Screening out Factors of Bloom Manufacturing Using Placket–Burman Design

R. P. Sinha1 and Dr. K. C. Arora2

1Department of Mechanical Engineering, AnandEngineeringCollege, Keetham, Agra 282 007

2Director, Vikrant Institute of Technology & Management, Gwalior 474 006

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Abstract---In a multistage integrated steel manufacturing system the number of influencing factors of quality characteristics of surface defects are large. It is essential to investigate and discover the potential factors or key factors for the process design and development of manufacturing. This paper is an illustration of applying fractional factorial Placket-Burman 2 level screening design of experiment to investigate factors of variation and establish their significance. This design is a preliminary study prior to apply the state of art optimization technique like Taguchi Method. The quality of fine-semi-finished steel product is comprehensively influenced by the quality of semi finished product produced directly by continuous casting or Ingot casting with subsequent hot rolling. This design helps the researcher in finding key factors of the manufacturing process of semi finished steel product, blooms. In this illustration 7 control factors have been employed to design 2 levels- 12 runs P- B design. This P-B design of experiment resulted with 4 significant factors.

Key Words: Multistage Integrated Steel Manufacturing,, potential/ key factors, P-B Design of Experiment, Taguchi Method, Blooms.

  1. INTRODUCTION

Design of Experiments (DOE) is a powerful statistical technique to discover a set of potential factors which causes

variations in the quality characteristics or in process performance. Placket-Burman factorial design of experiments (P-B DOE) involves 2- levels of selected factors. It determines the levels of factors or parameters to be kept to optimize the process performance [1]. The number of runs must be in multiple of 4. It reduces the initial cost of investigation and is a quick method of preliminary study of influencing factors. P-B DOE was applied maidenly by R. L. Placket and J.P. Burman in early 20th century, 1946 [9].

In an integrated manufacturing plant of steel, the fine semi finished products are produced by hot rolling or cold rolling. Input at this stage is semi finished steel products, billets, blooms or slabs which are output of previous stage of steel manufacturing. Stage-ii involves two manufacturing process, either hot rolling of ingot or direct continuous casting. Continuous casting is a quick, productive, cost effective and qualitative dynamic process of manufacturing semi finished

steel goods where the liquidsteel is allowed to solidify in the strand mould. The quality of the fine semi finished is greatly influenced by the quality characteristics of the semi finished steel products. Therefore, this paper is an attempt to identify the key factors and recommend them for further experiments of optimization for process development in a multistage situation.

Factorial Experiment: A factorial design is an experiment where one may vary all the factors in the experiment at their different levels simultaneously [11]. By Factorial Experiment Design it is meant that in each complete trial of the experiment all possible combination of the levels of the factors is investigated [3]. Factorial experiment categorically classified as Full Factorial or Partial Factorial. Full Factorial Design of experiments involves 2K number of setups for k number of factors each at 2 levels. In an industrial situation where number of factors is more, Fractional Factorial Experiment is employed. This design requires 2k-p number of setup, where 1/2p represents a fraction where p is an integer [6]. It may be nominated ½, ¼, 1/8, 1/16… fractional factorial. Full factorial is preferred when the number of factors are less than or equal to 4. P-B Design of Experiment is a specific design of 2 levels fractional factorial design.

  1. P.B DESIGN OF EXPERIMENTS

Often, an optimum process design involves excessively large numbers of variables which influence the process output or quality characteristics and causes variations in it. Screening experiments are useful in segregating the ‘vital few’; a manageable size of variables from the ‘trivial many’ to have economical and quick experiments performed with those few key factors [2].

This strategy of reduction of factors focuses on product or process design and development on those key variables.

.Objective of the P-B design is to extract those factors which

AKGEC JOURNAL OF TECHNOLOGY, vol.1, no.1

are insignificantly incorporated in design of experiments and

they are eliminated in the further advanced application of experimentation or optimization of process or product. Placket-Burman designs are a class of resolution III, two-level fractional factorial designs that are often used to study main effects. In a resolution III design, main effects are aliased with two-way interactions [7]. P-B design does ignore interactions. The number of trials is multiple of 4.

