ORIGINAL ARTICLE

Simultaneous optimization of multiple performancecharacteristics of carbonitrided pellets: a case study

Boby John

Received: 28 April 2010 /Accepted: 7 November 2011 /Published online: 26 November 2011# Springer-Verlag London Limited 2011

Abstract The performance of a product is generallycharacterized by more than one response variable. Hence,the management often faces the problem of simultaneousoptimization of many response variables. In recent years, alot of literature has been published on various methodolo-gies for tackling the multi-response optimization problems.Among them, the approach based on Taguchi’s quality lossfunction is very popular. This paper discusses a case studyon multiple response optimization in carbonitriding process.The surface hardness, case depth, and dimensional variationof carbonitrided pellets were simultaneously optimizedusing quality loss function methodology. The optimumobtained through loss function approach was found to besuperior to the ones obtained through optimizing theresponse variables separately. The result obtained throughthe implementation of the solution is also presented in thestudy.

Keywords Multiple response optimization . Quality lossfunction . Design of experiments . Analysis of variance .

Powder metallurgy . Carbonitriding

1 Introduction

Almost all manufactured products will have severalperformance characteristics. These response variables aregenerally correlated and may be measured in different units.

An example of a process with multiple response variables isa heat-treatment process like carbonitriding. The surfacehardness, case depth, dimensional variation, etc., of carbon-itrided products is critical to the customer application.These response variables or quality characteristics areusually controlled by a common set of independentparameters or factors. Hence, the management oftenencounters the problem of identifying the best values ofthese control parameters, which would simultaneouslyoptimize the response variables.

One of the popular approaches for simultaneous optimi-zation of multiple response variables is based on quadraticquality loss function proposed by Taguchi [1]. Detaileddiscussion on application of Taguchi method in multi-response optimization can be found in Logothetis andHaigh [2], Tong et al. [3] and Maghsoodloo and Chang [4].Reddy et al. [5] presented a case study in the Indian plasticindustry based on Taguchi’s methodology for multi-response optimization. While Tong and Su [6] suggestedoptimization of multiple quality characteristics using fuzzymultiple attribute decision-making, Wu [7] proposed simul-taneous optimization of several response variables based onpercentage reduction of Taguchi’s quality loss. This paperdiscusses a case study dealing with the problem of multipleresponse optimization. We used Taguchi’s loss functionapproach to simultaneously optimize the surface hardness,case depth and dimensional variations of carbonitridedpellets.

The reminder of this paper is arranged as follows: inSection 2, a brief description of carbonitriding process ispresented. Section 3 explains the Taguchi’s loss functionapproach. In Section 4, we describe the experimentationand analysis details of the case study. In Section 5, theresult obtained through the implementation of the solutionis presented and the paper concludes with Section 6.

B. John (*)SQC & OR Unit, Indian Statistical Institute,8th Mile, Mysore Road,Bangalore, Karnataka State, India 560 059e-mail: boby@isibang.ac.in

Int J Adv Manuf Technol (2012) 61:585–594DOI 10.1007/s00170-011-3751-2

2 Carbonitriding process

The powder metallurgy technique is a relatively cost-effective and simple way to produce parts with good wearresistance and better mechanical properties. Carbonitridinghas become the most popular process for surface hardeningof pellets. In carbonitriding, ammonia is added to thefurnace atmosphere of endo gas and hydrocarbon. Theammonia dissociates at the metallic surface and atomicnitrogen is formed, which will diffuse into the materialalong with carbon. The nitrogen not only increases thesurface hardness but also stabilizes the austenilite and thusincreases the hardenability of sintered steel.

Usually, the customer would specify the target values of thesurface hardness and case depth of the carbonitrided pellets.These targets would vary from customer to customer based onthe application of the pellets. Hence, the management mustknow the effect of various input/process parameters (likesoaking time, temperature, green density, etc.) of carbon-itriding process on the heat-treated properties of the pellets.Therefore, this study was undertaken to identify the significantparameters influencing the surface hardness and case depth ofcarbonitrided pellets using design of experiments. Moreover,dimensional changes were observed on carbonitrided parts.Hence, this study also aimed at minimizing the dimensionalvariation of pellets during carbonitriding. The simultaneousoptimization of the response variables (surface hardness, casedepth, and dimensional variation) was achieved usingTaguchi’s loss function methodology.

