research article a survival analysis on fuel cell technology...

Research ArticleA Survival Analysis on Fuel Cell Technology Patent Maintenanceand Values Exploration between 1976 and 2001

Seng-Su Tsang1 Feng-Chen Chang1 and Wen-Cheng Wang12

1Department of Business Administration National Taiwan University of Science and Technology No 43 Sec 4 Keelung RoadDarsquoan District Taipei City 106 Taiwan2Department of Business Administration Hwa Hsia University of Technology No 111 Gongzhuan Road Zhonghe DistrictNew Taipei City 235 Taiwan

Correspondence should be addressed to Wen-Cheng Wang wcwangcchwhedutw

Received 17 November 2014 Revised 10 February 2015 Accepted 3 March 2015

Academic Editor Jaehwan Kim

Copyright copy 2015 Seng-Su Tsang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Fuel cell RampD activities desirably arrive in patents the costly maintenance fee challengesmanagers as well as researchers to whetheror not renew existing patents The key is will the fuel cell patentrsquos value be worth renewing Thus assessment of patent valueis essential Our study focus online searching was made available after 1976 as the initial year to conduct the patent search Upto 2001 there are 2269 patents classified in the H01M 00800simH01M 00824 category which is the category concerning fuelcell under the classification of the International Patent Classification Effective exploitation of technology values is subject to thecomplementarities of organizational resourcesThe present study used the emerging technology of Fuel Cells as an example to showthat firms may commercialize the values of technology according to their organizational resources By aligning firmsrsquo patentingstrategies and the imparities between book values andmarket values this study concludes a technological ambidexterity with respectto firmsrsquo technology development The exploitative firms tend to file patents to defend their leadership in the product market as aresult their technology is constrained within a firmrsquos boundaries The results show that patent renewing decisions are consequenceof firmrsquos constraints of complementary resources

1 Introduction

Along the 20-year perspective legal entitlement durationeach patent would go through three renewal decisionmoments Patent holder may check patentrsquos status firstly suchas the citations and then make the renewal decision Thisdecision becomes tougher nowadays for increasing holdingnumbers of patents and the maintenance cost particularly[1] The United States Patent amp Trade Office (USPTO) datashowed that from 1976 to 2009 therewere one-third of patentsabandoned before the 20 years of legitimate term arrivedUSPTO for example sets the renewal fees at the three renewalpoints at $1600 $3600 and $7400 respectively Danguyand de la Potterie [2] estimate the impact of renewal fees onpatent maintenance rate and found that an increase of 1000Euros in renewal fees increased the abandoned rate by 12It is a patent maintenance dilemma where on the one hand

patent application is desirable for showing the performanceof RampD activities on the other hand limited resource is forpatent maintenance The key is will the patentrsquos value beworth renewingThus assessment of patent value is essentialUnfortunately patentrsquos value is rarely observable with eitherpatent transaction or technology licensing for confidentialreason involved parties are often constrained disclosingdetails particularly the price and due diligences To this endpatent citations are recognized as an indicative index whicheffectively reflects a firmrsquos values of intangible assets [3ndash5]

Nevertheless the citations regarding the fuel cell patentscollected by the present study show a puzzling situation ofpatent holderrsquos renewal decision-makings in which a handfulof holders chose to renew their patents where there wereno citations or only a small number In other words patentholders may renew patents in the light of other factors inaddition to the valueThis puzzling renewal behavior concurs

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 387491 9 pageshttpdxdoiorg1011552015387491

2 Advances in Materials Science and Engineering

with Bessen [6] where he showed that the patent citationsexplain little variance of the patent values To resolve thispuzzle we propose a rationale by adopting the perspectiveof complementary resources of technology innovation [78] to gain insights into firmsrsquo patent renewal decisionsWe postulated that firm may choose to exploit the valuesof patents either with firmrsquos own resources such as themanufacturing and marketing channels to launch productsor to gain immediate profits by licensing the technologyto others that own those complementary resources Thiscomplementary resource perspective may affect the patentrenewal decisions in the above two cases as follows

When firm owns the complementary resources its goalis to produce products for customers therefore technologyas well as the patents is for the enhancement of protectionin competitive competency Citations particularly the other-citations may indicate the adoption of owned-technology bycompetitors consequently deteriorating the competency inproduct market In other words patents that make no cita-tions may actually benefit the firm by avoiding competitionfrom others using similar technology As a result we postulatethat the firm with complementary resources would renewowned patents that make no or few citations

Upon the second case where firm does not own comple-mentary resources to gain by selling products is less likelyLicensing therefore becomes an alternative widely adoptedPer technology licensee being holdup by the technologysector is a critical problem that has to be resolved inadvance [9] To ease the holdup concern of licensee patentthat receives many other-citations could be indicative ofthe popularity and prospects of the technology in avoidingits obsolescence As a result we postulate that the firmwithout complementary resources would renew patents ifpatents receive many citations For the transaction of IPs(Intellectual Properties) such as patents on the one handas Arora and Ceccagnoli [7] pointed out that a potentiallicensee would naturally wish to verify the quality of theinvention before paying for it However once the inventordiscloses the invention the potential licensee would havelittle incentive to pay for it On the other hand licensee maybe afraid of being holdup with licensorrsquos IPs Patentrsquos value israrely observablewith either patent transaction or technologylicensing for confidential reason involved parties are oftenconstrained disclosing details particularly the price and duediligences Patent citations are recognized as an indicativeindex which effectively reflects a firmrsquos values of intangibleassets [3 5] However the patent citations regarding the fuelcell technology collected by the present study show that ahandful of patent holders choose to renew their patents wherethere are no citations or only a small number

Our study proposes a rationale by adopting the perspec-tive of complementary resources of technology innovation[7 8] to gain insights of firmsrsquo patent renewal decisions Thepresent study postulates that firms may seek to avoid themoral hazards by adopting the exploratory or exploitativestrategies which are the consequences of firmsrsquo comple-mentary resources And the imparity (gap) of firmrsquos bookand market values serves the revelation of those intentionsFirms of wider imparity hinge on exploratory strategy that

seeks wider acceptance of technology developed by otherfirms whereas firms of smaller imparity hinge on exploitativestrategy that aims to sell products rather than the technologyA key antecedence for the imparity is the complementaryassets for products production and marketing The findingimplies that firms could reveal their intentions (exploitationor exploration) by widening or narrowing the market-to-book value imparity and consequently reducing the likeli-hood of the double moral hazards

