude sensing(adjusting fuel flow to match the inlet air pressure),acceleration and deceleration control, shaft speed gov-erning, idle setting, etc. The resulting systems werehighly complex with hundreds or thousands of partsincluding valves, springs, levers, cams, shafts, andseals. Although the early systems had high part count,they had a relatively simple mapping between func-tional requirements and design parameters. Figure 8shows many parts or subsystems related directly to a

single functional requirement, such as the “idlingvalve” or “acceleration control unit.” This trend sug-gests the early designs were generally consistent withthe Independence Axiom in Axiomatic Design.

As engine systems evolved in the 1970s and 1980s,higher by-pass ratios needed for fuel efficiency weredemanding more sophistication in thrust managementand cockpit interfacing which could not be met withhydro-mechanical control systems. This led to the in-troduction of electronic supervisory systems. TheRB211-535 supervisory control is an example. On thisengine, an Engine Supervisory Controller only pro-vided limited authority to trim fuel flow to optimizeengine thrust, and hence reduce specific fuel consump-tion. In this case, the addition of the supervisory con-troller increased the part count because a fully capablehydro-mechanical fuel flow governor was maintained.Additionally, a separate Bleed Valve Control Unit wasdeveloped for controlling compressor bleed valves.This used analog electronics for control, with digitalfault detection. All jet engines need a system for pro-tecting the engine from a hazardous shaft over-speedcondition, and the RB211-535 included a separate me-chanical system to achieve this.

The next evolutionary step emerged when the firstdual channel full authority digital electronic control(FADEC) for a commercial engine was introduced onthe Pratt & Whitney PW2037 in the early 1980s. By the1990s all large engines were being developed with

Table I. Principal Parts in Engine Control Systems with Type of Computation Technology Used, Adapted from Prencipe [2000]



FADEC controls. The Rolls Royce Trent engines aretypical of how these control systems are designed. Atthe heart of the FADEC system is an Electronic EngineController, which performs all the computation pre-viously dispersed among several units. A Fuel MeteringUnit receives an electrical command to control theposition of a fuel metering valve. The position of thevalve is sensed and fed back to enable closed loopcontrol. There are no longer any parts specifically asso-ciated with functions such as acceleration control orspeed governing; The electronic controller manages allof these functions in software. Therefore, the introduc-tion of FADEC control systems reduced the physicalpart count by integrating many functions into one unit.The integration of information and the increases inprocessing power also create an opportunity to expand

the functional capability of the system. This tends toincrease the part count again. For example, in olderengines, the air-cooled oil cooler had no regulationcapability and was designed to provide cooling airsufficient for the worst case oil cooling demand. Thevalves could not be regulated and hence for much of thetime the oil was being cooled more than needed, with aconsequent loss in fuel efficiency. The introduction ofFADEC control provided an opportunity to control theoil cooler in response to oil temperature measurement.This allowed the bleed air demand to be reduced andimproved fuel efficiency at he cost of added actuatorsand sensors.

It is a useful exercise to view the evolution of jetengine controls through the lenses of TRIZ and HOT.Due to escalating demands (especially demands for

Figure 8. Example of a hydromechanical control system. Reprinted from Rolls-Royce 1986] with permission from Rolls-Royce,plc, © 1986.

214 FREY ET AL.


robustness and reliability), new systems were initiallylayered onto existing ones as described in HOT theory.In tension with the TRIZ ideality principle, these evo-lutionary steps added to system part count. However,the intermediate steps involving part count increase areexplicitly allowed for under TRIZ. For example, thelayering of electronic engine controls onto hydro-me-chanical systems to avoid failure modes is a goodexample of the TRIZ tactic of the “previously placedcushion.” Such intermediate steps in technological evo-lution are a practical necessity, especially in safetycritical systems such as jet engine controls, because thereliability of new technology must be proven in thefield. Later, when confidence in the technology is suf-ficient, the new functions may be consolidated intointegrated systems as was observed in the adoption ofFADEC. Once this consolidation occurs, we aretempted to say that the TRIZ ideality principle hasfinally been satisfied. However, the observed phenome-non in jet engine controls is that system part countcontinued rising despite ongoing part consolidation atthe component level because increased demands forexception handling and reliability were satisfied byadding more sensors and actuators to the control sys-tem. As suggested by HOT theory, we observe a positivenet effect on jet engine reliability and robustness, be-cause of and not despite of increased system complex-ity. It may be said therefore that part count is not a very

reliable surrogate measure for desirable system proper-ties such as reliability because often the parts beingreplaced (in this case, mechanical parts) differ so muchfrom the new parts (mostly solid state devices in thiscase).