3 Quality loss function approach

Taguchi methods provide lasting solutions to complexproblems and engineers and other applied users tend to findthese techniques more practical and easier to implement in theindustrial workplace [8]. Taguchi method is a powerful toolwhen the process is affected by a number of parameters andusing this approach the entire parameter space can be studiedwith minimum number of experiments [9]. Moreover, lots ofsuccessful applications of Taguchi methods were reported inthe past [10–20]. Hence, Taguchi’s quality loss functionapproach was used in this study for simultaneous optimiza-tion of multiple response variables.

In loss function approach, the loss value for eachresponse is calculated based on the deviation from therespective targets. The general form of quality loss functionproposed by Taguchi [21] is

lðyÞ ¼ kðy� TÞ2 ð1Þwhere y is the quality characteristic or response variable, Tis the target, and k is a proportionality constant namelyquality loss coefficient. The value of k needs to be chosen

based on economical considerations. An alternate approachis to choose k as

k ¼ 2

USL � LSL

� �2

ð2Þ

where USL is upper specification limit and LSL is thelower specification limit of the response variable. So,whenever the response variable y is at the specificationlimits (either USL or LSL), loss function l(y) becomes 1and whenever y goes beyond the specification limits, l(y) isgreater than 1. When the response falls within the toleranceinterval but not on the target, the corresponding loss will liebetween 0 and 1. The loss function with k calculated usingEq. 2 is called standardized quality loss function.

The class of quality loss functions is defined for three typesof response variables, namely nominal the best (NTB), smallerthe better (STB), and larger the better (LTB). Let y1, y2,…,ynbe the n observations of response variable y, then theexpected quality loss l(y) is defined using Eq. 1 as

lðyÞ ¼

1

nkXni¼1

yi � Tð Þ2 for NTB

1

nkXni¼1

y2i for STB

1

nkXni¼1

1

y2ifor LTB

8>>>>>>>>><>>>>>>>>>:

ð3Þ

For STB and LTB cases also, the value k can be chosensuch way that the whenever the response is on thespecification limit, the corresponding loss becomes 1.

After calculating the expected loss for each responsevariable using Eq. 3, the overall expected loss is calculatedas the average of the expected losses of the responsevariables. Let y1, y2,…,yp be the p response variables withexpected losses l(y1), l(y2),…,l(yp), then the overallexpected loss is computed as

LðyÞ ¼ 1

p

Xpi¼1

lðyiÞ ð4Þ

Table 1 Factors with levels

SL no. Factor name Code Levels

1 2 3

1. Soaking time (min) A 30 60 90

2. Temperature (°C) B 820 840 860

3. Green density (g/cm3) C 6.7 6.9 7.1

4. Material D Fe FeCCua Distb

a FeCCU=Fe+0.3 C+1.5 CubDist=Fe+1.5 CU+0.5Mo+1.75 Ni

586 Int J Adv Manuf Technol (2012) 61:585–594

Finally, the combination of factors, which gives aminimum overall expected loss L(y) is chosen as theoptimum combination.

4 Experimentation and analysis

Through brainstorming, four parameters influencing theheat-treated properties of pellets were identified. Accord-ingly, an experiment was designed with four factors namelysoaking time (A), temperature (B), green density (C) and

the material (D). Three levels were chosen for each factor.The factors with the chosen levels are given in Table 1. Toconduct a full-factor experiment with four factors each atthree levels would require 81 experiments, which was notfeasible due to the cost and time constraints. Moreover, thetechnical and production professionals suggested that onlythe interaction between soaking time and temperature (A×B) and that between soaking time and green density (A×C)might have some impact on response variables. Hence, itwas decided to conduct only 27 experiments and L27 waschosen as the experimental plan. Kindly refer to Phadke[22] for more details on designing experiments usingorthogonal arrays. The surface hardness (in HRC), casedepth (in millimeters) and dimensional variations (inmicrometers) were taken as the responses for the experi-ments. The responses surface hardness and case depth werenominal the better type (NTB) and dimensional variationwas smaller the better type (STB). The response variableswith target, k and relevant specification limits are given inTable 2. The value of k was calculated using the Eq. 2 for

