Application of AHP and EIE in Reliability Analysis of ...

Research ArticleApplication of AHP and EIE in Reliability Analysis ofComplex Production Lines Systems

Guo-cheng Niu 12 YifanWang1 Zhen Hu 1 Qingxu Zhao1 and Dong-mei Hu 2

1College of Electronic Information Engineering Changchun University of Science and Technology Changchun Jilin Province China2School of Electrical And Information Engineering Beihua University Jilin Jilin Province China

Correspondence should be addressed to Zhen Hu zhucusteducn

Received 5 November 2018 Revised 10 February 2019 Accepted 20 February 2019 Published 10 March 2019

Academic Editor Elena Zaitseva

Copyright copy 2019 Guo-chengNiu et alThis 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

It is necessary to grasp the operation state of the production system for scientific scheduling process improvement fault analysisequipment maintenance or replacement The matter-element information entropy is proposed to evaluate the health index of theproduct line and the parameter self-optimization support vector machine is used to predict the future health index A new type ofthree-dimensional cross compound element is established by synthesizing the operation state of equipment energy consumptionproduction efficiency and human factors The subjective objective and joint weights are determined by the analytic hierarchyprocess (AHP) method entropy and the combination weighting method respectively The health index is calculated by complexelement correlation entropy The calculations of the beer filling production line show that the combined weighting method is aneffective method on the health index calculation and can accurately reflect the actual operation state of the production Supportvector machine (SVM) optimized by multiparameters is established to predict the health index the simulation shows that LeastSquares Support Vector Machine (LSSVM) based on radial basis function (RBF) has prominent prediction effect It can provideaccurate data support for the production and management of enterprises

1 Introduction

In recent years the organizational reliability analysis of theproduction system the human reliability analysis and thesystem reliability analysis under the dynamic environmenthave become one of the most concerned hot issues in theindustrial engineering and other scientific circles [1]

Health index is one of the main indexes to measurethe reliability of the system Health assessment refers torelying on advanced testing methods combining reliableand effective assessment methods using complete operationdata to analyze predict and judge thus it can effectivelyimprove the system maintenance support capability andreduce maintenance costs and save spare parts [2 3] Theresearch of its evaluation method is mainly concentratedon two directions one is system modeling and analysisHowever the modeling of the system is difficult and theadaptability of the method is not strongThe other is the data-drivenmethodThemethod is flexible and adaptable with the

maturity of machine learning and statistical analysis meth-ods data-driven method becomes the mainstream algorithmfor system health assessment [4 5]

Reddy proposed a stochastic fuzzy reliability analysismethod which effectively improved the overall system reli-ability of mining production system [6] Soualhi et alproposed an artificial ant colony clustering method to classifythe degraded state of HMM By using the adaptive fuzzyneural method the determination of the degenerate stateof the bearing and the prediction of the remaining life arerealized [7] Dong et al proposed a hidden semi-Markovmodel (HSMM) to predict the residual life of deterioratingequipment This method only obtains the expected value ofresidual life and is not used to analyze and apply in thehealth management of equipment [8] Yu Shui proposed anovel approach by combining the extreme value momentmethod and the improved maximum entropy method whichcan efficiently estimate the time-variant reliability account-ing for multiple failure modes and temporal parameters at

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 7238785 10 pageshttpsdoiorg10115520197238785

2 Mathematical Problems in Engineering

Identify the reference variables and the evaluation indicators

Establish the evaluation of three-dimensional cross elements of production

line efficiency by using AHP

Step 1

Establish the parameter self-seeking support vector machineprediction model

Step 2

Step 3

Step 4

Establish the model of complex element stereo crossover

evaluation by information entropy

Calculate the Subjective Weights by using AHP

Calculate the objective weights by using information entropy

Calculate the joint weights by using maximum information entropy

Calculate the real time health indexes

Pretreat the historical health Indexes

Verify the health indexes prediction modelStep 5

Figure 1 The flowchart of health calculation and prediction for beer filling production line

the same time In the same year [9] he also proposed amethod based on fault process decomposition to improvecomputational efficiency and ensure computational accuracy[10] Li Fangyi proposed a sequential sampling methodbased on the hybrid model of probability and convex setto solve the reliability-based design optimization problem[11] Qiu Na proposed the simple uncertainty quantificationmethod is for numerical uncertainty (noise) and surro-gate model uncertainty (error) in the optimization process[12]

Beer filling production is the main link of beer produc-tion The system has the characteristics of large scale multi-equipment high energy consumption and complex couplingrelations so the line reliability is difficult to be guaranteed Atpresent the key performance indicator (KPI) is commonlyused to evaluate the efficiency of filling production line Therules of this method are simple the adaptability is not strong[13 14]

Combining the energy consumption real time outputrawmaterial consumption alcohol loss and key performanceindex (KPI) in beer filling production the three-dimensionalcross compound element is established The quantitativecalculation of the health index of the filling production lineis designed by AHP combined weights and the compoundmatter-element correlation entropy

According to historical health index LSSVM is adapted tomodel and predict the future health index of the productionline thus a new method of the overall evaluation of theoperation of the line is formed to predict the future health

index of the line The detailed calculation flowchart is shownin Figure 1

2 Theoretical Calculation of Health Index

In this section we illuminate the details of using AHP toestablish the compound matter-element model of the beerfilling production line and calculate the theoretical weightsof the health index

21 Problem Statement AHP is a method that makes useof less amount of information and makes the decision-making process digitized It is suitable for the situationwhich is artificial qualitative judgment of its subjective roleand measures the results directly and accurately it has thecharacteristics practicability systematicness simplicity andso on [15ndash19] So a compound element model of beer fillingproduction line is established by AHP and the theoreticalweights of each decision index affecting the health index arecalculated