To verify our hypotheses survival analysis was performedon patent data of the fuel cell technology and the resultreveals a positive nonlinear impact of firmsrsquo market-to-book value ratio on patentrsquos legal entitlement durations Asfirmrsquos market-to-book value ratio increases patentrsquos legalentitlement duration increases firstly and downturns as themarket-to-book value ratio further increases

2 Literature Review

Compared to other information patents are often consid-ered to be a superior source for the timely recognition oftechnological changes [10] This may be attributed to thelegal protectionmechanisms that patents can induce for firmrsquosRampD investment which means patents can effectively blockrivals from competition [11] Since not all of the technologyinventors own sufficient resources to convert developedtechnologies into products for end consumption spot marketfor technology transaction as a result burgeoned in the lastdecades Nevertheless the uncertainty related to technologytransaction particularly the double moral hazard problemstated above shadows the market In the following we willreview the literature about patent valuation and move ontofirmrsquos ambidextrous strategies in realizing benefits

21 Patent Valuation and Citations Research concerninga firmrsquos RampD activities influencing market value has beenabundant in the past two decades wheremostlymotivated bythe eminent work of Griliches [12] in which adopted TobinrsquosQ to measure firmsrsquo market value with respect to patentnumber and RampD expenditure Connolly and Hirschey [13]adoptThomadakisrsquo [14] approach to show the positive impactof a patent on firm value where Thomadakis calls hisapproach the ldquorelative excess valuation (EV)rdquo defined as

Trajtenberg [5] also echoes this finding that a patentrsquosvalue positively correlates with the citation number ofpatents Besides Jaffe et alrsquos [15] survey shows that citedpatents are more valuable than patents without any citationIn addition to value patent citation considerations have alsomotivated further research into citation behavior such asCarpenter et al [3] who found that patents listed in RI100attracted twice the citations of other patents outside the listTrajtenberg [16] shows that there is a huge imparity betweenthe US and Israel by comparing patent qualities in terms ofcitations Breitzman et al [17] indicate that the patent citationcount is superior to the patent count for validating a patentrsquosquality and a firmrsquos technological competitiveness [18]

Klemperer [19] and Gilbert and Shapiro [20] forinstance introduced patent-breadth to instrument patent

Advances in Materials Science and Engineering 3

Table 1 Renewal and citation records of the fuel cell technology patents

Renewal Citations0 1 2 3 4 5ndash10 11ndash15 gt15

0 128 21 7 3 3 21 10 81 49 40 21 21 19 42 16 182 2 4 4 10 7 24 6 323 3 4 8 13 4 28 16 21

value Greene and Scotchmer [21] construct a model toexamine the impact factors of technical nonobviousness(inventive activity) and patent value disclosure Gallini [22]suggests that the difficulty of ldquoinventing aroundrdquo a patentis of importance in determining its value Not surprisinglythe evident positive correlation between patent counts andfirmrsquosmarket value renders a legitimate call for firm to engagein RampD activities From 1982 to 2002 the patent volume ofthe United States Patent amp Trade Office (USPTO) increasedalmost triple from 63381 to 184530

Nevertheless the huge quality variations among patentscall for better instrument to disentangle [23] To avoidinfringement of intelligent rights patent citations arerequired to be stated clearly upon patent application whichis also a crucial reference grant the application boundariesof patents In light of this rigorous process Hall et al [23]conjured that patent citations contain information regardingmarket evaluation on technology innovations and thus maybe helpful for weighting the imparities of quality amongpatents By comparing the patent qualities between the USand Israel Trajtenberg [16] showed that there is a hugeimparity between the two and patent value or technologyleadership is positively correlated with citations Jaffe et al[15] survey also confirmed the finding that cited patentsare more valuable than patents without any citation Inaddition Yang and Chen [24] concluded with electronicsindustry cases that weighting patents with the number ofcitations is a superior proxy for firmrsquos market value Thispatent citation approach receives tremendous attention andis furthermore refined with backward citations (being cited)[25] and forward citation (citing others) [5]

Thomas [26] indicated that while 90 of cited patentswith more than 50 citations are renewed 60 of uncitedpatents were renewed as well This means that certain strate-gic values specific to patent holders are not fully reflectedby the market evaluation Besides our data about the fuelcell technology shows the same puzzle in Table 1 Table 1reports the counts of patents with respect to their renewaland citation counts The rows show the renewal counts andthe columns depict the citations According to Table 1 therecords in the first column indicated that in our sample 128patents are not renewed and have not received any citationseither And there are 54 patents were renewed only 1sim3times received no citations respectively More than half of thepatents were renewed with citations less than 5

This puzzle motivates the present work to explore thedeterminants for patent renewal decisions Maurseth [27]found that the patents receiving high citations from across

technology field survive longer whereas the patents receivinghigh citations from the same field lapse earlier Typical firmof the type would be Valence Technology which is a batterycompany in the US that specializes in lithium-ion polymerbut owns several important patents in fuel cell technologyTypical firm of the type would be Motorola that is a well-known enterprise worldwide for its communication products(although its handset unit was divested to Google later on)and the battery is one of the major development applicationon fuel cell technology

22 Antecedents of Exploration and Exploitation The objec-tives of technology innovation are often multifold For exam-ple it may help to gain protection from imitation in light oflaws acquire necessary complementary resources enhancecapabilities in imitating rivalsrsquo technologies or pursue theleadership on the technological edges To these ends certainpatenting strategies are important and necessary for exam-ple one can gain market exclusivity to deter followers (orrivals) by patenting critical technologies or use patents togain revenues via licensing as others step into the boundariesset up by other patents or use patents as RampD performancemeasures to motivate RampD personnel [4]