Table 3 Experimental layout with response values

Exp no Soaking time Temperature Green density Material Surface hardness Case depth Dimensional variation

1 30 820 6.7 Fe 420 435 0.55 0.5 0.157 0.157

2 30 820 6.9 FeCCu 458 420 0.5 0.55 0.423 0.431

3 30 820 7.1 Dist 544 544 0.25 0.2 0.126 0.126

4 30 840 6.7 FeCCu 441 427 0.8 0.85 0.448 0.464

5 30 840 6.9 Dist 456 458 0.4 0.35 0.102 0.118

6 30 840 7.1 Fe 557 561 0.25 0.2 0.126 0.118

7 30 860 6.7 Dist 483 471 0.95 0.9 0.126 0.126

8 30 860 6.9 Fe 487 556 0.75 0.7 0.165 0.173

9 30 860 7.1 FeCCu 511 559 0.45 0.35 0.407 0.391

10 60 820 6.7 Fe 464 480 0.55 0.6 0.157 0.173

11 60 820 6.9 FeCCu 460 454 0.4 0.35 0.423 0.431

12 60 820 7.1 Dist 544 513 0.35 0.3 0.126 0.118

13 60 840 6.7 FeCCu 435 435 0.85 0.9 0.446 0.438

14 60 840 6.9 Dist 455 452 0.55 0.55 0.102 0.102

15 60 840 7.1 Fe 549 573 0.35 0.3 0.11 0.125

16 60 860 6.7 Dist 459 450 0.6 0.55 0.126 0.118

17 60 860 6.9 Fe 487 556 0.55 0.55 0.173 0.157

18 60 860 7.1 FeCCu 528 559 0.45 0.4 0.399 0.43

19 90 820 6.7 Fe 463 487 0.65 0.6 0.157 0.157

20 90 820 6.9 FeCCu 467 498 0.45 0.4 0.43 0.414

21 90 820 7.1 Dist 538 536 0.35 0.35 0.126 0.126

22 90 840 6.7 FeCCu 476 455 1 1.05 0.437 0.445

23 90 840 6.9 Dist 450 459 0.85 0.9 0.11 0.102

24 90 840 7.1 Fe 549 572 0.7 0.7 0.11 0.11

25 90 860 6.7 Dist 555 540 1 1 0.141 0.133

26 90 860 6.9 Fe 513 490 0.85 0.8 0.172 0.157

27 90 860 7.1 FeCCu 444 455 0.55 0.6 0.411 0.403

Table 2 Responses with specification

SL no Response LSL USL Target k

1. Surface hardness 400 600 500 0.0001

2. Case depth 0.1 0.9 0.5 6.25

3. Dimensional variation – 0.4 0.0 6.25

Int J Adv Manuf Technol (2012) 61:585–594 587

the responses surface hardness and case depth. Fordimensional variation, k was calculated using Eq. 5.

k ¼ 1

USL2 ð5Þ

The Eq. 5 ensured that the loss becomes 1 when thedimensional variation was at USL. The experiments wereconducted as per the plan and data were collected for all the27 experiments. The experimental layout with responsevalues is given in Table 3.