22 Establishment of Compound Matter-Element HierarchicalStructure Model The compound matter-element hierarchi-cal structure model reflects the interrelationship between thetarget level the standard layer and the decision level Thetarget layer is the health index of the beer filling productionline the standard layer consists of energy consumption indexproductivity index and KPI and the decision layer consists

Mathematical Problems in Engineering 3

of beer consumption unit energy consumption unit timecapacity unit time raw material consumption total assetutilization wool production rate total equipment utilizationand line efficiency

23 Construction of Judgment Matrix In the AHP methodthe target layer weight matrix A and the index layer weightmatrix B are established The square root method is used tocalculate the maximum feature value 120582max of the judgmentmatrix Its corresponding normalized eigenvector 119882 = (12059611205962 sdot sdot sdot 120596119899)119879 and 119860119882 = 120582max119882 The judgment matrix of thetarget layer and the criterion layer are calculated by the samemethod

24 Consistency Test (a) Calculate the consistency index119862119868119862119868 = (120582max minus 119899)(119899 minus 1) In the formula n is the order ofthe judgment matrix

(b) Calculate the average random consistency index 119877119868(c) Calculate the conformance ratio 119862119877119862119877 = 119862119868119877119868 If 119862119877 le 01 it is considered that the

consistency of the judgment matrix is acceptable

25 Calculation of Influence Weight of the Target LayerCalculate the weight of each layer that is the impact weightof the scheme layer on the target layer

1205961015840 = 119882119862 times119882119860 (1)

where 119882119862 = [1205961198621 1205961198622 sdot sdot sdot 120596119862119899 ] is the eigenvector ofeach decision parameter119882119860 = [1205961198601 1205961198602 sdot sdot sdot 120596119860119899]119879 is the ei-genvector of the target layer

3 Information Entropy andJoint Weights of Stereoscopic CrossCompound Matter Element

Theldquoentropyrdquo is ameasurement to systemic confusion extentwhich can objectively reflect the utility value of systeminformation [20] For the various decision data of the beerfilling production line at different time the compoundmatterelement is set up and the objective weights of the health indexare calculated by using the maximum discrete entropy of thecompound matter element

31 Establishment of the Stereoscopic Cross Compound Ele-ment Matrix 119877119898119899 is the stereoscopic cross composite ele-ment matrix with mlowastn

119877119898119899 =[[[[[[[[[[

1198721 1198722 sdot sdot sdot 1198721198981198621 11990911 11990912 sdot sdot sdot 11990911198981198622 11990921 11990922 sdot sdot sdot 1199092119898 d

119862119899 1199091198991 1199091198992 sdot sdot sdot 119909119899119898

]]]]]]]]]]

(2)

119872119894 is the 119894-th operation state of filling production line 119862119895is the 119895-th evaluation index of the stereoscopic cross scheme

119909119894119895 is the corresponding 119895-th index value of the 119894-th operationstate

32 Standardization of the Stereoscopic Cross Matter ElementIt is necessary to standardize the evaluation index Formula(3) will be used to standardize the one who has the propellingeffect on the evaluation index Formula (4) will be used tostandardize the one who can weaken the evaluation index

120575119894119895 = (119909119894119895 minusmin1le119894le119899119909119894119895)(max1le119894le119899119909119894119895 minus 119909119894119895) (119894 = 1 2 sdot sdot sdot 119899 119895 isin 119869+) (3)

120575119894119895 = (max1le119894le119899119909119894119895 minus 119909119894119895)(max1le119894le119899119909119894119895 minusmin1le119894le119899119909119894119895)

(119894 = 1 2 sdot sdot sdot 119899 119895 isin 119869minus)(4)

After standardized the stereoscopic cross matter elementis set up as 119877119898119899 it is shown in formula (5)

119877119898119899 =[[[[[[[[[[


119862119899 1205751198991 1205751198992 sdot sdot sdot 120575119899119898

]]]]]]]]]]

(5)

33 Determination of Correlation Function and Weights Coef-ficient of Evaluation Indexes for Interchange Schemes Theweights of evaluation index directly affect the evaluationresults and the objective weights coefficients of each indexare determined by correlation entropy method Firstly thecorrelation function 119910119895 = max1le119894le119898120575119894119895 (119895 = 1 2 sdot sdot sdot 119899)is determined and the ideal reference series is 119884 =11991011199102 sdot sdot sdot119910119899 According to the maximum discrete entropytheory [21] the entropy is maximum when the occurrenceprobability of each symbol is equal and the value is 119867max =ln 119899The correlation function of the first index of the complexelement is shown in formula (6)

120577119894119895 = min119894min11989510038161003816100381610038161003816120575119894119895 minus 11991011989510038161003816100381610038161003816 + 05max119894max119895

10038161003816100381610038161003816120575119894119895 minus 1199101198951003816100381610038161003816100381610038161003816100381610038161003816120575119894119895 minus 11991011989510038161003816100381610038161003816 + 05max119894max11989510038161003816100381610038161003816120575119894119895 minus 11991011989510038161003816100381610038161003816 (6)

The entropy values of the j-third index of the stereoscopiccross are

119865119895 = 119870 119898sum119894

119891119894119895ln119891119894119895 (7)

In formula (7) 119870 = minus(119867max)minus1 = minus(ln119899)minus1 119891119894119895 =120577119894119895sum119898119894=1 120577119894119895 119895 = 1 2 sdot sdot sdot 119899 119865119895 isin [0 1]The weight coefficient of the index 119888119895 is shown as follows

12059610158401015840 = 119890119895sum119899119895=1 119890119895 (8)

The deviation degree of entropy value is shown as follows

119890119895 = 1 minus 119865119895 (9)


34 Determination of the Joint Weights Considering theshortcomings of the subjective and objective weights thejoint weights are determined by the combined empowermentmethod and theweights of theAHPmethod and informationentropy are integrated with the additive integration methodThe formula is shown as follows