Advantages of P-B Design: There are numeral benefits of using P-B Design of Experiments. Few are listed as under in:

Efficient Process estimation

Two-Level matrix structure

Reduced number of runs irrespective of large no. of factors

Minimal Wastage of Time and Money

Interpretations are based on statistical principles

Determine the priority of control on the factors

 Runs are multiple of 4 rather power of 2.

 Ignoring interactions makes experimenter easy to understand,

Here, 2-Level P-B design of factorial experiments was developed using MINITAB-13 software, a Statistical Package for 7 selected control factors of influencing quality characteristic,’ Crack Severity’. Crack severity expresses the degree of surface cracks or surface defects of bloom produced by ingot route in an integrated steel plant. The minimum number of runs were chosen based on the formula k = (N-1)/(L-1) where k, is the number of factors, N is number of trials or runs and l, is levels of factors. P-B Designs are based on Hadamard Matrices in which the number of trials are multiple of 4, i.e. 4, 8, 12 16, 20, 24, 28, and so on. Factors are set to 2-levels to simplify the experimentations and save time and money towards optimization.

The P-B design presents the columns of the matrix structure as factors and the rows are runs. Cells represent the levels usually – 1 and 1 in a coded structure which states the lower and upper levels of the factors. In an un-coded structure the true low levels and the upper levels are presented in the cells. In this paper the response, dependent variable or outcome of the experiments that also may be called quality characteristics are signal to noise ratio (SNR) which was computed based on ‘ Smaller is better’ as –10LOG10(y2). Criterion is chosen on the basis of objective. Here the objective is to minimize the ‘Crack severity’. Therefore, smaller is better mode has been chosen to compute the SNR as outcome. SNR compute the societal losses in the form of variations by maximizing the SNR.

The proposed P-B fractional factorial design incorporates 7

factors which is more than 4. 12 runs have been chosen because it exceeds the number of degree of freedom11. This clearly satisfies the criterion that the number of experimental runs required for an experiment must be greater than the degree of freedom associated with the factors [10].

III. EXPERIMENTATION

Steps of Screening Experiment:

  1. Conduction of Brain storming and interview with the Executives, supervisors, and operators on manufacturing shop.
  2. Listing of factors influencing the response, quality characteristics.
  3. Identification of controllable factors and their levels and response.
  4. Layout of P-B Design for the chosen number of runs or trials and replications.
  5. Conduction of experiments on manufacturing floor.
  6. Tabulation of observed responses.
  7. Conduct analysis of experimental results
  8. Draw inferences.
  9. Recommend significant factors and their levels for further experimentation.

Table 1 illustrates the 7 factors,their codes and set 2 levels to set the factors to perform experiments. These 7 control factors and their 2 levels were identified through interviewing and brainstorming at the shop floor in which executives, supervisors and operators were involved with the approximation of truthfulness in the out come. The response of the experiment was identified as ‘Crack severity’, CSR which is a function of number of blooms salvaged, Ns, number of blooms rejected, Nr; and total number of blooms inspected Nt. expressed below.

CSR = ƒ (Ns, Nr.Nt) (1)

This function is expressed as

CSR = 0.7Ns / Nt + 0.2 Nr / Nt (2)

TABLE 1

RunOrder / CenterPt / Blocks / PRC / PRS / PRSi / PRMn / PRP / TTM / STM
3 / 1 / 1 / 1 / -1 / 1 / -1 / -1 / -1 / 1
5 / 1 / 1 / 1 / 1 / -1 / 1 / -1 / -1 / -1
7 / 1 / 1 / -1 / 1 / 1 / -1 / 1 / -1 / -1
9 / 1 / 1 / 1 / -1 / 1 / 1 / -1 / 1 / -1
1 / 1 / 1 / 1 / 1 / -1 / 1 / 1 / -1 / 1
11 / 1 / 1 / 1 / 1 / 1 / -1 / 1 / 1 / -1
4 / 1 / 1 / -1 / 1 / 1 / 1 / -1 / 1 / 1
10 / 1 / 1 / -1 / -1 / 1 / 1 / 1 / -1 / 1
6 / 1 / 1 / -1 / -1 / -1 / 1 / 1 / 1 / -1
8 / 1 / 1 / 1 / -1 / -1 / -1 / 1 / 1 / 1
12 / 1 / 1 / -1 / 1 / -1 / -1 / -1 / 1 / 1
2 / 1 / 1 / -1 / -1 / -1 / -1 / -1 / -1 / -1