The responses were individually subjected to analysis ofvariance to identify the significant main effects andinteractions. More details on analysis of variance can befound in Montgomery [23]. The ANOVA table for the

response surface hardness is given in Table 4. The ANOVAtable revealed that while the factors green density (C) andmaterial (D) and the interaction soaking time×green density(A×C) were significant at 5% level (p value<0.05), thefactor temperature (B) was significant at 10% level (p value<0.1). The residual plots for the response surface hardnessare given in Fig. 1. Figure 1 revealed that the residuals areapproximately normally distributed. Similarly, theresponses case depth and dimensional variation were alsosubjected to analysis of variance. But the residual plots ofboth case depth and dimensional variation revealed that theresiduals were not normally distributed. Whenever thenormality assumption on residuals was violated [24], onehas to use non-parametric methods or transformations. Inthis study, the author used the approach based on trans-

Residual

Per

cen

t

50250-25-50

99

90

50

10

1

Fitted Value

Res

idu

al

560520480440400

50

25

0

-25

-50

Residual

Fre

qu

ency

40200-20-40

10.0

7.5

5.0

2.5

0.0

Observation Order

Res

idu

al

50454035302520151051

50

25

0

-25

-50

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for Surface Hardness

Fig. 1 Residual plots for surface hardness

Table 4 ANOVA table forsurface hardness Source DF SS MS F P

Soaking time 2 710 355 0.42 0.663

Temperature 2 4847.4 2423.7 2.8 0.070

Green density 2 50948.1 25474.1 29.83 0.000

Material 2 14444 7222 8.5 0.000

Soaking time × temperature 4 2487.2 621.8 0.73 0.578

Soaking time × green density 4 11573.7 2893.4 3.39 0.019

Error 37 31594.1 853.9

Total 53 116604.6

588 Int J Adv Manuf Technol (2012) 61:585–594

formations. Through trial and error, the best transformationsfor the responses case depth and dimensional variation wereidentified as

Case depthtransformed ¼ 1

Case depthð6Þ

Dimensional variationtransformed ¼ ðDimensional variationÞ2ð7Þ

The ANOVA table for transformed case depth is given inTable 5 and that of transformed dimensional variation isgiven in Table 6. The ANOVA table of case depth (Table 5)revealed that the factors soaking time (A), temperature (B),green density (C), material (D) and the interactions soakingtime×temperature (A×B) and soaking time×green density(A×C) were significant (p value<0.05). The ANOVA tableof dimensional variation (Table 6) revealed that only thefactors green density (C) and material (D) were significant(p value<0.05). The residual plots of transformed responsevariables case depth and dimensional variation are given inFigs. 2 and 3, respectively. Figures 2 and 3 revealed that theresiduals were normally distributed.

After identifying the significant factor effects andinteraction effects on the response variables, the expectedvalues of the response variables were estimated for all thepossible 81 combination of factor levels (81 combinations

are possible with four factors each having three levels). Theexpected response for all these combination can beestimated as the sum of overall mean and the contributingeffects of significant factors and interactions. More detailson estimating the expected response values based onsignificant factor and interactions, kindly refer to Peace[8]. Afterwards, these expected values were transformedinto corresponding expected losses using Eq. 3 and finallythe overall expected loss was computed using Eq. 4) for allthe 81 combinations. The results are given in Table 7.

From Table 7, the optimum combination with minimumoverall expected loss of 0.0027 was identified as A2B3C2D1

(combination number 49 in Table 7). The estimated surfacehardness, case depth and dimensional variation values forthe optimum combination were 493.444, 0.5190, and0.1506 which were close to the respective targets of 500,0.5, and 0.00.

The optimum combination obtained through loss func-tion method was compared with the best combinationobtained through optimizing each response separately. Theoptimum combinations were identified as the ones close tothe respective targets from Table 7. The comparison resultsare shown in Table 8. Table 8 showed that optimizingsurface hardness alone would give a surface hardnessalmost on target but would result in case depth going outof the specification limits and a dimensional variation of0.1727 not very close to target. More or less same problemswere found with the best combinations arrived using

