Taguchi methods to minimize variation: An example ...

Taguchi methods to minimize variation: An example with plain ring gages Aikaterini Poustourli Dipl. Production & Management Engineer PhD Candidate of NTUA (School of Mechanical Engineering, Industrial Management and Operational Research Sector, Metrotechnics Laboratory) Tel.: (+30) 2321049138 email: [email protected] TEI of Serres, Terma Magnesias, 62124 Greece Leopoulos Vrasidas Associate Professor of National Technical University of Athens, School of Mechanical Engineering, Sector of Industrial Management and Operational Research, General Manager of Metrotechnics Laboratory Tel.: (+30) 210 7723585, Fax: (+30) 210 7723571. email: [email protected] Heroon Polytechniou 9, 15780 Zografou, Athens, Greece 1.Abstract In this study we consider a strategy to minimize variation in plain ring gages measurement. Quality Improvement efforts in many instances have been directed at reducing the variation of a particular characteristic around a nominal design specification. The case study which developed in this study uses Taguchi methods to develop equations witch model the amount of measurement variation in ring gages internal diameter measurement as functions of environmental conditions. The application of Taguchi’s robust engineering methods was employed to investigate the effects of measurements factors (plain ring gages internal diameter), so as to yield continues improvement measurement practice for reducing measurement variability. Robust designs were used to investigate the effects of several measurement factors simultaneously. In order to achieve these objectives we organized and executed controlled experiments in the accredited infrastructures of the Dimensional Laboratory of the Industrial Management & Operation Research Sector of Mechanical Engineering School of NTUA. The robust design method was used to design a series of experiments, and the analysis of variance was employed to quantify the effect of each factor. The experiments focused on the comparison of effect of four control factors in ring gages internal diameter measurement process with interactions and presence of controllable noise factor. All factors had two levels. The results of the experiment have indicated strong interactions between the main factors of the experiment. The analysis identified a less variable measurement practice. 1.1.Scope  The study is conducted based on the data obtained from Plain Ring Gages Measurement PhD project at a specific infrastructures of the Dimensional Laboratory of the Industrial Management & Operation Research Sector of Mechanical Engineering School of NTUA  Output characteristic measured is Internal Diameter of Plain Ring Gage  The NTUA Dimensional Laboratory is accredited from Hellenic Accreditation System SA (five type of test/ measured properties, Certificate No. 512 /23-2-2009) .

2. Taguchi philosophy : Introduction to fundamental terms (Control and Noise Factors) Taguchi's emphasis on minimizing deviation from target led him to develop measures of the process output that incorporate both the location of the output as well as the variation. These measures are called Signal to Noise ratios (S/N). The signal to noise ratio provides a measure of the impact of noise factors on performance. The larger the S/N, the more robust the product is against noise. Calculation of the S/N ratio depends on the experimental objective. Goal of the Taguchi’s model is to minimize one of three typical signal-to-ratios (SNRs): For (non-negative) smaller-the-better  = – 10 Log10 ( 1/n  Yi2 )

1

The Y variable denotes the raw performance of a system of n repeated measurements per experiment. Maximization of the smaller-the-better Signal-to-Ratio is equivalent to minimization of the loss function. For larger-the-better  = – 10 Log10 ( 1/n  1/Yi2 ) For target-the better (nominal the best)  = 10 Log10 ( 2 / 2 ) where μ is the mean and σ2 is the variance. Yi or Y1, Y2,…, Yn are n data points (measured results) and Y0 is the target value. S/N ratio measured in dB. 3. Research Methodology Quality/Robust Engineering is identical to Taguchi methodology. Robustness has been viewed as three steps in optimizing a process such as dimensional measurement. The three steps are: 1. system design the concept developmental stage 2. parameter design - enhancement of the system design so that the process consistently performs as intended or better 3. tolerance design - determining the tolerances and grades of materials and nominal values defined in the parameter design stage Taguchi methods focus on the second phase, parameter design, and specifically on design of experiments (DOE). The idea is to make the process as good as possible at the lowest possible cost, without emphasizing cost more than quality. Quality is improved by optimizing those parameters that are the least expensive to optimize, thereby increasing quality at minimal cost. Then, instead of eliminating all causes of variation, the process is designed to minimize the effect of the variation in parameters that are expensive to control (Peace, 1993). The research methodology is completed in nine steps as the following diagram reflects:

Figure 1: Nine step approach for research methodology

2

3.1 Problem statement and objective of the experiment  To identify the critical factors which influence the measurement quality (figure 2a), their level of importance and the effect of their interactions. Based on the results, arriving at action plans to improve quality levels  Brainstorming session : Identify control, noise factors and interactions affecting the Measuring Process of Plain Rings (figure 2b)  Improvement of measurement practice for reducing measurement variability: “The value of measurement result as closed as to nominal value “. Object: Robustness of Measurement Process.

3.2. Identification of Factors and interactions Structured brainstorming session with General Manager of Laboratory, project leader (PhD Candidate), technical metrologist, operators and quality manager identify the critical factors which influence the measurement quality (figure 2a), and identify control, noise factors and interactions affecting the Measuring Process of Plain Rings (figure 2b):

P-diagram Process of Comparative Dimensional Measurement of Internal Diameter Plain Ring in Mahr Opal ULM 600 Noise Factors-NF = ο C of reference plain ring

NominalValue Internal Diameter of Plain Ring gage (54,9900mm)

Process of Comparative Dimensional Measurement

Result of Internal Diameter Measurement

Control Factors-CF = Ambient Temperature (o C), 55mm Plain Ring Temperature, Humidity, Operator Interactions

(b) (a) Figure 2: General diagram of Measuring Process (a) and P-diagram for Internal Diameter Plain Ring Measurement process (b).

The Control Factors that identified are:  Factor A - Ambient Temperature of Measurement Room  Factor B - Part (plain ring) Temperature  Factor C - Operator (level of proficiency)  Factor D - Humidity of Measurement Room Possible interactions between factors are:  AXB  AXC  BXC The Noise Factors that identified and selected is the temperature of reference plain ring.

3

3.3 Choice of factor levels In the following table reflected the critical control and noise factors that selected for the Taguchi experiment as well as their selected levels and interactions. α/ α

Factor Description 1

2

3

Ambient Temperature of Measurement Room

Level

Factor

1=19.00-19.70 oC,

(Cooling System of Liebert HirossHPM for temperature and humidity control )

2=19.71-20.50 oC

Part (plain ring) Temperature (of 54,99900 mm internal diameter plain ring gage)

1=19.00-19.70 oC, 2=19.71-20.50 oC

Operator(level of proficiency)

A

B

1=Operator, 2=Expertise C

4

Humidity of Measurement Room (Cooling System of Liebert HirossHPM for temperature and humidity control )

5

1=38.00-43.00 %, 2=43.01-48.00 %

D

Interaction “Part- Operator”

2

BXC 6

7

8

Interaction “Ambient Temperature Operator”

2

Interaction “Ambient Temperature Part”

2

Reference part (plain ring) Temperature (of 14,00000 mm) internal diameter reference plain ring)

AXC

AXB N1=19.00-19.70 oC, N2=19.71-20.50 oC

N

Table 1: Selected factors and their levels . 3.4. Selection of appropriate Orthogonal Array (OA) The selection of OA is based on number of factors and the number of levels of factors. This selection should satisfy the following conditions:

LN ≥ required for factors and interactions Were LN are the degrees of freedom available in an OA LN - N-1, were N is the number of trials and

 (for a factor) = number of levels -1

In accordance to table 1 and their degrees of freedom, an L8 OA is selected based on the inequality. The international symbolism for the orthogonal arrays is L n (XY), were L n (XY) n = number of runs (experiments) X = number of levels Y = number of factors In our experiment, the L8 (27) OA symbolism, means that we have an experiment with : 8 = number of runs 2 = number of levels 7 = number of factors

4

The optimum assignment of factors and their interactions in orthogonal array achieved with the usage of the Taguchi’s triangular tables and linear graphs tools. In fourth column of the following table 2 reflected the degree of freedom for each factor and in the fifth column reflected the OA column assignment.