TABLE 2 (P-B) 2x12DESIGN LAYOUT FOR 7 FACTORS (CODED)

Control Factors / Codes / Lower
Level (-1) / Higher
Level(1)
Percent of Carbon / PRC / 0.130 / 0.230
Percent of Sulphur / PRS / 0.024 / 0.032
Percent of Manganese / PRMn / 0.550 / 1.600
Percent of Silicon / PRSi / 0.160 / 0.300
Percent of Phosphorous / PRP / 0.024 / 0.034
Track Time / TTM / <6 Hrs. / >6 Hrs.
Soak time / Pit Time / STM / 13 / 18

BLOOM MANUFACTURING

For each trial Crack severity, CSR was computed from the observed number of salvaged, number of rejected and total number of inspected blooms under the set conditions of runs or trials as in Tables 2 &3 using (2). Each run was replicated twice. Signal tonoise ratio, SNR was computed as are tabulated in Table 3 for each run.

RUNS / PRC / PRS / PRSi / PRMn / PRP / TTM / STM / CSR1 / CSR2 / SNR
1 / 0.23 / 0.024 / 0.30 / 0.55 / 0.024 / <6 / 18 / 0.218 / 0.530 / 7.840
2 / 0.23 / 0.032 / 0.16 / 1.20 / 0.024 / <6 / 13 / 0.577 / 0.450 / 5.723
3 / 0.13 / 0.032 / 0.30 / 0.55 / 0.034 / <6 / 13 / 0.336 / 0.000 / 12.480
4 / 0.23 / 0.024 / 0.30 / 1.20 / 0.024 / >6 / 13 / 0.300 / 0.476 / 8.005
5 / 0.23 / 0.032 / 0.16 / 1.20 / 0.034 / <6 / 18 / 0.620 / 0.270 / 6.408
6 / 0.23 / 0.032 / 0.30 / 0.55 / 0.034 / >6 / 13 / 0.328 / 0.558 / 6.788
7 / 0.13 / 0.032 / 0.30 / 1.20 / 0.024 / >6 / 18 / 0.100 / 0.522 / 8.500
8 / 0.13 / 0.024 / 0.30 / 1.20 / 0.034 / <6 / 18 / 0.637 / 0.453 / 5.150
9 / 0.13 / 0.024 / 0.16 / 1.20 / 0.034 / >6 / 13 / 0.315 / 0.550 / 6.971
10 / 0.23 / 0.024 / 0.16 / 0.55 / 0.034 / >6 / 18 / 0.372 / 0.500 / 7.117
11 / 0.13 / 0.032 / 0.16 / 0.55 / 0.024 / >6 / 18 / 0.489 / 0.008 / 9.222
12 / 0.13 / 0.024 / 0.16 / 0.55 / 0.024 / <6 / 13 / 0.218 / 0.328 / 11.103

IV. STATISTICAL ANALYSIS AND INFERENCES

Table 3 illustrates the setup of the experiment and observed response ,’CSR’, Crack severity and signal to noise ratio at each combination of factor levels selected at two levels. Experiment could be repeated twice to smoothen the variability. Further Signal to Noise ratio, SNR was computed by using the formula mentioned as in equation-(2) to be used as response. The objectiveof minimization of CSR was transformed with the objective of maximization of SNR. Now, objective is to maximize the SNR, which simultaneously minimize the Crack severity which is our main objective. To compute the SNR, criterion of ‘Smaller is better’ hasbeen adopted.

SNR = -10 LOG10 ((CSR12+CSR22)/2) (3)

Statistical analysis had been carried out by assuming SNR as response. Objective of the experiment is to minimize the crack severity. That is why, the problem is of smaller is better kind and henceforth, the SNR was computed by using the equation-2. And It was decided to take SNR as Response to carryout further analysis. Normal probability plots and Pareto plots were plotted at different levels of significance, i.e. 0.01, 0.05, 0.1, 0.15 and 0.2 using MINITAB-13 statistical software.