Table 6 ANOVA table fordimensional variation Source DF SS MS F P

Soaking time 2 0.000022 0.000011 0.15 0.862

Temperature 2 0.000239 0.00012 1.6 0.216

Green density 2 0.002167 0.001084 14.48 0.000

Material 2 0.321758 0.160879 2149.09 0.000

Soaking time × temperature 4 0.000149 0.000037 0.5 0.737

Soaking time × green density 4 0.000084 0.000021 0.28 0.889

Error 37 0.00277 0.000075

Total 53 0.327189

Table 5 ANOVA table for casedepth Source DF SS MS F P

Soaking time 2 6.3866 3.1933 24.26 0.00

Temperature 2 6.8051 3.4025 25.85 0.00

Green density 2 21.6368 10.8184 82.2 0.00

Material 2 1.0054 0.5027 3.82 0.03

Soaking time × temperature 4 3.4746 0.8686 6.6 0.00

Soaking time × green density 4 5.0756 1.2689 9.64 0.00

Error 37 4.8696 0.1316

Total 53 49.2537

Int J Adv Manuf Technol (2012) 61:585–594 589

optimizing case depth alone or dimensional variation alone.But the simultaneous optimization of surface hardness, case

depth and dimensional variation using loss function gave acompromise solution of surface hardness equal to 493.44,

Residual

Per

cen

t

0.020.010.00-0.01-0.02

99

90

50

10

1

Fitted Value

Res

idu

al

0.200.150.100.050.00

0.02

0.01

0.00

-0.01

-0.02

Residual

Fre

qu

ency

0.0160.0080.000-0.008-0.016

20

15

10

5

0

Observation Order

Res

idu

al

50454035302520151051

0.02

0.01

0.00

-0.01

-0.02

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for SQ(D_M)

Fig. 3 Residual plots for dimensional variation

Residual

Per

cen

t

0.80.40.0-0.4-0.8

99

90

50

10

1

Fitted Value

Res

idu

al

4321

0.8

0.4

0.0

-0.4

-0.8

Residual

Fre

qu

ency

0.60.40.20.0-0.2-0.4-0.6

10.0

7.5

5.0

2.5

0.0

Observation Order

Res

idu

al50454035302520151051

0.8

0.4

0.0

-0.4

-0.8

Normal Probability Plot of the Residuals Residuals Versus the Fitted Values

Histogram of the Residuals Residuals Versus the Order of the Data

Residual Plots for 1/Case_Depth

Fig. 2 Residual plots for case depth

590 Int J Adv Manuf Technol (2012) 61:585–594

Table 7 Estimated responses and overall expected loss for all possible 81 combinations

Exp no Soaking time Temperature Green density Material Surface hardness Case depth Dimensional variation Expected loss