120596119895 = 12057212059610158401015840119895 + (1 minus 120572) 1205961015840119895 (10)

where 12059610158401015840119895 is the objective weight of the j index calculatedbyAHP1205961015840119895 is the subjective weight of the j index calculated byAHP 120596119895 is the joint weight of the j index calculated by AHPand 120572 is the undetermined coefficient calculated by formula(11)

120572 = 1119899 minus 1119866119860119867119875 (11)

where 119866119860119867119875 is the difference coefficient of each index inAHP

119866119860119867119875 = 2119899 (11199011 + 21199012 + sdot sdot sdot + 119899119901119899) 119899 + 1119899 (12)

where 11990111199012 sdot sdot sdot 119901119899 are the ascending sorting values ofsubjective weight 1205961015840119895 (see the values in Table 2) in AHP nis the number of indexes The weight matrix of evaluationindexes is shown as follows

119877120596119895 = [ 1198621 1198622 sdot sdot sdot 119862119899120596119895 1205961 1205962 sdot sdot sdot 120596119899] (13)

35 Calculation of Health Index The compound correlationentropy matter element 119877

119867119894based on the comprehensive eval-

uation of M beer filling production line can be constructedby formulas (5)-(11)

119877119867119894= [ 1198721 1198722 sdot sdot sdot 119872119894 sdot sdot sdot 119872119898119867119894 1198671 1198672 sdot sdot sdot 119867119894 sdot sdot sdot 119867119898] (14)

119867119894 = minus 119899sum119895=1

119875 (120596119895120575119894119895) ln119875 (120596119895120575119894119895) (15)

119875 (120596119895120575119894119895) = 120596119895120575119894119895 [[119899sum119895=1

120596119895120575119894119895]]minus1

119894 = 1 2 sdot sdot sdot119898 119895 = 1 2 sdot sdot sdot 119899(16)

From the definition of entropy the bigger the entropy isthe better operation state of the production line is Thereforesort the health index of the beer filling production lineaccording to the entropy value According to the sort situationcombined with the demand of production reasonably andscientifically arrange the production schedulingThismethodprovides theoretical and data support for production linemaintenance and technological improvement

4 Health Index Calibration and Analysis

41 Experimental Data In order to scientifically and compre-hensively assess the operation state of beer filling productionlines in addition to taking into account traditional keyperformance indicators KPI (total asset utilization rate lineargross yield rate total equipment utilization rate and lineefficiency) the experimental data also include unit beerconsumption unit energy consumption unit time produc-tion capacity and unit raw material consumption Energyconsumption alcohol loss production and raw materialsconsumption data come from the energy metering manage-ment system KPI data come from the filling shop controlsystem All data are collected in the filling workshop of ChinaResources Snow Beer Tonghua Co Ltd The first line offilling production line works for 19 days in June 10 days inNovember 23 days in June and 12 days in November 2016The line 1 is the old one and the line 3 is the new one Thenormalized KPI data coming from beer filling productionlines are shown in Figure 2

42 Experiments Based onTheories 1 and 2 and Data Analysis

421 Composite Element Structure of Beer Filling ProductionLines Using AHP to establish a three-dimensional crosscomplex element for evaluating the health status of beerfilling production lines the target layer A is the health indexof beer filling production lines the standard layer is theindexes affecting the health index such as energy consump-tion (B1) capacity (B2) and KPI (B3) The decision layerincludes beer consumption (C1) unit energy consumption(C2) unit time production capacity (C3) unit time rawmaterial consumption (C4) and KPI(C5-C8) The structureand interrelationships are shown in Figure 3

According to the incidence relation between differentlevels of the hierarchical structure model the 1-9 scalingmethod [22] is used to construct the AHP weight matrixesof the target layer matrix A and the index layer matrixesB1 B2 and B3 The value of each element in the matrixrefers to the method of material accounting heat accountingand parameter weight relation reflected by KPI calculationformula after calculation the matrix is shown in formulas(17)-(20)

119860 =[[[[[[[[

119860 1198611 1198612 11986131198611 1 12 121198612 2 1 121198613 2 2 1

]]]]]]]]

(17)

1198611 = [[[[

1198611 1198621 11986221198621 1 121198622 2 1

]]]]

(18)

1198612 = [[[[[

1198612 1198623 11986241198623 1 31198624 13 1

]]]]]

(19)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Date (Day)

(a) Production data of line 1 in June 2016

000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11Date (Day)

(b) Production data of line 1 in November 2016

0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Date (Day)

020

040

060

080

100

120

Norm

alized

(c) Production data of line 3 in June 2016

0 1 2 3 4 5 6 7 8 9 10 11 12 13Date (Day)

000

020

040

060

080

100

120

Norm

alized

(d) Production data of line 3 in November 2016

Figure 2 KPI data coming from beer filling production lines (i) Beer consumption (C1) (ii) unit energy consumption (C2) (iii) unit timeproduction capacity (C3) (iv) unit time raw material consumption (C4) (v) total asset utilization rate (C5) (vi) linear gross yield rate (C6)(vii) total equipment utilization rate (C7) (viii) line efficiency (C8)

Energyconsumption

Healthindex(A)

capacity

KPITotal equipment utilization

Target layerStandard layer

unit time raw material

Decision layer

(1)

(2)

(3)

beer consumption(1)

unit energy consumption(2)

Unit time capacity(3)

consumption(4)

Total asset utilization rate(5)

Line hair production rate(6)

rate(7)

Line efficiency(8)

Figure 3 Structure diagram of complex elements

1198613 =[[[[[[[[[[[[[

1198613 1198625 1198626 1198627 11986281198625 1 23 12 251198626 32 1 12 131198627 2 2 1 121198628 52 3 2 1

]]]]]]]]]]]]]

(20)

The consistency check is carried out for each judgmentmatrix The RI value is 112 The average random consistencyindex obtained after calculating 1000 times is shown inTable 1

The CR value which is the result of the total level ofsorting is far less than 01 with satisfactory consistency