Figure1 and figure2 are normal plot and pareto plot respectively at level of significance, α=0.2. The Normal plot and pareto chart of effects depict the effects of factors on the response and their significance. The pareto charts is a graphical presentation of the absolute standardized effects in descending order marked with intersecting line as reference line. Any effect extended past to reference line is to have significant effect on response. Here, PRMn and PRC are significant as they are extended beyond reference line. In the normal plot, PRC and PRmn are indicated points away from the line and marked with their name.This indicates theirsignificance. Thus The

percent of manganese and the percent of carbon are the

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significant factors at level of significance, α=0.2. At all other levels of significance i.e. 0.15, 0.10, 0.05 and 0.01, no factors was significant but the order of effects remain unaltered as PRMn,PRC, STM , PRP, PRS, PRSi TTM.

(P-B) 2x12 Design Layout for 7 Factors (Coded)

V. ANOM (Analysis of Means)

The Table 4 illustrates the mean effects of factors at their selected 2 levels and the overall standard deviation. The figure -03 shows the main effects of the factors on the response, SNR. From the figure it is evident that all factors affect response, SNR as no lineof joining of effects at set two levels are parallel tomean line. As an individual i.e. oneway effect

TABLE4 ANOM, AVERAGE MEAN OF SNR AT ALL LEVELS

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Levels / Factors / Mean / SE Mean
0.1300 / PRC / 8.904 / 0.8095
0.2300 / 6.980 / 0.8095
0.0240 / PRS / 7.698 / 0.8095
0.0320 / 8.187 / 0.8095
0.1600 / PRSi / 7.757 / 0.8095
0.3000 / 8.127 / 0.8095
0.5500 / PRMn / 9.092 / 0.8095
1.2000 / 6.793 / 0.8095
0.0240 / PRP / 8.399 / 0.8095
0.0340 / 7.486 / 0.8095
<6 / TTM / 8.117 / 0.8095
>6 / 7.767 / 0.8095
13 / STM / 8.512 / 0.8095
18 / 7.373 / 0.8095

of factor PRC and PRMn are distinctively larger as it was concluded from the pareto chart and normal plot that the effects of these factors are significant. Factors TTM, PRS and PRSi may be pooled down as their effects are minimal.

Table5 represents the ANOVA table of a generalized regression model of all 7 factors opted for experimentation. The selected levelofsignificance is 0.2. The table shows the Degree freedom, Sum of squares, SS; adjusted SS, adjustedMean square, MS, F value and p-value. If the p-valueof a factor is less than the selected level ofsignificance, α, the factor is significant. The selectedlevel of significance is 0.2. The table illustrates thatthe p- values of PRMn, and PRC are less than 0.2, therefore, they are significant factors.

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P-values of TTM, PRSi and PRS are larger than 0.2 that is why these factors were dropped from the regression.

Further, ANOVA on pooled regression of.4 factors PRC, PRMn, PRP and STM was performedas tabulated in Table-6.

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Source / DF / Seq SS / Adj SS / Adj MS / F / P
PRC / 1 / 11.107 / 11.107 / 11.107 / 2.82 / 0.168
PRS / 1 / 0.718 / 0.718 / 0.718 / 0.18 / 0.691
PRSi / 1 / 0.410 / 0.410 / 0.410 / 0.10 / 0.763
PRMn / 1 / 15.854 / 15.854 / 15.854 / 4.03 / 0.115
PRP / 1 / 2.502 / 2.502 / 2.502 / 0.64 / 0.470
TTM / 1 / 0.368 / 0.368 / 0.368 / 0.09 / 0.775
STM / 1 / 3.891 / 3.891 / 3.891 / 0.99 / 0.376
Error / 4 / 15.727 / 15.727 / 3.932
Total / 11 / 50.577

TABLE 5 ANALYSIS OF VARIANCE FOR

SNR,USING ADJUSTED SS FOR TESTS

BLOOM MANUFACTURING

TABLE6 ANALYSIS OF VARIANCE FOR SNR,

USING ADJUSTED SS FOR TESTS OF POOLED REGRESSION

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On comparing ANOVA Table5 and Table6, it is evident that there is significant improvement in the effects of these 4 factors on response, SNR in turn the Crack severity.Table-06 depicts that the degree of freedom of pooled regression improved from 4 to 7.