The history of jet engine controls also sheds somelight on Axiomatic Design. The long-term trend inengine control has been to achive part count reductionat the component level by moving away from largelyuncoupled mechanical and hydrauilc systems towardselectronic controls. Figure 9 presents a Design Struc-ture Matrix (DSM) for a modern jet engine, the Pratt &Whitney PW4098 [Sosa, Eppinger, and Rowles, 2000].The matrix lists design tasks as labels for each row, andthe same tasks are also labels for each column. Ifinformation is required by a task and that informationcomes from a task earlier in the list, an entry is placedin the corresponding element below the diagonal. Ifinformation is required by a task from a task listed later,an entry is placed above the diagonal. Thus, the DSMrepresents the information flow structure in a designprocess. Although a DSM is not the same as a designmatrix within Axiomatic Design, it does present infor-mation sufficient to infer whether coupling exists. Ele-ments in the DSM above the diagonal indicate flows ofinformation from a later design task to a previous designtask and therefore represent a potential for rework cy-cles. Since only designs that are “coupled” according to

Figure 9. A design structure matrix of the Pratt & Whitney PW4098. Reprinted from Sosa, Eppinger, and Rowles [2000] withpermission from ASME, © 2000.



the “idependence axiom” require rework cycles, ele-ments above the diagonal of a DSM are evidence ofcoupling as defined within the theory. It is clear fromthis DSM that modern jet engines are more nearly blockdiagonal than lower triangular. Certain sets of designtasks are strongly coupled to one another. In addition,control systems and other integrative systems are asso-ciated with especially dense bands of the matrix farfrom the diagonal. As a practical matter, this introc-duces the possibility of fairly large blocks of rework. Infact, these rework cycles are made less likely or lesssevere by either an evolutionary approach, avoidingdesigns far from current experience, or else good pre-dictive modeling capabilities. Notwithstanding this,Figure 9 presents evidence that modern jet engine con-trol systems are a particularly strong source of coupling.These facts clearly conflict with the predictions ofAxiomatic Design.

3.4. Overall Jet Engine Trends

The three previous sub-sections have been just a sampleof the many technological and design advances made inthe past several decades. These advances have all con-tributed to improvements in overall performance, cost,and reliability.

One of the key indices of overall performance isthrust to weight ratio—high ratios are especially valuedin military applications. Figure 10 presents data from25 military jet engines produced since 1960 [Younossiet al., 2002]. It also presents a line indicating the overalltrend based on statistical analysis of this data. This linesuggests that, as far as thrust to weight ratio is con-cerned, jet engines have long since passed the inflectionpoint on the “S-curve” if there ever was one.

Similarly, Figure 11 presents data on thrust specificfuel consumption. Reductions in this figure of merit arevalued in commercial transport applications. To thisfigure, we added a curve that bounds the data frombelow. There appears to be an asymptotic improvementover time in the best available performance. Again, itappears that an inflection point on the “S-curve” isdecades in the past.

Now consider Figure 12, which plots jet engine partcount data from a single manufacturer and a singlethrust class [Slagle, 2006]. Part count appears to haverisen at least through 1980 at which time jet engineswere at least two decades beyond the “S-curve” for attwo major measures of their technological evolution.This appears to be a counterexample to Mann’s hy-pothesis based on TRIZ that part count will reach amaximum at the inflection point of its S-curve [Mann,2000a]. Because the part count data in Figure 12 issparse and highly uncertain due the different standardsfor definition of separate parts, it is not known whetherpart count increases are continuing today or a reversaloccurred in the recent past. Most experts suggest jetengine part count is still rising.

One reason for part count to rise after the S-curveinflection is that even small improvements can result inlarge differences in market share within a competitiveindustry. Therefore the high part count and its attendantcosts are justified economically. As Arthur [1993, p.144] observed:

… over the years, jet engines steadily become morecomplicated. Why? Commercial and military interestsexert constant pressure to overcome limits … and tohandle exceptional situations. Sometimes these im-provements are achieved by using better materials,

Figure 10. Improvement in overall engine thrust to weight ratio over time (adapted from Younossi et al. [2002]).

216 FREY ET AL.


more often by adding a subsystem…. But all theseadditions require subsystems to monitor and controlthem and to enhance their performance when they runinto limitations.… On the outside, jet engines are sleekand lean; on the inside, complex and sophisticated. Innature, higher organisms are this way too. On theoutside a cheetah is powerful and fast, on the inside,even more complicated than a jet engine. A cheetah,too, has temperature-regulating systems, sensing sys-tems, control functions, maintenance functions-all em-bodied in a complex assembly of organs, cells andorganelles, modulated not by machinery and electron-ics but by interconnected networks of chemical andneurological pathways. The steady pressure of compe-tition causes evolution to “discover” new functionsoccasionally that push out performance limits.