To simplify understanding we will begin with a novicecondition where the market is composed of firms equippedeither with or without complementary assets such as mar-keting resources For those equipped with complementaryassets they may take invented technologies as input produc-tion factors and share the goal of selling their final productsproduct oriented firms On the other hand those whichdo not have complementary assets have no choice but tosell or license their invented technologies to generate profittechnology oriented firms For product-oriented firms dueto their revenues being gained by selling end products it isessential for them to deter any harmful imitations by theirrivals Patents are one of the most powerful instruments toachieve this end Meanwhile it is critical for leading firms toinnovate as fast as possible to shake out their followersrsquo bypassinventions As a result those leading firms with powerfulpatented technologiesmay take two patenting actions Firstlythey use patents as one of the weapons to deter followersWhen they choose a technology for patenting its goal is todefend their territory therefore knowledge-spillover bene-fiting followers due to the declaration of patent applicationsis strongly prohibited Secondly to speed up innovationit may be helpful to have knowledge diffused within anorganization Building new technology on those existing andowned technologies may help not only utilize those existing


technologies but also strengthen technology leadership Inlight of these two patenting actions the first action is likelyto cause a low score for other-cited citations and a high scorefor self-citing citations due to the second action This is whywe call the firms with these two characteristics ldquoexploitersrdquo

For technology oriented firms they generate revenue byselling or licensing Therefore it is critical to have technolo-gies that are widely recognized by industrial users that isfirms that do not have critical technologies to compete withthe leading players To this end technology oriented firmscan choose to invent and patent technologies for the reasonof solely selling or licensing them These types of firms actas an explorer for those firms that choose not to develop thetechnologies by themselves

From a strategic perspective firms make choices in linewith resources at hand That is to say firms may choose tomatch their patenting strategies with their own resourcesto optimize investment returns In the present study wehypothesize that a product oriented firm would choose toemploy the ldquoexploiterrdquo style patenting strategy to matchits resources in manufacturing and marketing whereas thetechnology oriented one would take the ldquoexplorerrdquo stylepatenting strategy to compromise the lack of resources inmanufacturing and marketing in order to achieve competi-tiveness with strong RampD capabilities

3 MethodsmdashSurvival Analysis

The studied patents are collected from a database providedby the US Patent and Trademark Office As online searchingwas made available after 1976 the present study took 1976as the initial year to conduct the patent search Up to 2001there are 2269 patents classified in the H01M 00800simH01M00824 category which is the category concerning fuel celltechnologies under the classification of the internationalpatent classification (IPC) Since the market-to-book ratiois only available for public firms and can be acquired fromthe Compustat database the 2269 data set is reduced to 1090patents owned by 93 companies Excluding those companiesholding patents without any citations the data set is further-more reduced to 70 companies for analysis

Survival analysis is a method widely used in medicalresearches such as the effects of treatment resulting in thelength of patentsrsquo life spell This method is also adopted bynumerous social studies to investigate social problems such asthe length of striking and the length of unemployment Quiteoften it is given another name as ldquoduration analysisrdquo to reflectits usage

A typical duration analysis would begin with a definitionabout the time horizon of the studied topic including thetime of origin (noted 119905

0) and the spot of the change (noted

119905

1) For the present study 119905

0is set at the moment when patent

is granted and 1199051is the moment when patent holder chooses

not to renew the patent For some cases observations areterminated due to reasons such as the end of study insteadof intended renewal decision This kind of cases is treatedas censored observations which are pervasive and usuallyunavoidable cases in the duration analysis

For duration analysis the duration function is definedas follows Let 119891(119905) be a continuous probability density ofa random available 119879 where 119905 a realization of 119879 is the rep-resentation of the duration The corresponding cumulativedistribution is given by 119865(119905) = int119905

0119891(119904)119889119904 = Pr(119879 le 119905) Then

the probability that the spell is of length of 119905 can be expressedby 119878(119905) = 1minus119865(119905) = Pr(119879 ge 119905) which is the survivor functionGiven that the life spell has lasted until 119905 the probability thatit will be terminated at the next instant time change (Δ) canbe defined as Prob(119905 le 119879 le 119905 + Δ | 119879 ge 119905) which can becharacterized by a hazard function

ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 le 119905 + Δ119905 | 119879 ge 119905)Δ119905

= limΔ119905rarr0

119865 (119905 + Δ119905) minus 119865 (119905)

Δ119905119878 (119905)

=

119891 (119905)

119878 (119905)

(1)

The hazard function specifies the instantaneous rate ofcompletion of a spell at 119879 = 119905 conditional upon survival totime 119905

Two frequently used assumptions to adjust the effects ofcovariates on the survival are accelerated failure-time (AFT)model andmultiplicative or proportional hazard (PH)modelIn the accelerated failure-time model the natural logarithmof the survival time ln(119905) is a linear function of the covariatesyielding a linear equation ln 119905

119895= 119883

119895120573 + 119885

119895 where 119883

119895is a

vector of covariates 120573 is a vector of regression coefficientsand 119885

119895is the error with density 119891(119905) The distribution of

the error term determines the regression model If 119891(119905) isa normal density function the lognormal regression modelcan be obtained Similarly if 119891(119905) is a logistic density thelog-logistic regression model is obtained If 119891(119905) is extreme-value density then the exponential and theWeibull regressionmodels result (STATA release 8)

In this paper we adopted the commonly used propor-tional hazard ratemodel (known as Cox PHmodel) in whichthe explanatory variables or covariates have a multiplicativeeffect on the hazard functionThe basic proportional hazardsregression assumes the relationship ℎ(119905) = ℎ

0(119905) exp(120573

1119909

1+

120573

2119909

2+ sdot sdot sdot +120573

119896119909

119896) where ℎ

0(119905) is the baseline hazard function

(STATA release 8)The analysis will focus on estimating the survival function119878(119905) and the hazard function ℎ(119905) using nonparametric aswell as parametric methods to fit the regression equationsParametric methods assume that survival spell follows par-ticular distributions such as Weibull lognormal and log-logistic distributions

The dependent variable of themodels is the length of legalentitlement for patent This entitlement requires periodicrenewal and along the 20 years lifespan three renewal pointsare set by the USPTO Figure 1 shows the coding for thevariable Basically each patent is assumed of 20 years of legalentitlement That is to say it survives only 20 years at mostA typical 20-year lifespan is divided into four periods as indi-cated in Figure 1 before the fourth year from the fourth yearto the eighth year from the eighth year to the twelfth yearand after the twelfth year Consequently the three renewaldecision points are around the 35th 75th and 115th year For