422 Calculation of AHP Weights Through the calculationof the hierarchical single sorting and hierarchical total


Table 1 Consistency verification each parameter value

Judgment matrix 120582max CI RI CRA 3054 00268 112 0024B1 2 0 112 0B2 2 0 112 0B3 4054 0017 112 0015

Table 2 Theoretical weight calculations

Index Weights Sub indexes Relativeweights 1205961015840

B1 01958 C1 03333 00653C2 06667 01305

B2 03108 C3 075 02331C4 025 00777

B3 04934

C5 01358 0067C6 01584 00782C7 02651 01308C8 04407 02174

ordering of the matrix the AHP weight 1205961015840 can be calculatedthe calculations are shown in Table 2

423 Calculation of Information Entropy Weights and JointWeights Using test data from different production lines eachmonth to build composite element matrix 119877119898119899 in 8 decisionindicators alcohol loss energy consumption and materialconsumption per unit time are low the higher the efficiencythe higher the other variables but the other variables arehigh so the energy consumption alcohol loss and unitconsumption are standardized by formula (3) and othervariables are standardized by formula (4) The deviation 119890119895and weight 12059610158401015840119895 for each evaluation indicator are calculatedby formulas (7) (8) and (9) the calculations are shown inTable 3

The joint weight 120596119895 for each evaluation indicator iscalculated by formulas (10) (11) and (12) the calculations areshown in Table 4

43 Calculation and Sorting of Health Index For the oldand new production lines based on the data collected andcalculated in Sections 3 and 4 when the objective weights andjoint weights respectively and the health index are calculatedby formula (15) and (16) the calculations are shown in Figures4ndash7

From Figures 4 5 6 and 7 the trend of health indexcalculated under subjective objective and joint weights is thesame the change trend of the health index curves calculatedunder the objective weights is eased and it indicates thatthere is little difference in information state in a short timeThe health index curves calculated under subjective weightschange dramatically it indicates that subjective weights pref-erence trends to certain evaluation indicators Small changesin relevant evaluation indicators lead to drastic changes inhealth index The joint weight synthesizes the advantages of

Subjective health indexObjective health indexJoint health

0 2 4 6 8Time (Day)

10 12 14 16 18 200

05

1

15

2

25

3

Hea

lth In

dex

1

Figure 4 Health index curves of line 1 in June 16


2 3 4 5 6 7 8 9 101Health Index1

0

05

1

15

2

25Ti

me (

Day

)

Figure 5 Health index curves of line 1 in November 16

subjectivity and objectivity and not only reflects the changeof objective information but also reflects the fluctuationof expertsrsquo preferences which increases the reliability ofhealth assessment and reflects the change of production lineoperation more accuratelyThe average monthly health indexof each filling production line is shown in Table 5

In actual production under the same month the newproduction line has less output downtime less wine lossgood thermal insulation and less energy consumption sothe production efficiency is better than the old one June isthe peak season for production The equipment has a longcontinuous running time high ambient temperature goodKPI parameters low energy consumption and high produc-tion efficiency November is an off-season and production isintermittent So the production line is healthier in June than


Table 3 Weights of each evaluation indicator

Evaluationindicators

Production Line1 June

Production Line1 November



119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207

Table 4 Joint weights of each evaluation indicator

evaluationindicators

120596 (AHP) Production Line1 June




1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035


5 10 15 20 250Health Index1

0

05

1

15

2

25

Tim

e (D

ay)


in November From Table 5 it is shown the average healthindex of the calculation of the method is consistent with theactual situation which proves that the scheme is reasonableand accurate and the health index is quantified which has acertain practical reference value


2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)


5 Health Index Prediction

51 Forecast Modeling Method In practical applicationspredicting the future health index of production lines is more


Table 5 Average monthly health index

production line Line 1 Line 3month June Nov June NovAverage health index 1926 1802 1943 1872

2

Original DataGASVMPSOSVMLSSVM

Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

205

Figure 8 Health index training set fitting curves

valuable for production schedule and equipment mainte-nance [23ndash27] According to the data of 65 samples calculatedin Section 43 25 samples are taken as the testing set and 40samples are used as the training set the input to the LSSVM istimeday and the output is the health index by the MATLAB7110 development software using the LSSVM lab toolboxdeveloped by K Pelekmans JAK and Suykens to establishan optimal model

For the same training set the regression model is estab-lished by using LSSVM optimized by Grid-search with crossvalidation and epsilon-SVM algorithm optimized by geneticalgorithm and particle swarm algorithm these are abbrevi-ated as LSSVM GASVM and PSOSSVM respectively Thedecision function 119891(119909) = sum119899119894=1119882119894119870(119909 119909119894) + 119887 is lookedas the final health index expression where Wi are supportvector coefficients 119909119894 are support vectors 119909 are the inspectedsamples n is the number of support vectors b is constantand119870(119909 119909119894) is a scalar radial basis kernel function computedas 119870(119909 119909119894) = exp(minus119892119909 minus 1199091198942)(119892 gt 0) The fitting curve isshown in Figure 8 The testing set validation curve is shownin Figure 9

52 Comparison of Performance of Three Modeling MethodsThe best prediction model for the health index of the beerfilling production line should be one with high fitting degreethe best correlation coefficient and the least prediction errorThe performances (c119892 1205902 120574 Train-MSE Train-R Test-MSETest-R) of the three modeling methods are shown in Table 6c and g are the penalty parameter and the span coefficientof RBF function in SVM 1205902and 120574 are the kernel parameter

Hea

lth In

dex

1

GASVMPSOSVMLSSVMOriginal Data

5 10 15 20 25 300Time (Day)