Arthur’s analysis is nearly the one offered by HOT,but not exactly since HOT emphasizes robustness rather

than “new functions.” We view the emphasis on robust-ness as more consistent with recent evolutionary trendsin jet engine system design. In general, the pressure forincreased robustness has influenced modern commer-cial jet engine design practices more than any othersingle factor. This is most dramatically illustrated by thejet engine reliability trend depicted in Figure 13. Therehas been a hundredfold reduction in the frequency ofin-flight shutdowns over the past several decades, astunning achievement of systems engineering. Becausereliability has been the most salient driver of jet enginedesign evolution, we judge that HOT is broadly consis-tent with the case studies presented here and with agrowing body of related scholarship.

Figure 11. Improvement in overall engine thrust specific fuel consumption over time [adapted from Koff [1991]).

Figure 12. Evolution of jet engine part count for a singlemanufacturer and thrust class (adapted from Slagle [2006]).

Figure 13. Evolution of jet engine reliability (adapted fromBallal and Zelina [2004]).



4. CONCLUSIONS

Part count reduction, at the component level, is amongthe most prevalent engineering strategies, especiallywithin highly evolved, stable engineering systems un-dergoing evolution over long periods of time (such asjet engines). This paper considers three system designtheories comparing the predictions of the theories toactual events in the evolution of jet engines. The con-clusion is that Axiomatic Design and TRIZ generallyfail to explain the systems-level phenomena and thatHOT provides more valuable insights.

As predicted by TRIZ, opportunities for part con-solidation have consistently been adopted in the jetengine industry as technological advancements haverendered them practicable. As part count has been re-duced at the component level, significant benefits havebeen attained, especially when low reliability parts areeliminated. However, at the system level, overall jetengine part count seems to rise after the inflection pointon the S-curve is long past. Therefore, we conclude thatthe “law of ideality” in TRIZ must be modified by (1)viewing it only as a component-level evolutionary prin-ciple and/or (2) by expanding and refining the definitionof “performance” of the system to include, as a mini-mum, a quantitative measure of robustness as principaldriver of system design. Despite the necessity of someadjustments to TRIZ, it continues to be a useful tool forgenerating ideas.

In contradiction with the theory of Axiomatic De-sign, part consolidation in jet engines has frequentlymade the design more coupled while nevertheless im-proving probability of success. The coupling of modernjet engines is observed at the component level in mod-ern compressor design, across design and manufactureas observed in blisks, and at the system level as ob-served in engine control systems design. This couplinghas increased the difficulty of executing the design andhas led to much greater reliance on iterative approachesto subsystem optimization and system-level trade stud-ies. However, the jet engine industry has largely suc-ceeded in overcoming the challenges of executingcoupled designs, mostly by means of computer-aidedengineering. Large investments have been made in spe-cialized software tools for detailed modeling of fluids,structures, thermodynamics, and manufacturing, andall these disciplines have become more fully integratedvia computer models. Furthermore, the reliability of jetengines has risen as coupling has become stronger,which is clearly counter to Axiomatic Design. There isstill value in cautioning engineers against the designchallenges posed by coupling, but the strict prescriptionwithin Axiomatic Design to avoid coupling at all costsis not supported by analysis of jet engine design. We

propose that the information axiom and its related theo-rems regarding summative information require majorrework since the restrictions to independent events ren-ders them of little use in tightly interconnected systemssuch as jet engines.

In accordance with the theory of Highly OptimizedTolerance, even as parts are consolidated at the compo-nent and subsystem levels, recent history of jet enginesreveals a consistent trend toward rising system partcount. Despite common misconceptions regarding thebenefits of simplicity, the rise in complexity of jetengines has improved system reliability and robustness.The myriad components of jet engines have co-evolvedinto a tightly coupled system. Due to escalating de-mands for robustness, the components and subsystemsare architected in layers creating barriers to cascadingfailure. As a result, the modern jet engine is among themost complex, yet most reliable engineering systems inexistence today. HOT is not intended to explain orsupport the detailed considerations in design of jetengines or other complex electro-mechanical systems.However, since the system-level trends are consistentwith HOT, we suggest that this theory should be studiedby systems engineers and used to inform their practice.