Patentgranted

Duration = 1

Duration = 2

Duration = 3

Duration = 4

35th75th 115th Patent

Time

Censoredfail to renew

Failure = 0Failure = 1

Failure = 0

Failure = 0

Failure = 1

Failure = 1


0

4th year 8th year 12th year 20th year

Figure 1 Patent classifications in the survival regression

the present analysis duration is coded ldquo1rdquo if it is not renewedcoded ldquo2rdquo if it is renewed only once coded ldquo3rdquo if it is renewedtwice coded ldquo4rdquo if it is renewed thrice Since duration analysisallows censored data this censorship is included with codingof the ldquofailurerdquo option The ldquofailurerdquo option is coded ldquo0rdquo ifthe patent is observed within the 20-year lifespan otherwisecoded ldquo1rdquo Observations are sorted according to the averagedMTB ratio from 2000 to 2002 The top 25 percent of theobservations are classified as persuader type firms and codedldquo1rdquo for the dummy variable ldquopersuaderrdquo The bottom 25percent firms are assigned as the defender type firms andcoded ldquo1rdquo for the dummy variable ldquodefenderrdquo Other firms arecoded ldquo0rdquo for both dummy variables

To verify our hypotheses analysis of variance (ANOVA)was performed with the following independent variables

(i) Self-Citing When applying for a patent applicanthas to state clearly the existing technologies and theliterature which the invention is based on Self-citingdepicts those cited patents that are owned by the samepatent assignee for the present case it is the companythat owns the patents

(ii) Other-CitingThis variable is similar to self-citing butwith patents that are not owned by the same assignee

(iii) Self-CitedTheUSPTOdatabase provides informationabout citations made by other following patents oncethe patents are granted A self-cited citation recodesthe number of accumulated citations of a firmrsquospatents cited in the following patents that are alsoowned by the same firms

(iv) Other-Cited This variable is similar to the self-citedvariable which recodes the accumulated cited cita-tions that are made by other patent owners

The dependent variable for ANOVAmodeling is ldquomarket-to-book value ratiordquo Market-to-book value is a ratio widelyadopted in financial analyses [28 29] for explaining businessfinancial behavior It is also attempted for the valuation ofa firmrsquos intelligent assets [28ndash32] Book value is the numbercalculated with the traditional accounting system that isthe balance sheet which records the tangible assets such

as machines and land Hence when the tangible assets arededucted from the market value the rest might most likelyreflect the value for the intangible assets For comparisonacross firms the following ratio with normalization isadopted in the present study

Market-to-book ratio =1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

market value minus book valuebook value

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(2)

4 Analysis and Results

41 Descriptive Statistics The patent data were collected bya group of experts in fuel cell technology from United StatesPatent andTrademarkOffice (USPTO) and the search engineKnowledgist was used for the identification of fuel celltechnology related patents Our data range is for the patentsbetween 1976 and 2001 thatwere granted in theUSAccordingto the IPC definition on fuel cell technology there were 2269patents during this period By matching with the Compustatdatabase of the 2269 patents 1090 patents belong to 93public companies in the US By excluding companies that donot have any citations 70 companies were used for furtheranalysis The mean citations for self-citing is 062 988 forother-citing 058 for self-cited and 600 for other-cited Themean value for the market-to-book ratio is 204

42 ANOVA Self-Citing versus Other-Cited To verify ourhypotheses regarding the patenting strategy fit (exploiter ver-sus explorer) argument we perform an analysis of varianceon self-citing and other-cited factors The results are shownin Table 2

The modeling in Table 2 attains significance at a 1 level(119865 = 416 119875 = 00092 1198772 = 01590) The ldquoself-citingrdquomain effect is not significant (119865 = 043 119875 = 05137)however the ldquoother-citedrdquo main effect is significant at a 5level (119865 = 664 119875 = 00122) The interactive effect of thetwo variables which is the primary concern of the presentstudy is significant at a 10 level (119865 = 318 119875 = 00791)A 119905-test on the two cells (explorer versus exploiter) of theinteraction effect is conducted and the derived 119905-value is 150(119875 value = 008)Themean value of the market-to-book ratio


Table 2 Analysis of the variance results for the market-to-book-ratio on self-citing and other-cited citations

Source Partial SS Df MS 119865 Prob gt 119865Model 11155 3 3718 416 00092lowastlowastlowast

Self-citing 385 1 385 043 05137Other-cited 5938 1 5938 664 00122lowastlowast

Interaction 2844 1 2844 318 00791lowast

Residual 59002 66 894Total 70157 69 1017Note lowast represents 119875 lt 01 lowastlowast represents 119875 lt 005 and lowast lowast lowast represents 119875 lt 001

Table 3 The statistical means for the market-to-book-ratio withrespect to the four situations composed of the two self-citing andother-cited citations

Other-citedHigh Low

Self-citing High 167 127 (exploiter)Low 278 (explorer) 168

for the explorer patenting style is 278 (standard deviation of103) and 127 (standard deviation of 036) for the exploiterpatenting style Table 3 shows the statistical means for thefour situations composed of the two self-citing and other-cited citations at both high and low levels respectively

43 Cases of Exploiter Style Patenting Strategy Motorola is awell-known enterprise in the US that specializes partially incommunication products such as mobile handsets For fuelcell technologyMotorola is one of the leading companies spe-cializing in portable fuel cells for mobile usage It particularlyfocuses on direct methanol fuel cells that can be employed asa power source for mobile phone handsets PDA and suchproducts Motorolarsquos fuel cell related patents attain an averageself-citing citation rate of 064 per patent (higher than thesample mean of 062) and an average other-cited citation rateof 286 per patent (lower than the sample mean of 600) Itsmarket-to-book ratio is 147 (lower than the sample mean of204) It is a typical exploiter style firm

Daimler Chrysler (DC) is a well-known Germancompany that gained its brand equity largely in luxuryautomobiles It produces more than four million automobilesyearly Concerning fuel cell technology DC is famous forits Proton-Exchange Membrane technologies It helps DC tomaintain a leading position in powering automobiles withfuel cell engines Back in 1994 DC made the first prototypefuel cell car Today the technology has been applied topublic transportation for a test run DC is also allied withUPS providing delivery vehicles for a test run in the cityof Hamburg The fuel cell patents owned by DC attain anaverage self-citing citation rate of 075 per patent (gt samplemean 062) and an average other-cited citation rate of 442(lt sample mean 600) Its market-to-book ratio is 038 (ltsample mean 204) It is another example of an exploiter stylecompany