182

184

186

188

19

192

194

196

198

2

Figure 9 Health index testing set regression curves

Table 6 Performances comparison

Performance GASVM PSOSVM LSSVM

Optimal parameters c= 135401 c= 157359 1205902= 05875119892 = 13132 119892 =15760 120574 = 34367Train-MSE 00093 00107 00094Train-R 09396 09398 09506Test-MSE 00131 00129 00106Test-R 09210 09152 09227TIME 9718s 1757s 0037s

and the normalized parameter in LSSVM and Train-MSEandTrain-R are the error and correlation coefficient in fittingTest-MSE and Test-R are the error and correlation coefficientwhen testing is verified

From Table 6 in the GASVM model the fitting errorand correlation coefficient are 000939396 the predictederror and correlation coefficient are 001319210 and in thePSOSVM model the fitting error and correlation coefficientare 001079398 respectively The forecast error and corre-lation coefficient are 001299152 The prediction effect inthe LSSVM model is better the fitting error and correlationcoefficient are 000949506 respectively and the predictederror and correlation coefficient are 001069227 whichcan meet the needs of the production line health indexprediction

6 Conclusion

Aiming at the problem of health index evaluation and predic-tion of complex production lines a new data mining methodbased on extension matter-element entropy and supportvector machine is designed A newmethod for evaluating thehealth of the beer filling production line is put forward which


integrates energy utilization rawmaterial consumption pro-duction efficiency beer loss and equipment operation stateAHP and matter-element information entropy are used todetermine subjective and objective weights the combinationweighting method is used to calculate joint weights whichimproves the reliability of information entropy weightsQuantitative calculations of the health index are consistentwith the actual qualitative analysis results Using the opti-mized support vector machine algorithm to construct thehealth index prediction model the experiment proves thatthe health index calculation is reasonable and the forecastaccuracy is satisfactory This method provides data supportfor beer filling process improvement equipment overhauland production scheduling

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This work is supported by the National 973 Project (no613225) National Natural Science Foundation Project (no91338116) and Jilin Provincial Department of EducationldquoThirteen Five Yearsrdquo Science and Technology Project (no20180338KJ)

References

[1] A Hess and L Fila ldquoThe Joint Strike Fighter (JSF) PHMconcept Potential impact on aging aircraft problemsrdquo in Pro-ceedings of the 2002 IEEE Aerospace Conference vol 36 pp3021ndash3026 Nyack NY USA March 2002

[2] B Lin D Song and L He ldquoComplex system health assessmentbased on Mahalanobis distance and bin-width estimation tech-niquerdquoChinese Journal of Scientific Instrument vol 37 no 9 pp2022ndash2028 2016

[3] N Thanthry and R Pendse ldquoAircraft health management net-work A user interfacerdquo IEEE Aerospace and Electronic SystemsMagazine vol 24 no 7 pp 4ndash9 2009

[4] Y Peng and D Liu ldquoData-driven prognostics and healthmanagement A review of recent advancesrdquo Chinese Journal ofScientific Instrument vol 35 no 3 pp 481ndash495 2014

[5] D A Tobon-Mejia K Medjaher N Zerhouni and G TripotldquoA data-driven failure prognostics method based on mixtureof gaussians hidden markov modelsrdquo IEEE Transactions onReliability vol 61 no 2 pp 491ndash503 2012

[6] J P A Ioannidis and J Lau ldquoEvidence on interventions toreduce medical errors An overview and recommendations forfuture researchrdquo Journal of General Internal Medicine vol 16no 5 pp 325ndash334 2001

[7] A Soualhi H Razik G Clerc and D D Doan ldquoPrognosis ofbearing failures using hidden markov models and the adaptive

neuro-fuzzy inference systemrdquo IEEE Transactions on IndustrialElectronics vol 61 no 6 pp 2864ndash2874 2014

[8] M Dong and Y Peng ldquoEquipment PHM using non-stationarysegmental hidden semi-Markov modelrdquo Robotics andComputer-Integrated Manufacturing vol 27 no 3 pp 581ndash5902011

[9] S Yu Z Wang and D Meng ldquoTime-variant reliability assess-ment for multiple failure modes and temporal parametersrdquoStructural andMultidisciplinary Optimization vol 58 no 4 pp1705ndash1717 2018

[10] S Yu and Z Wang ldquoA novel time-variant reliability analysismethod based on failure processes decomposition for dynamicuncertain structuresrdquo Journal of Mechanical Design vol 140 no5 Article ID 051401- 1-11 2018

[11] F Li J Liu G Wen and J Rong ldquoExtending SORA methodfor reliability-based design optimization using probability andconvex set mixed modelsrdquo Structural and MultidisciplinaryOptimization vol 31 no 8 pp 1ndash17 2018

[12] NQiu YGao J Fang G SunQ Li andNHKim ldquoCrashwor-thiness optimization with uncertainty from surrogate modeland numerical errorrdquo Thin-Walled Structures vol 129 pp 457ndash472 2018

[13] X Feng W Liu and C Yan ldquoIntelligent evaluation systemof filling packaging production linersquos efficiencyrdquo Light IndustryMachinery vol 34 no 3 pp 97ndash102 2016

[14] B Liu HWang andW Fan ldquoReal-time health level assessmentfor complex production line systembased on big datardquoTsinghuaScience amp Technology vol 54 no 10 pp 1377ndash1383 2014

[15] F-S Kong J Wang and H-G Sun ldquoFuzzy comprehensiveevaluation of equipment usability of engine cylinder blockproduction line based on AHPrdquo Journal of Jilin University(Engineering Edition) vol 38 no 6 pp 1332ndash1336 2008

[16] Z Zhang and L Chen ldquoAnalysis on decision-making modelof plan evaluation based on grey relation projection andcombination weight algorithmrdquo Journal of Systems Engineeringand Electronics vol 29 no 4 pp 789ndash796 2018

[17] J Xu J Wang K Zhu P Zhang and Y Ma ldquoCredit index mea-surement method for Android application security based onAHPrdquo Journal of Tsinghua University (Science and Technology)vol 58 no 2 pp 131ndash136 2018