1 30 820 6.7 Fe 430.167 0.4394 0.1727 0.1643

2 30 820 6.7 FeCCu 390.333 0.4808 0.4353 0.4110

3 30 820 6.7 Dist 413.944 0.4146 0.1483 0.2484

4 30 820 6.9 Fe 467.611 0.2964 0.1506 0.0384

5 30 820 6.9 FeCCu 427.778 0.3147 0.4270 0.1854

6 30 820 6.9 Dist 451.389 0.2849 0.1218 0.0820

7 30 820 7.1 Fe 600 0.1602 0.1197 0.3403

8 30 820 7.1 FeCCu 560.167 0.1653 0.4172 0.1359

9 30 820 7.1 Dist 583.778 0.1567 0.0806 0.2406

10 30 840 6.7 Fe 432.111 0.4347 0.1727 0.1554

11 30 840 6.7 FeCCu 392.278 0.4752 0.4353 0.3969

12 30 840 6.7 Dist 415.889 0.4104 0.1483 0.2374

13 30 840 6.9 Fe 469.556 0.2942 0.1506 0.0344

14 30 840 6.9 FeCCu 429.722 0.3123 0.4270 0.1762

15 30 840 6.9 Dist 453.333 0.2829 0.1218 0.0759

16 30 840 7.1 Fe 601.944 0.1595 0.1197 0.3534

17 30 840 7.1 FeCCu 562.111 0.1647 0.4172 0.1439

18 30 840 7.1 Dist 585.722 0.1561 0.0806 0.2516

19 30 860 6.7 Fe 451.167 0.8543 0.1727 0.0878

20 30 860 6.7 FeCCu 411.333 1.0262 0.4353 0.2869

21 30 860 6.7 Dist 434.944 0.7652 0.1483 0.1460

22 30 860 6.9 Fe 488.611 0.4408 0.1506 0.0057

23 30 860 6.9 FeCCu 448.778 0.4825 0.4270 0.0972

24 30 860 6.9 Dist 472.389 0.4158 0.1218 0.0266

25 30 860 7.1 Fe 621 0.1946 0.1197 0.4938

26 30 860 7.1 FeCCu 581.167 0.2023 0.4172 0.2336

27 30 860 7.1 Dist 604.778 0.1896 0.0806 0.3714

28 60 820 6.7 Fe 437.833 0.7215 0.1727 0.1330

29 60 820 6.7 FeCCu 398 0.8404 0.4353 0.3631

30 60 820 6.7 Dist 421.611 0.6569 0.1483 0.2073

31 60 820 6.9 Fe 472.444 0.4068 0.1506 0.0270

32 60 820 6.9 FeCCu 432.611 0.4421 0.4270 0.1613

33 60 820 6.9 Dist 456.222 0.3854 0.1218 0.0654

34 60 820 7.1 Fe 598.333 0.2371 0.1197 0.3268

35 60 820 7.1 FeCCu 558.5 0.2487 0.4172 0.1267

36 60 820 7.1 Dist 582.111 0.2297 0.0806 0.2290

37 60 840 6.7 Fe 439.778 1.1114 0.1727 0.1424

38 60 840 6.7 FeCCu 399.944 1.4212 0.4353 0.3891

39 60 840 6.7 Dist 423.556 0.9652 0.1483 0.2075

40 60 840 6.9 Fe 474.389 0.5071 0.1506 0.0231

41 60 840 6.9 FeCCu 434.556 0.5631 0.4270 0.1527

42 60 840 6.9 Dist 458.167 0.4743 0.1218 0.0592

43 60 840 7.1 Fe 600.278 0.2681 0.1197 0.3388

44 60 840 7.1 FeCCu 560.444 0.2829 0.4172 0.1336

45 60 840 7.1 Dist 584.056 0.2586 0.0806 0.2390

46 60 860 6.7 Fe 458.833 1.1702 0.1727 0.0820

47 60 860 6.7 FeCCu 419 1.5187 0.4353 0.2842

48 60 860 6.7 Dist 442.611 1.0092 0.1483 0.1248

49 60 860 6.9 Fe 493.444 0.5190 0.1506 0.0027

Int J Adv Manuf Technol (2012) 61:585–594 591

case depth equal to 0.51901, and dimensional variationof 0.1506 reasonably close to the respective targets of500, 0.5, and 0. Hence, it was decided to implement theoptimum combination arrived through loss functionapproach.

5 Implementation of Solution

A pilot lot of ten pellets were carbonitrided with theoptimum combination of factors and the responsevariables surface hardness, case depth and dimensional

Table 7 (continued)

Exp no Soaking time Temperature Green density Material Surface hardness Case depth Dimensional variation Expected loss