44 Explorer Style Patenting Strategy Cases Valence Technol-ogy (VT) is a US battery company operating The companyspecializes in lithium-ion polymer that is essential formateri-als used in rechargeable batteries VT owns several importantfuel cell technology patents VT is also a research partnerin the area of backup powers for military uses for the USgovernment VT attains an average self-citing citation of 05(lt sample mean of 062) and other-cited citation of 115 (gtsample means of 600) The average market-to-book ratio is976 (gt sample mean of 204) VT is a typical model of acompany using explorer style patenting

Another case is Imperial Chemical which attains an aver-age self-citing of 0 (lt sample mean of 062) and other-cited of8 (gt samplemean of 600) Its averagemarket-to-book ratio is1066 (gt sample mean of 204) Texas Instruments also attainsan average self-citing of 0 (lt sample mean of 062) and other-cited of 7 (gt samplemeanof 600) Its averagemarket-to-bookratio is 309 (gt samplemean of 204)This is a typical exampleof an explorer style patenting company

In addition to the product market which usually pro-cesses armrsquos length transactions there exists a market fortechnology transactions in which buyerrsquos value and sellerrsquoscost are initially uncertain [33] This technology marketmay not be operated as efficiently as the product mar-ket since asymmetric information could end with seriousholdup problems between the two parties By distinguishingthe patent holders into explorers (technology-oriented) andexploiters (product-oriented) the renewal data analyses showa significant effect where firms are maintaining their patentsin the light of accrued citations and the complementaryresources that the holders owned The anomaly that patentsare renewed without or with few citations is consequentlyresolved by this differentiation Since the MTB indicator (indistinguishing explorers from exploiters) is available for firmsvia public information sources using it to evaluate the patentvalue to buyer as well as seller could significantly ameliorateasymmetric information in between and as a result improvethe market efficiency of technology transactions

Johnstone et al [34] criticized that the existing patentanalysis is short for the link between patents and the releaseof successful products An obvious reason is attributed to theneed of a bundle of patents to design and produce productsNevertheless a subtle and less addressed hindrance maybe attributed to the ineffective market for transacting needpatents among technology developers and business parties Asuccessful product would not be released unless the needed


set of technologies is systemized Our study shows that theenhancement of technology transactions may benefit fromthe recognition of firmrsquos characteristics in developing tech-nology

5 Conclusion

This paper adopts survival analysis to investigate firmrsquosdecision-making on patent renewal By holding the patentrelated information as control variables the survival regres-sion results show that patent renewal decisions are subject tofirmrsquos complementary resourcesThe result confirms our the-ory that technology-oriented firms (explorers) are less likelyto renewpatents than the product-oriented firms (exploiters)Therefore it resolves the puzzle of why patents are renewedeven without any citations The study furthermore identifiesa nonlinear relationship in inverse U shape between theMTBratio and the patent legal entitlement duration

Previous works show that patent citations are usefulinstrument to estimate a patentrsquos value In light of thoseongoing works the relationship between a firmrsquos RampD per-formance (eg the count of patents) and economic valueis explored As production factors switch from tangiblelabor land and capital inputs to intangible technology andknowledge inputs the latter have taken a large share offirmsrsquo strategic attention To compete in this new battle firmsnot only need to focus on the accumulation of strategicassets but also utilize those assets optimally Amit andSchoemaker [35] show that firms adopt RampD strategies toachieve favorable patent portfolios due to the uniquenessof the resources they own This patent portfolio helps toreduce the costs and time consumption to achieve valuableinnovation In other words the cause and effect relationshipbetween a firmrsquos value and intangible assets (eg patents) isalmost indisputable Nevertheless this understanding is farfrom appreciation in the evaluation of the contribution ofintangible assets to a firmrsquos value The present study aimsto provide a strategic perspective on how firms in the fuelcell industry implement patenting strategies in light of theircomplementary resources

Our empirical results show that fuel cell firms can exploitthe value of their RampD activities through two differentstrategies exploitation or exploration Exploitative firmschoose to deter their rivals by limiting knowledge diffusionacross firms for imitation To this end exploitative firmsmay cast heavy fixed investment on tangible assets such asland and machines to utilize the developed techniques andproduce end products to reach customers Our samples offuel cell firms in exploitative strategy indicate a mechanismfor attaining this goal via a patent consolidation of technologyportfolio with characteristics of high number of self-citingcitations and low number of other-cited citations

Exploratory firms on the other hand seek to generateprofit by technology licensing In this case it is essentialto develop technologies that have been adopted by relevant(particularly downstream) firms In the long run knowledge-spillover may be beneficial for a firm by gaining thedominant position in supplying the required technologies

Consequently these firms may try to profit by distributingdeveloped technologies with a role of technology ldquoexplo-rationrdquo a mechanism for attaining the goal by carryingpatenting characteristics of high external citations and lowself-citing ones In the light of the two (exploitation versusexploration) orientations our samples show that the gapbetween market value and book value is significantly widerfor exploratory firms than it is for the exploitative ones

It is not uncommon for wide imparities between a firmrsquosbook value andmarket value to existThis is evenmorewidelyobserved in the knowledge-based and technology intensiveindustries A common explanation about this imparity is thatthe book value merely reflects the tangible assets owned by afirm such as plants and equipment whereas themarket valueincludes not only those tangible assets but also intangibleassets such as a firmrsquos brand technologies and managementcapabilities [36ndash38]

Earlier studies have shown that the accumulation ofpatents does affect firmsrsquo value However when holding con-stant of patent number firmsrsquo value still varies at a wide differ-enceThis hints at the existence of other affects besides patentcounts Thus citations per patent are considered as weightsfor each patent Nevertheless patent owners who also play acritical role in exploiting the potentials of patents attractmin-imal attentionThe present study shows that patenting strate-gies abided by firmsrsquo complementary assets do induce differ-ent valuation concerns by both market and shareholders

For firms that hold complementary assets such as mar-keting capabilities may take a product orientation approachto generate profits by selling end products directly to buyersThe firms may strengthen their leadership in the productmarket by building a technology ldquoexploiterrdquo The exploiter isconstructed with a number of patents developed and linkedto each other These patents carry two characteristics in lowother-citied and high self-citing citations For firms that lackcomplementary assets they are likely to be limited in theirability to generate profits by selling or licensing technologiesAs a result their RampD resources may be spent on buildingleadership in technologies which would attract the attentionof firms which are short of competitive technologies tocompete in the relevant product market In other wordsthey act as technology ldquoexplorersrdquo for downstream firmsAn explorer may consider developing technologies renderedin patents with two characters in citations of high other-cited and low self-citing The two patenting strategies affect afirmrsquosmarket-to-book ratio by stretching to the two extremesOn one hand the exploiter patenting style reduces the gapbetween the market value and the book value hence themarket-to-book ratio moves toward the minimum due totangible assets dominating the ratio On the other hand theexplorer patenting style enlarges the gap hence it makes theratio move toward the maximum such that the intangibleassets become the dominator