[18] X Xu Q Huang Y Ren and X Liu ldquoDetermination of indexweights in suspension bridge condition assessment based ongroup-AHPrdquo Journal of Hunan University (Natural Sciences)vol 45 no 3 pp 122ndash128 2018

[19] N Guo-Cheng H Zhen and H Dongmei ldquoApplication ofmatter element information entropy and svm in lithium batteryefficiency evaluation and predictionrdquo in Proceedings of the 201810th International Conference on Modelling Identification andControl (ICMIC) pp 1-1 July 2018

[20] K Alvehag and L Soder ldquoRisk-based method for distributionsystem reliability investment decisions under performance-based regulationrdquo IETGeneration Transmission ampDistributionvol 5 no 10 pp 1062ndash1072 2011

[21] C Jiang W Liu and J Zhang ldquoRisk assessment of generationand transmission systems considering wind power penetra-tionrdquo Transactions of China Electrotechnicalociety vol 29 no2 pp 260ndash270 2014

[22] S Lahmiri and M Boukadoum ldquoBiomedical image denoisingusing variational mode decompositionrdquo in Proceedings of the10th IEEE Biomedical Circuits and Systems Conference BioCAS2014 vol 36 pp 340ndash343 Lausanne SwitzerlandOctober 2014


[23] D Hu L Song and G Niu ldquoNew method to measure phaseretardation of wave plates based on SVMrdquo Chinese Journal ofScientific Instrument vol 37 no 7 pp 1517ndash1523 2016

[24] Y Zhang Z Cheng and Z Xu ldquoApplication of optimizedparameters SVMbased on photo acoustic spectroscopymethodin fault diagnosis of power transformer spectroscopy andspectral analysisrdquo Spectroscopy and Spectral Analysis vol 35 no1 pp 10ndash12 2015

[25] D Hu Q Liu L Yu and Y Zhu ldquoLCVR phase retardationcharacteristic calibration method using the LSSVM modelrdquoInfrared and Laser Engineering vol 45 no 5 Article ID0517004-1-0517004-5 2016

[26] M Gu Y Chen and X Wang ldquoMulti-index modeling forsimilarity-based residual life estimation based on real-timehealth degreerdquoComputer IntegratedManufacturing Systems vol23 no 2 pp 362ndash372 2017

[27] Y Zhang X Xu G Sun X Lai and Q Li ldquoNondeterministicoptimization of tapered sandwich column for crashworthinessrdquoThin-Walled Structures vol 122 pp 193ndash207 2018

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


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International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


Identify the reference variables and the evaluation indicators

Establish the evaluation of three-dimensional cross elements of production

line efficiency by using AHP

Step 1

Establish the parameter self-seeking support vector machineprediction model

Step 2

Step 3

Step 4

Establish the model of complex element stereo crossover

evaluation by information entropy

Calculate the Subjective Weights by using AHP

Calculate the objective weights by using information entropy

Calculate the joint weights by using maximum information entropy

Calculate the real time health indexes

Pretreat the historical health Indexes

Verify the health indexes prediction modelStep 5

Figure 1 The flowchart of health calculation and prediction for beer filling production line

the same time In the same year [9] he also proposed amethod based on fault process decomposition to improvecomputational efficiency and ensure computational accuracy[10] Li Fangyi proposed a sequential sampling methodbased on the hybrid model of probability and convex setto solve the reliability-based design optimization problem[11] Qiu Na proposed the simple uncertainty quantificationmethod is for numerical uncertainty (noise) and surro-gate model uncertainty (error) in the optimization process[12]

Beer filling production is the main link of beer produc-tion The system has the characteristics of large scale multi-equipment high energy consumption and complex couplingrelations so the line reliability is difficult to be guaranteed Atpresent the key performance indicator (KPI) is commonlyused to evaluate the efficiency of filling production line Therules of this method are simple the adaptability is not strong[13 14]

Combining the energy consumption real time outputrawmaterial consumption alcohol loss and key performanceindex (KPI) in beer filling production the three-dimensionalcross compound element is established The quantitativecalculation of the health index of the filling production lineis designed by AHP combined weights and the compoundmatter-element correlation entropy

According to historical health index LSSVM is adapted tomodel and predict the future health index of the productionline thus a new method of the overall evaluation of theoperation of the line is formed to predict the future health

index of the line The detailed calculation flowchart is shownin Figure 1

2 Theoretical Calculation of Health Index

In this section we illuminate the details of using AHP toestablish the compound matter-element model of the beerfilling production line and calculate the theoretical weightsof the health index

21 Problem Statement AHP is a method that makes useof less amount of information and makes the decision-making process digitized It is suitable for the situationwhich is artificial qualitative judgment of its subjective roleand measures the results directly and accurately it has thecharacteristics practicability systematicness simplicity andso on [15ndash19] So a compound element model of beer fillingproduction line is established by AHP and the theoreticalweights of each decision index affecting the health index arecalculated

22 Establishment of Compound Matter-Element HierarchicalStructure Model The compound matter-element hierarchi-cal structure model reflects the interrelationship between thetarget level the standard layer and the decision level Thetarget layer is the health index of the beer filling productionline the standard layer consists of energy consumption indexproductivity index and KPI and the decision layer consists








1205961015840 = 119882119862 times119882119860 (1)





119877119898119899 =[[[[[[[[[[


119862119899 1199091198991 1199091198992 sdot sdot sdot 119909119899119898

]]]]]]]]]]

(2)








119877119898119899 =[[[[[[[[[[


119862119899 1205751198991 1205751198992 sdot sdot sdot 120575119899119898

]]]]]]]]]]

(5)





119865119895 = 119870 119898sum119894

119891119894119895ln119891119894119895 (7)


12059610158401015840 = 119890119895sum119899119895=1 119890119895 (8)


119890119895 = 1 minus 119865119895 (9)