To summarize, neither TRIZ nor Axiomatic Designcan adequately explain the phenomena observed in theevolution of jet engines as parts are consolidated insome areas and expanded in others. Although part countreduction is eventually observed at the component levelas suggested by TRIZ, when the scope is enlarged to thesystem context, escalating demands for system robust-ness have generally resulted in increased number ofparts and number of unique parts in jet engines. Further,this part consolidation at the component-level and lay-ering of barriers to cascading failures at the system-level have increased coupling and simultaneouslyimproved reliability in direct conflict with the predic-tions of Axiomatic Design. Because these system-leveltrends are precisely those predicted by Highly Opti-mized Tolerance, we therefore regard HOT as a usefulframework for understanding evolution of complex en-gineering systems.

5. SUGGESTIONS FOR FUTURE WORK

The conclusions of this paper are based on the technicalevolution of a single class of engineering systems—jetengines. It seems plausible to the authors that theconclusions will generalize to other complex, electro-mechanical equipment. We must acknowledge that in-duction from any finite number of incidents to generalstatements is subject to difficulties [Goodman, 1954].Nevertheless, if many other engineering systems were

218 FREY ET AL.


subject to similar analysis, systems engineering practi-tioners might come to feel justifiably confident in anyconclusions consistently supported by the set of studies.We therefore suggest that other engineering systemsshould be analyzed to determine if TRIZ, AxiomaticDesign, and HOT are able to explain their historical partcount trends.

If the weight of evidence leads people to seek revi-sions of TRIZ and/or Axiomatic Design, we suggestthose people study the work of the philosopher ofscience Imre Lakatos: “…In a progressive researchprogramme, theory leads to the discovery of hithertounknown novel facts. …In degenerating programmes,however, theories are fabricated only in order to accom-modate known facts” [Lakatos, 1973, p. 101]. Based onour reading of Lakatos, we have a specific suggestionfor future research. Those disagreeing with the conclu-sions of this paper might use TRIZ, Axiomatic Design,and HOT to make some predictions about future partcount trends in specific industries, publish those predic-tions, and then review the full set of predictions later toassess their accuracy.

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O. Younossi, M.V. Arena, R.M. Moore, M. Lorell, J. Mason,and J.C. Graser, Military jet engine acquisition: Technol-ogy basics and cost estimating methodology, RAND,Santa Monica, CA, 2002.

Dan Frey earned the B.S. degree in aeronautical engineering from Rensselaer Polytechnic Institute in1987. After serving as a Naval Officer for 4 years, he earned his M.S. from the University of Colorado in1993 and Ph.D. from the Massachusetts Institute of Technology in 1997. Since then, he has been a facultymember conducting research in robust design, statistics, design methodology, and systems engineering.He currently holds a dual key faculty position at MIT in the Department of Mechanical Engineering andin the Engineering Systems Division.

Joe Palladino earned the bachelor of aerospace engineering degree from Georgia Tech in 1966. Afterworking for Douglas Aircraft for 2 years he joined the General Electric Co., Aviation Division in Lynn,MA, where he worked for 36 years until his retirement in 2004. He earned his M.S. and PhD in MechanicalEngineering from Northeastern University as part of the GE Advanced Course in Engineering. He spentmany years in the engine dynamics area, and for the last 20 years he was the Engine System DesignManager for many GE engine programs—most notably the CF34 family of regional jets.

Mal Atherton earned a B.S. degree in electrical and mechanical engineering from the University ofEdinburgh, Scotland, UK in 1988. He then completed a Postgraduate Diploma in Control and InformationTechnology at the University of Manchester Institute of Science and technology, UK, in 1990. Since thenhe has worked at Rolls-Royce aircraft engines, initially in Derby, England, and then moving to RR’s USdivision in Indianapolis, Indiana, in 1999. Apart from an 18-month period completing the System Designand Management (SDM) S.M. at Massachusetts Institute of Technology (MIT) in 2005, Mal has workedin the engine controls field at Rolls-Royce all his professional career. This has included engine controllaws, fault detection and accommodation designs, and systems engineering management for severalprojects. Currently mal is the Lead engine control systems engineer on the T56 engine for the NorthropGrumman Advanced Hawkeye aircraft Program.

220 FREY ET AL.


John P. Sullivan earned a B.S. degree in Mechanical Engineering from the University of Florida in 1983.He joined UTC/Pratt & Whitney shortly thereafter and since 1990 has led groups in compression systems,turbine aerodynamics (Williams International), and overall Jet Engine Component Design (Pratt &Whitney Canada). In 1999 he earned a Master’s Degree in System Design and Management from theMassachusetts Institute of Technology, and led a major commercial certification program at Pratt andWhitney as Chief Engineer. He is currently the Engineering Director of the Compression Systems ModuleCenter, where he has responsibility for all engineering activities for Fans and Compressors at Pratt andWhitney.



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Part count and design of robust systems