This finding provides the following managerial impli-cations for RampD management For firms that do not holdcomplementary assets to sell their end products to buyersit is essential for them to build technologies that attractdownstream users The present study shows that to attractdownstream users they need to develop technologies that


result in patents with two citations characteristics low self-citing and high other-cited Low self-citing indicates thatthe technology is relatively independent of earlier tech-nologies which can reduce buyersrsquo concern about piracyaccusations and technology holdup The technology buyerconcern upgrading issue especially high other-cited indicatesthat the technology may have been widely adopted by theindustry

In addition this study provides an alternative perspec-tive about exploiting the information contained in patentcitations (an extension of Lin and Chenrsquos [18] framework)By dividing citation information into four dimensions self-citing other-citing self-cited and other-cited a refinedstrategic fit could be achieved in light of firmsrsquo RampDapproaches and their complementary assets resources Oneissue lacking in this study is how a strategic fit could affectfirm performance This question is difficult to answer fortwo reasons Firstly most fuel cell related products are notcommercialized yet The estimation of profits solely on fuelcell technology is subject to a large variation Secondlythe economic contribution attributed to fuel cell technologywithin a firm is unclearThis is especially true for conglomer-ates such asMotorola 3M andDupont all of which producethousands of products

There are limits of the study like first of all the datalimit By modeling the patent durations to examine thedeterminants of patent renewal in addition to the patentinformation the firm specific indicator (MTB) was the mainvariable used for our hypothesis testing Nevertheless thisindicator is incomplete for some of the private firms andtherefore was dropped from the analyses This may draw aconcern for the firms operated privately Second though weexplain patent duration using the firm characteristics (MTB)other firm level variables may be worth being included infuture study such as marketing power to better representfirmrsquos complementary resources Finally the fuel cell industrymay not be representative of other industries whichmay limitthe generalizability of the findings in the present study

Despite the limits the study reveals some interestingresults that contribute to the literature First few studies in thepatent literature discuss patent maintenance decisions whichare worthy of notice in the light of costly patent renewalfee nowadays de Rassenfosse and van Pottelsberghe de laPotterie [39] also call for an optimal fee policy via renewalfee structure from the policy making perspective The resultsof the present study imply that excluding factors of firmcharacteristics may hinder the approach of the ldquooptimalityrdquoin fee setting The information related to patents (such as thecitations) is limited in the revelation of patent value to firmsand certainly cannot justify thoroughly the motives in patentrenewal

Second since researchers regarded patent citations as animportant indicator in evaluating patent value we providea novel method to reveal patent value and patent renewalbehavior by using the firm characteristic variables whichplot a new scenario in describing firmrsquos consideration inpatent maintenance This novel method opens a gateway tolink another huge literature regarding asset specificity of thetransaction-costs economics [40]This linkagemay endeavor

the adoption of transaction-costs perspectives to deepen ourunderstanding of firmrsquos patenting strategy

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] X Jin S Spangler Y Chen et al ldquoPatent maintenance rec-ommendation with patent information network modelrdquo inProceedings of the IEEE 11th International Conference on DataMining (ICDM rsquo11) pp 280ndash289 IEEE Vancouver CandaDecember 2011

[2] J Danguy and B V P de la Potterie ldquoCost-benefit analysis of thecommunity patentrdquo Journal of Benefit-Cost Analysis vol 2 no2 pp 1ndash43 2011

[3] B Carpenter J LHart and J PMiller ldquoJump starting the patentsearch process by using subject-oriented databasesrdquo Databasevol 21 no 6 pp 20ndash23 1998

[4] B H Hall A Jaffe and M Trajtenberg ldquoMarket value andpatent citationsrdquo The RAND Journal of Economics vol 36 no1 pp 16ndash38 2005

[5] M Trajtenberg ldquoA penny for your quotes Patent citations andthe value of innovationsrdquoThe RAND Journal of Economics vol21 no 1 pp 172ndash187 1990

[6] J Bessen ldquoThe value of US patents by owner and patentcharacteristicsrdquoResearch Policy vol 37 no 5 pp 932ndash945 2008

[7] A Arora and M Ceccagnoli ldquoPatent protection complemen-tary assets and firmsrsquo incentives for technology licensingrdquoManagement Science vol 52 no 2 pp 293ndash308 2006

[8] D J Teece ldquoCapturing value from knowledge assets thenew economy markets for know-how and intangible assetsrdquoCalifornia Management Review no 3 pp 55ndash79 1998

[9] J Bessen ldquoHoldup and licensing of cumulative innovationswithprivate informationrdquo Economics Letters vol 82 no 3 pp 321ndash326 2004

[10] H Ernst ldquoPatent information for strategic technology manage-mentrdquo World Patent Information vol 25 no 3 pp 233ndash2422003

[11] W M Cohen R R Nelson and J P Walsh ldquoProtectingtheir intellectual assets appropriability conditions and whyUSmanufacturing firms patent (or not)rdquo NBERWorking Paper no7552 The National Bureau of Economic Research 2000

[12] Z Griliches ldquoMarket value RampD and patentsrdquo EconomicsLetters vol 7 no 2 pp 183ndash187 1981

[13] R A Connolly and M Hirschey ldquoMarket value and patents abayesian approachrdquo Economics Letters vol 27 no 1 pp 83ndash871988

[14] S BThomadakis ldquoA value-based test of profitability andmarketstructurerdquo Review of Economics amp Statistics vol 59 no 2 pp179ndash185 1977

[15] A B Jaffe M Trajtenberg and M S Fogarty ldquoKnowledgespillovers and patent citations evidence from a survey ofinventorsrdquo The American Economic Review vol 90 no 2 pp215ndash218 2000

[16] M Trajtenberg ldquoInnovation in Israel 1968ndash1997 a comparativeanalysis using patent datardquo Research Policy vol 30 no 3 pp363ndash389 2001