120596119895 = 12057212059610158401015840119895 + (1 minus 120572) 1205961015840119895 (10)


120572 = 1119899 minus 1119866119860119867119875 (11)


119866119860119867119875 = 2119899 (11199011 + 21199012 + sdot sdot sdot + 119899119901119899) 119899 + 1119899 (12)







119867119894 = minus 119899sum119895=1

119875 (120596119895120575119894119895) ln119875 (120596119895120575119894119895) (15)

119875 (120596119895120575119894119895) = 120596119895120575119894119895 [[119899sum119895=1

120596119895120575119894119895]]minus1








119860 =[[[[[[[[

119860 1198611 1198612 11986131198611 1 12 121198612 2 1 121198613 2 2 1

]]]]]]]]

(17)

1198611 = [[[[

1198611 1198621 11986221198621 1 121198622 2 1

]]]]

(18)

1198612 = [[[[[

1198612 1198623 11986241198623 1 31198624 13 1

]]]]]

(19)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Date (Day)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11Date (Day)


0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Date (Day)

020

040

060

080

100

120

Norm

alized


0 1 2 3 4 5 6 7 8 9 10 11 12 13Date (Day)

000

020

040

060

080

100

120

Norm

alized



Energyconsumption

Healthindex(A)

capacity




Decision layer

(1)

(2)

(3)

beer consumption(1)



consumption(4)



rate(7)

Line efficiency(8)


1198613 =[[[[[[[[[[[[[

1198613 1198625 1198626 1198627 11986281198625 1 23 12 251198626 32 1 12 131198627 2 2 1 121198628 52 3 2 1

]]]]]]]]]]]]]

(20)









B1 01958 C1 03333 00653C2 06667 01305

B2 03108 C3 075 02331C4 025 00777

B3 04934

C5 01358 0067C6 01584 00782C7 02651 01308C8 04407 02174







0 2 4 6 8Time (Day)

10 12 14 16 18 200

05

1

15

2

25

3

Hea

lth In

dex

1



2 3 4 5 6 7 8 9 101Health Index1

0

05

1

15

2

25Ti

me (

Day

)











119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207







1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035



0

05

1

15

2

25

Tim

e (D

ay)




2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)







2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

205





Hea

lth In

dex

1


5 10 15 20 25 300Time (Day)

182

184

186

188

19

192

194

196

198

2







6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018















1205961015840 = 119882119862 times119882119860 (1)





119877119898119899 =[[[[[[[[[[


119862119899 1199091198991 1199091198992 sdot sdot sdot 119909119899119898

]]]]]]]]]]

(2)








119877119898119899 =[[[[[[[[[[


119862119899 1205751198991 1205751198992 sdot sdot sdot 120575119899119898

]]]]]]]]]]

(5)





119865119895 = 119870 119898sum119894

119891119894119895ln119891119894119895 (7)


12059610158401015840 = 119890119895sum119899119895=1 119890119895 (8)


119890119895 = 1 minus 119865119895 (9)



120596119895 = 12057212059610158401015840119895 + (1 minus 120572) 1205961015840119895 (10)


120572 = 1119899 minus 1119866119860119867119875 (11)


119866119860119867119875 = 2119899 (11199011 + 21199012 + sdot sdot sdot + 119899119901119899) 119899 + 1119899 (12)







119867119894 = minus 119899sum119895=1

119875 (120596119895120575119894119895) ln119875 (120596119895120575119894119895) (15)

119875 (120596119895120575119894119895) = 120596119895120575119894119895 [[119899sum119895=1

120596119895120575119894119895]]minus1








119860 =[[[[[[[[

119860 1198611 1198612 11986131198611 1 12 121198612 2 1 121198613 2 2 1

]]]]]]]]

(17)

1198611 = [[[[

1198611 1198621 11986221198621 1 121198622 2 1

]]]]

(18)

1198612 = [[[[[

1198612 1198623 11986241198623 1 31198624 13 1

]]]]]

(19)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Date (Day)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11Date (Day)


0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Date (Day)

020

040

060

080

100

120

Norm

alized


0 1 2 3 4 5 6 7 8 9 10 11 12 13Date (Day)

000

020

040

060

080

100

120

Norm

alized



Energyconsumption

Healthindex(A)

capacity




Decision layer

(1)

(2)

(3)

beer consumption(1)



consumption(4)



rate(7)

Line efficiency(8)


1198613 =[[[[[[[[[[[[[

1198613 1198625 1198626 1198627 11986281198625 1 23 12 251198626 32 1 12 131198627 2 2 1 121198628 52 3 2 1

]]]]]]]]]]]]]

(20)









B1 01958 C1 03333 00653C2 06667 01305

B2 03108 C3 075 02331C4 025 00777

B3 04934

C5 01358 0067C6 01584 00782C7 02651 01308C8 04407 02174







0 2 4 6 8Time (Day)

10 12 14 16 18 200

05

1

15

2

25

3

Hea

lth In

dex

1



2 3 4 5 6 7 8 9 101Health Index1

0

05

1

15

2

25Ti

me (

Day

)











119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207







1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035



0

05

1

15

2

25

Tim

e (D

ay)




2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)







2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

205





Hea

lth In

dex

1


5 10 15 20 25 300Time (Day)

182

184

186

188

19

192

194

196

198

2







6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018










120596119895 = 12057212059610158401015840119895 + (1 minus 120572) 1205961015840119895 (10)


120572 = 1119899 minus 1119866119860119867119875 (11)


119866119860119867119875 = 2119899 (11199011 + 21199012 + sdot sdot sdot + 119899119901119899) 119899 + 1119899 (12)







119867119894 = minus 119899sum119895=1

119875 (120596119895120575119894119895) ln119875 (120596119895120575119894119895) (15)

119875 (120596119895120575119894119895) = 120596119895120575119894119895 [[119899sum119895=1