50 60 860 6.9 FeCCu 453.611 0.5778 0.4270 0.0818

51 60 860 6.9 Dist 477.222 0.4847 0.1218 0.0181

52 60 860 7.1 Fe 619.333 0.2713 0.1197 0.4782

53 60 860 7.1 FeCCu 579.5 0.2866 0.4172 0.2224

54 60 860 7.1 Dist 603.111 0.2617 0.0806 0.3578

55 90 820 6.7 Fe 480 −8.5796 0.1727 4.4117

56 90 820 6.7 FeCCu 440.167 −3.1982 0.4353 0.8589

57 90 820 6.7 Dist 463.778 50.5725 0.1483 133.7651

58 90 820 6.9 Fe 474.611 1.2932 0.1506 0.0563

59 90 820 6.9 FeCCu 434.778 1.7327 0.4270 0.2326

60 90 820 6.9 Dist 458.389 1.0994 0.1218 0.0777

61 90 820 7.1 Fe 569.667 0.4498 0.1197 0.1627

62 90 820 7.1 FeCCu 529.833 0.4934 0.4172 0.0390

63 90 820 7.1 Dist 553.444 0.4238 0.0806 0.0959

64 90 840 6.7 Fe 481.944 −0.8283 0.1727 0.1066

65 90 840 6.7 FeCCu 442.111 −0.7125 0.4353 0.2002

66 90 840 6.7 Dist 465.722 −0.9337 0.1483 0.1500

67 90 840 6.9 Fe 476.556 −3.1495 0.1506 0.7299

68 90 840 6.9 FeCCu 436.722 −1.9470 0.4270 0.4625

69 90 840 6.9 Dist 460.333 −5.5195 0.1218 1.9857

70 90 840 7.1 Fe 571.611 0.8832 0.1197 0.1795

71 90 840 7.1 FeCCu 531.778 1.0682 0.4172 0.0602

72 90 840 7.1 Dist 555.389 0.7883 0.0806 0.1070

73 90 860 6.7 Fe 501 −0.9332 0.1727 0.1112

74 90 860 6.7 FeCCu 461.167 −0.7888 0.4353 0.1490

75 90 860 6.7 Dist 484.778 −1.0692 0.1483 0.1402

76 90 860 6.9 Fe 495.611 −5.5004 0.1506 1.9221

77 90 860 6.9 FeCCu 455.778 −2.6461 0.4270 0.6028

78 90 860 6.9 Dist 479.389 −21.9904 0.1218 26.9919

79 90 860 7.1 Fe 590.667 0.7887 0.1197 0.2792

80 90 860 7.1 FeCCu 550.833 0.9330 0.4172 0.1054

81 90 860 7.1 Dist 574.444 0.7121 0.0806 0.1875

Table 8 Comparison of optimum combination

Optimum using Soaking time Temperature Green density Material Surface hardness Case depth Dimensional variation Loss

Expected loss 60 860 6.9 Fe 493.444 0.5190 0.1506 0.0027

Surface hardness 90 860 6.7 Fe 501.000 −0.9332 0.1727 0.1112

Case depth 90 820 7.1 FeCCu 529.833 0.4934 0.4172 0.0390

Dimensional variation 30 840 7.1 Dist 585.722 0.1561 0.0806 0.2516

592 Int J Adv Manuf Technol (2012) 61:585–594

variations were measured. The results obtained werecompared with the 95% confidence interval on expectedresult. The confidence interval was calculated using theformula [25]

100 1� að Þ% CI ¼ mexp �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFa;1;vVe

1

ne

� �sð6Þ

where ν is degrees of freedom of error, Ve, mean square(MS) of error, and ne total number of experiments/(1+sumof degrees of freedom for significant factors and inter-actions). The data on the pilot implementation of thesolution is given in Table 9. Table 9 showed that the pilotimplementation results were within the 95% confidenceinterval values of response variables. Hence, it wasconcluded that the experimentation was successful anddecided to go ahead with the full-scale implementation ofoptimum combination.

Since the target values of the response variables wouldvary from customer to customer based on the application ofpellets, a program was written in Visual Basic forApplication for calculating the total expected loss of allthe possible 81 factor level combinations with customerspecified targets. The program also highlights the combi-nation with smallest loss. This enabled the management toidentify the optimum factor setting for a given set of targetsand run the carbonitriding process accordingly.

6 Conclusions

The paper presented a case study on optimizing the heat-treated properties of carbonitrided pellets using design ofexperiments. Since optimizing the responses individuallywould adversely impact the performance of otherresponses, the response variables surface hardness; casedepth and dimensional variation were simultaneously

optimized using Taguchi’s loss function. Moreover, thestudy became a useful and effective input to design theproduction process to manufacture pellets with customerspecified heat-treated properties.

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Table 9 Pilot implementationresults SL no Surface hardness Case depth Dimensional variation

1 507 0.47 0.145

2 528 0.55 0.156

3 505 0.48 0.159

4 479 0.53 0.139

5 511 0.46 0.148

6 510 0.49 0.156

7 496 0.54 0.146

8 512 0.52 0.162

9 509 0.58 0.155

10 484 0.54 0.151

95% CI (455.6521, 531.2359) (0.3984, 0.7443) (0.1230, 0.1739)

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