[17] A Breitzman P Thomas and M Cheney ldquoTechnologicalpowerhouse or diluted competence techniques for assessingmergers via patent analysisrdquo R amp D Management vol 32 no1 pp 1ndash10 2002

[18] B-W Lin and J-S Chen ldquoCorporate technology portfolios andRampD performance measures a study of technology intensivefirmsrdquo R amp DManagement vol 35 no 2 pp 157ndash170 2005

[19] P Klemperer ldquoHow broad should the scope of patent protectionberdquo RAND Journal of Economics vol 21 no 1 p 113 1990

[20] R Gilbert and C Shapiro ldquoOptimal patent length and breadthrdquoTheRAND Journal of Economics vol 21 no 1 pp 106ndash112 1990

[21] J R Green and S Scotchmer ldquoOn the division of profit insequential innovationrdquo RAND Journal of Economics vol 26 p20 1995

[22] N TGallini ldquoPatent policy and costly imitationrdquoRAND Journalof Economics vol 23 p 52 1992

[23] B H Hall A B Jaffe and M Trajtenberg ldquoMarket value andpatent citations a first lookrdquo NBER Working Paper no 7741National Bureau of Economic Research 2000

[24] C-H Yang and J-R Chen ldquoInnovation and market value innewly-industrialized countries the case of Taiwanese electron-ics firmsrdquo Asian Economic Journal vol 17 no 2 pp 205ndash2202003

[25] M P Carpenter M Cooper and F Narin ldquoLinkage betweenbasic research literature and patentsrdquo Research Managementvol 23 no 2 pp 30ndash35 1980

[26] P Thomas ldquoThe effect of technological impact upon patentrenewal decisionsrdquo Technology Analysis amp Strategic Manage-ment vol 11 no 2 pp 181ndash197 1999

[27] P B Maurseth ldquoLovely but dangerous the impact of patentcitations on patent renewalrdquo Economics of Innovation and NewTechnology vol 14 no 5 pp 351ndash374 2005

[28] E F Fama and K French ldquoSize and book-to-market factors inearnings and returnsrdquoThe Journal of Finance vol 50 no 1 pp131ndash155 1995

[29] E F Fama and K R French ldquoAverage returns BM and shareissuesrdquo Journal of Finance vol 63 no 6 pp 2971ndash2995 2008

[30] G Roos and J Roos ldquoMeasuring your companyrsquos intellectualperformancerdquo Long Range Planning vol 30 no 3 pp 413ndash4261997

[31] T A Stewart ldquoBrain powerrdquo Fortune vol 135 no 5 pp 104ndash1081997

[32] K-E Sveiby ldquoIntellectual capital thinking aheadrdquo CPA Aus-tralia vol 68 no 5 pp 18ndash23 1998

[33] O Hart ldquoHold-up asset ownership and reference pointsrdquoQuarterly Journal of Economics vol 124 no 1 pp 267ndash3002009

[34] N Johnstone I Hascic and D Popp ldquoRenewable energypolicies and technological innovation evidence based on patentcountsrdquo Environmental and Resource Economics vol 45 no 1pp 133ndash155 2010

[35] R Amit and P J H Schoemaker ldquoStrategic assets and organi-zational rentrdquo Strategic Management Journal vol 14 no 1 pp33ndash46 1993

[36] M E Booth and G Philip ldquoTechnology competencies andcompetitiveness the case for reconfigurable and flexible strate-giesrdquo Journal of Business Research vol 41 no 1 pp 29ndash40 1998

[37] G Hamel ldquoThe end of progressrdquo Business Strategy Review vol11 no 3 pp 69ndash78 2000

[38] Johnson ldquoMaking the most of technologyrdquo in FoodserviceEquipment amp Supplies vol 52 Reed Business Information 1999

[39] G de Rassenfosse and B van Pottelsberghe de la Potterie ldquoTherole of fees in patent systems theory and evidencerdquo Journal ofEconomic Surveys vol 27 no 4 pp 696ndash716 2013

[40] O E WilliamsonThe Economic Institutions of Capitalism FreePress New York NY USA 1985

Submit your manuscripts athttpwwwhindawicom

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CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


BioMed Research International

MaterialsJournal of


Nano

materials


Journal ofNanomaterials


with Bessen [6] where he showed that the patent citationsexplain little variance of the patent values To resolve thispuzzle we propose a rationale by adopting the perspectiveof complementary resources of technology innovation [78] to gain insights into firmsrsquo patent renewal decisionsWe postulated that firm may choose to exploit the valuesof patents either with firmrsquos own resources such as themanufacturing and marketing channels to launch productsor to gain immediate profits by licensing the technologyto others that own those complementary resources Thiscomplementary resource perspective may affect the patentrenewal decisions in the above two cases as follows

When firm owns the complementary resources its goalis to produce products for customers therefore technologyas well as the patents is for the enhancement of protectionin competitive competency Citations particularly the other-citations may indicate the adoption of owned-technology bycompetitors consequently deteriorating the competency inproduct market In other words patents that make no cita-tions may actually benefit the firm by avoiding competitionfrom others using similar technology As a result we postulatethat the firm with complementary resources would renewowned patents that make no or few citations

Upon the second case where firm does not own comple-mentary resources to gain by selling products is less likelyLicensing therefore becomes an alternative widely adoptedPer technology licensee being holdup by the technologysector is a critical problem that has to be resolved inadvance [9] To ease the holdup concern of licensee patentthat receives many other-citations could be indicative ofthe popularity and prospects of the technology in avoidingits obsolescence As a result we postulate that the firmwithout complementary resources would renew patents ifpatents receive many citations For the transaction of IPs(Intellectual Properties) such as patents on the one handas Arora and Ceccagnoli [7] pointed out that a potentiallicensee would naturally wish to verify the quality of theinvention before paying for it However once the inventordiscloses the invention the potential licensee would havelittle incentive to pay for it On the other hand licensee maybe afraid of being holdup with licensorrsquos IPs Patentrsquos value israrely observablewith either patent transaction or technologylicensing for confidential reason involved parties are oftenconstrained disclosing details particularly the price and duediligences Patent citations are recognized as an indicativeindex which effectively reflects a firmrsquos values of intangibleassets [3 5] However the patent citations regarding the fuelcell technology collected by the present study show that ahandful of patent holders choose to renew their patents wherethere are no citations or only a small number