120596119895120575119894119895]]minus1








119860 =[[[[[[[[

119860 1198611 1198612 11986131198611 1 12 121198612 2 1 121198613 2 2 1

]]]]]]]]

(17)

1198611 = [[[[

1198611 1198621 11986221198621 1 121198622 2 1

]]]]

(18)

1198612 = [[[[[

1198612 1198623 11986241198623 1 31198624 13 1

]]]]]

(19)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Date (Day)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11Date (Day)


0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Date (Day)

020

040

060

080

100

120

Norm

alized


0 1 2 3 4 5 6 7 8 9 10 11 12 13Date (Day)

000

020

040

060

080

100

120

Norm

alized



Energyconsumption

Healthindex(A)

capacity




Decision layer

(1)

(2)

(3)

beer consumption(1)



consumption(4)



rate(7)

Line efficiency(8)


1198613 =[[[[[[[[[[[[[

1198613 1198625 1198626 1198627 11986281198625 1 23 12 251198626 32 1 12 131198627 2 2 1 121198628 52 3 2 1

]]]]]]]]]]]]]

(20)









B1 01958 C1 03333 00653C2 06667 01305

B2 03108 C3 075 02331C4 025 00777

B3 04934

C5 01358 0067C6 01584 00782C7 02651 01308C8 04407 02174







0 2 4 6 8Time (Day)

10 12 14 16 18 200

05

1

15

2

25

3

Hea

lth In

dex

1



2 3 4 5 6 7 8 9 101Health Index1

0

05

1

15

2

25Ti

me (

Day

)











119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207







1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035



0

05

1

15

2

25

Tim

e (D

ay)




2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)







2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

205





Hea

lth In

dex

1


5 10 15 20 25 300Time (Day)

182

184

186

188

19

192

194

196

198

2







6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018









000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Date (Day)


000

020

040

060

080

100

120

Norm

alized

0 1 2 3 4 5 6 7 8 9 10 11Date (Day)


0000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Date (Day)

020

040

060

080

100

120

Norm

alized


0 1 2 3 4 5 6 7 8 9 10 11 12 13Date (Day)

000

020

040

060

080

100

120

Norm

alized



Energyconsumption

Healthindex(A)

capacity




Decision layer

(1)

(2)

(3)

beer consumption(1)



consumption(4)



rate(7)

Line efficiency(8)


1198613 =[[[[[[[[[[[[[

1198613 1198625 1198626 1198627 11986281198625 1 23 12 251198626 32 1 12 131198627 2 2 1 121198628 52 3 2 1

]]]]]]]]]]]]]

(20)









B1 01958 C1 03333 00653C2 06667 01305

B2 03108 C3 075 02331C4 025 00777

B3 04934

C5 01358 0067C6 01584 00782C7 02651 01308C8 04407 02174







0 2 4 6 8Time (Day)

10 12 14 16 18 200

05

1

15

2

25

3

Hea

lth In

dex

1



2 3 4 5 6 7 8 9 101Health Index1

0

05

1

15

2

25Ti

me (

Day

)











119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207







1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035



0

05

1

15

2

25

Tim

e (D

ay)




2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)







2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

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Hea

lth In

dex

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5 10 15 20 25 300Time (Day)

182

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6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018













B1 01958 C1 03333 00653C2 06667 01305

B2 03108 C3 075 02331C4 025 00777

B3 04934

C5 01358 0067C6 01584 00782C7 02651 01308C8 04407 02174







0 2 4 6 8Time (Day)

10 12 14 16 18 200

05

1

15

2

25

3

Hea

lth In

dex

1



2 3 4 5 6 7 8 9 101Health Index1

0

05

1

15

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25Ti

me (

Day

)











119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207







1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035



0

05

1

15

2

25

Tim

e (D

ay)




2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)







2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

205





Hea

lth In

dex

1


5 10 15 20 25 300Time (Day)

182

184

186

188

19

192

194

196

198

2







6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018















119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840 119890119895 12059610158401015840C1 0416 01278 01067 01446 05078 01271 01818 01274C2 0412 01265 00993 01346 05 01251 01848 01295C3 0412 01267 01051 014236 05042 01262 01897 01329C4 0406 01248 00863 011696 05018 01256 01825 01279C5 0402 01235 00858 011626 04964 01242 01825 01207C6 0402 01236 00854 01157 04963 01242 01825 01203C7 0402 01235 0085 01152 04954 0124 01825 01205C8 0402 01236 00845 01145 04938 01236 01825 01207







1205961015840 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895 12059610158401015840 120596119895C1 01645 01278 01461 01446 01545 01271 01458 01274 01459C2 03289 01265 02275 01346 02315 01251 02268 01295 02290C3 02331 01267 01798 01424 01876 01262 01795 01329 01829C4 00777 01248 01013 0117 00974 01256 01017 01279 01029C5 00266 01235 00752 01163 00716 01242 00755 01207 00738C6 0031 01236 00774 01157 00734 01242 00777 01203 00758C7 00519 01235 00878 01152 00836 0124 00880 01205 00863C8 00863 01236 01050 01145 01004 01236 01050 01207 01035



0

05

1

15

2

25

Tim

e (D

ay)




2 3 4 5 6 7 8 9 10 11 121Health Index1

0

05

1

15

2

25

Tim

e (D

ay)







2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

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195

205





Hea

lth In

dex

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5 10 15 20 25 300Time (Day)

182

184

186

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198

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6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018











2


Hea

lth In

dex

1

5 10 15 20 25 30 350Time (Day)

18

185

19

195

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Hea

lth In

dex

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5 10 15 20 25 300Time (Day)

182

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2







6 Conclusion




Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018










Data Availability




Acknowledgments


References





































Journal of












Journal of







Volume 2018






Volume 2018





















Journal of












Journal of







Volume 2018






Volume 2018








Application of AHP and EIE in Reliability Analysis of ...

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Transcript of Application of AHP and EIE in Reliability Analysis of ...