Source / DF / Seq SS / Adj SS / Adj MS / F / P
PRC / 1 / 11.107 / 11.107 / 11.107 / 4.51 / 0.071
PRMn / 1 / 15.854 / 15.854 / 15.854 / 6.44 / 0.039
PRP / 1 / 2.502 / 2.502 / 2.502 / 1.02 / 0.347
STM / 1 / 3.891 / 3.891 / 3.891 / 1.58 / 0.249
Error / 7 / 17.223 / 17.223 / 2.460
Total / 11 / 50.577

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Adjusted mean squares reduced from 3.92 to 2.4. P-values of the PRC, PRMn, PRP, and STM changes from 0.168 to 0.071; 0.115 to 0.039; 0.470 to 0.347 and 0.376 to 0.249 respectively. These changes are decrease in the p-values of the factors. This declination indicates the improvement in regression effects. This betterment in relationship is further proved by the increase in F-values.

VI. SURFACE PLOT

Contour and surface wire frame plot is a helpful graphical tool which visualize the pair wise i.e. two way effects of factors on the response. Contour plots and wireframe plots for each pair of numeric factors were plotted and they were investigated. Samples of contour plot and surface plot for a pair of significant factors PRC and PRMn is illustrated in the graph as mentioned in the Figure-04 and Figure-05.

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VII. CONCLUSION.

From the discussion in the statistical analysis and inferences, it is concluded that percentage of carbon (PRC), percentage of manganese (PRMn) and percentage of phosphorous (PRP) of compositional control factors along with soak pit time (STM) factors are potential factors for further experimentation. Out of these 4 factors PRC and PRMn are significant factors with the p-values 0.007 and 0.039 at 0.2 of α, level of significance. Levels of these factors at next stage of experiment are to be set at lower side of each factor which can be easily found in the ANOM Table-3 and main effect of factors plot in Figure3.

VIII. REFERENCES

[1]. Antony J. & Kaye M. (1999); ‘Experimental Quality: A strategic approach

to Achieve and Improve Quality’ Kulwer Academic, New York,

[2]. Antony Juu (2002), ‘Training for Design of Experiments Using

Catapult’, Quality and reliability Engineering International, Vol.18, pp.29-35.

[3]. Hines W. William, Montgomery C. Douglas, and et.al (2003), ‘Probability

and Statistics in Engineering ‘, John Willey & Sons, Inc.; 4e.

[4]. Millar Irwine and Freund E John(1985),‘Probability and statistics for

Engineers’; PHI, 3e,1 985.

[5]. Montgomery C. Douglas(1997), ‘Design and Analysis of Experiments’,

Jhon Willey and Sons.

[ 6]. Montgomery C. Douglas, Borror Connie M & Stanley James D(1998),

’Some Cautions in the Use of Placket- Burman Designs’,

Quality Engineering, 10(2), pp. 377-381,

[7]. Minitab User’s Guide,(2000) , ‘Data Analysis and Quality Tools,

Release 13’, Minitab, Inc, 2000, UK

[8]. Phadke S Madhav(1989),‘Quality Engineering Using Robust Design’,

Prentice Hall, Englewood Cliffs, New Jersey.

[9]. Placket R.L. and Burman J. P.(1946),’ The Design of optimal

multifactorial Experiments‘, Biometrika, Vol. 33, 305-325.

[10]. Ross P.J (1988), ‘Taguchi Techniques for Quality Engineering’,

McGraw Hill.

[11]. Willium G.W. (1999), ‘Experimental Design: Robustness and

Power issue.’ ASQ Congress Transaction, pp.1051-1056.

/ Ramjanam Prasad Sinha graduated from ‘Bihar Institute of Technology, Sindri (Dhanbad)’ in ‘Production Engineering ‘and completed post graduation from Indian school of Mines, Dhanbad in ‘Industrial Engineering and Management’. Thereafter, he joined teaching at Guru Nanak Dev Engineering College Bidar (Karnataka) and served for 14 years there. Presently, he is working at AnandEngineeringCollege, Keetham, Agra.

He was honoured with ‘Shreshtha Teacher Award’ in 2008 by SGI (Sharda Group of Institutions).His areas of interest in research are Manufacturing Technology, Quality Engineering and Optimization of Product and Process Design

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