Our study proposes a rationale by adopting the perspec-tive of complementary resources of technology innovation[7 8] to gain insights of firmsrsquo patent renewal decisions Thepresent study postulates that firms may seek to avoid themoral hazards by adopting the exploratory or exploitativestrategies which are the consequences of firmsrsquo comple-mentary resources And the imparity (gap) of firmrsquos bookand market values serves the revelation of those intentionsFirms of wider imparity hinge on exploratory strategy that

seeks wider acceptance of technology developed by otherfirms whereas firms of smaller imparity hinge on exploitativestrategy that aims to sell products rather than the technologyA key antecedence for the imparity is the complementaryassets for products production and marketing The findingimplies that firms could reveal their intentions (exploitationor exploration) by widening or narrowing the market-to-book value imparity and consequently reducing the likeli-hood of the double moral hazards

To verify our hypotheses survival analysis was performedon patent data of the fuel cell technology and the resultreveals a positive nonlinear impact of firmsrsquo market-to-book value ratio on patentrsquos legal entitlement durations Asfirmrsquos market-to-book value ratio increases patentrsquos legalentitlement duration increases firstly and downturns as themarket-to-book value ratio further increases

2 Literature Review

Compared to other information patents are often consid-ered to be a superior source for the timely recognition oftechnological changes [10] This may be attributed to thelegal protectionmechanisms that patents can induce for firmrsquosRampD investment which means patents can effectively blockrivals from competition [11] Since not all of the technologyinventors own sufficient resources to convert developedtechnologies into products for end consumption spot marketfor technology transaction as a result burgeoned in the lastdecades Nevertheless the uncertainty related to technologytransaction particularly the double moral hazard problemstated above shadows the market In the following we willreview the literature about patent valuation and move ontofirmrsquos ambidextrous strategies in realizing benefits

21 Patent Valuation and Citations Research concerninga firmrsquos RampD activities influencing market value has beenabundant in the past two decades wheremostlymotivated bythe eminent work of Griliches [12] in which adopted TobinrsquosQ to measure firmsrsquo market value with respect to patentnumber and RampD expenditure Connolly and Hirschey [13]adoptThomadakisrsquo [14] approach to show the positive impactof a patent on firm value where Thomadakis calls hisapproach the ldquorelative excess valuation (EV)rdquo defined as

Trajtenberg [5] also echoes this finding that a patentrsquosvalue positively correlates with the citation number ofpatents Besides Jaffe et alrsquos [15] survey shows that citedpatents are more valuable than patents without any citationIn addition to value patent citation considerations have alsomotivated further research into citation behavior such asCarpenter et al [3] who found that patents listed in RI100attracted twice the citations of other patents outside the listTrajtenberg [16] shows that there is a huge imparity betweenthe US and Israel by comparing patent qualities in terms ofcitations Breitzman et al [17] indicate that the patent citationcount is superior to the patent count for validating a patentrsquosquality and a firmrsquos technological competitiveness [18]

Klemperer [19] and Gilbert and Shapiro [20] forinstance introduced patent-breadth to instrument patent




0 128 21 7 3 3 21 10 81 49 40 21 21 19 42 16 182 2 4 4 10 7 24 6 323 3 4 8 13 4 28 16 21

















119905






0119891(119904)119889119904 = Pr(119879 le 119905) Then


ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 le 119905 + Δ119905 | 119879 ge 119905)Δ119905

= limΔ119905rarr0

119865 (119905 + Δ119905) minus 119865 (119905)

Δ119905119878 (119905)

=

119891 (119905)

119878 (119905)

(1)



119895= 119883

119895120573 + 119885

119895 where 119883

119895is a





0(119905) exp(120573

1119909

1+

120573

2119909


119896119909

119896) where ℎ





Patentgranted

Duration = 1

Duration = 2

Duration = 3

Duration = 4


Time



Failure = 0

Failure = 0

Failure = 1

Failure = 1


0












1003816

1003816

1003816

1003816

1003816

1003816

1003816


1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(2)












Other-citedHigh Low











5 Conclusion



















References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






0 128 21 7 3 3 21 10 81 49 40 21 21 19 42 16 182 2 4 4 10 7 24 6 323 3 4 8 13 4 28 16 21

















119905






0119891(119904)119889119904 = Pr(119879 le 119905) Then


ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 le 119905 + Δ119905 | 119879 ge 119905)Δ119905

= limΔ119905rarr0

119865 (119905 + Δ119905) minus 119865 (119905)

Δ119905119878 (119905)

=

119891 (119905)

119878 (119905)

(1)



119895= 119883

119895120573 + 119885

119895 where 119883

119895is a





0(119905) exp(120573

1119909

1+

120573

2119909


119896119909

119896) where ℎ





Patentgranted

Duration = 1

Duration = 2

Duration = 3

Duration = 4


Time



Failure = 0

Failure = 0

Failure = 1

Failure = 1


0












1003816

1003816

1003816

1003816

1003816

1003816

1003816


1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(2)












Other-citedHigh Low











5 Conclusion



















References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials












119905






0119891(119904)119889119904 = Pr(119879 le 119905) Then


ℎ (119905) = limΔ119905rarr0

Pr (119905 le 119879 le 119905 + Δ119905 | 119879 ge 119905)Δ119905

= limΔ119905rarr0

119865 (119905 + Δ119905) minus 119865 (119905)

Δ119905119878 (119905)

=

119891 (119905)

119878 (119905)

(1)



119895= 119883

119895120573 + 119885

119895 where 119883

119895is a





0(119905) exp(120573

1119909

1+

120573

2119909


119896119909

119896) where ℎ





Patentgranted

Duration = 1

Duration = 2

Duration = 3

Duration = 4


Time



Failure = 0

Failure = 0

Failure = 1

Failure = 1


0












1003816

1003816

1003816

1003816

1003816

1003816

1003816


1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(2)












Other-citedHigh Low











5 Conclusion



















References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Patentgranted

Duration = 1

Duration = 2

Duration = 3

Duration = 4


Time



Failure = 0

Failure = 0

Failure = 1

Failure = 1


0












1003816

1003816

1003816

1003816

1003816

1003816

1003816


1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

(2)












Other-citedHigh Low











5 Conclusion



















References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










Other-citedHigh Low











5 Conclusion



















References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





5 Conclusion



















References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials












References

















































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



research article a survival analysis on fuel cell technology...

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