Table 2: Informative table for the factors assignment. 3.5. Assignment of factors and interactions In the columns 1 to 7 of the following L8 OA (table 3) assigned the factors and their interactions (this part of OA called inner array). In the columns R1 to R6 will be placed the results of the experiments conduction (horizontal lines combination of conditions). This part of OA called outer array).

Exp

1 2 3 4 5 6 7 8

1 A 1 1 1 1 2 2 2 2

2 B 1 1 2 2 1 1 2 2

3 AXB 1 1 2 2 2 2 1 1

4 C 1 2 1 2 1 2 1 2

5 AXC 1 2 1 2 2 1 2 1

6 BXC 1 2 2 1 1 2 2 1

Ν 7 D 1 2 2 1 2 1 1 2

Ν1

Ν2

Ν1

Ν2

Ν1

Ν2

1 R1

2 R2

1 R3

2 R4

1 R5

2 R6

Table 3: Assignment of factors and their interactions in L8 OA.

5

3.6. Experimental preparation and run For the experimental conduction, were prepared the Measurement Equipment (Mahr Opal ULM 600), the parts (plain rings and reference plain ring) and the Cooling System. Then the Measurements conducting from 2 Operators and finally the Experiment data collection sheets were completed as the following data sheet shows:

3.7. Statistical data analysis For the Statistical data analysis, Minitab v.15 used on the data collected from the measurements:

6

After the data entry in the Minitab v.15 (for the Taguchi Design Analysis), the software outputs were: Welcome to Minitab, press F1 for help., Taguchi Design / Taguchi Analysis: Term A (oC Temperature of Measurement Room B (oC Temperature of Plain Ring C Operator D Humididty A*B A*C B*C Analysis of Variance for SN ratios Source DF Seq SS Adj SS Adj MS F P A (oC ΑΕΣ) 1 2,6285 2,6285 2,6285 * * B (oC Δακτυλίου) 1 4,2029 4,2029 4,2029 * * C Χειριστής) 1 7,0718 7,0718 7,0718 * * D (Υγρασία) 1 1,6714 1,6714 1,6714 * * A (oC ΑΕΣ)*B (oC Δακτυλίου) 1 8,6388 8,6388 8,6388 * * A (oC ΑΕΣ)*C Χειριστής) 1 18,4936 18,4936 18,4936 * * B (oC Δακτυλίου)*C Χειριστής) 1 13,1941 13,1941 13,1941 * * Residual Error 0 * * * Total 7 55,9012

7

Response Table for Signal to Noise Ratios, Nominal is best (10*Log10(Ybar**2/s**2)) A (oC B (oC Level ΑΕΣ) Δακτυλίου) C Χειριστής) D (Υγρασία) 1 104,3 104,4 102,8 103,3 2 103,2 103,0 104,7 104,2 Delta 1,1 1,4 1,9 0,9 Rank 3 2 1 4 Response Table for Means A (oC B (oC Level ΑΕΣ) Δακτυλίου) C Χειριστής) D (Υγρασία) 1 55,00 55,00 55,00 55,00 2 55,00 55,00 55,00 55,00 Delta 0,00 0,00 0,00 0,00 Rank 1 2 3 4 Response Table for Standard Deviations B (oC Level A (oC ΑΕΣ) Δακτυλίου) C Χειριστής) D (Υγρασία) 1 0,000351 0,000351 0,000413 0,000392 2 0,000401 0,000401 0,000338 0,000360 Delta 0,000050 0,000050 0,000075 0,000032 Rank 3 2 1 4 As the Response Table for S/N ratio shows, the most important factor in our measurement process is C (the Operator) and follows the B (temperature of plain ring), A (temperature of measurement room). The levels that minimize the variation (or optimize the process) are the level 2 for the operator (expertise) the level 1 for the factor B, the level 1 for the factor A and the level 2 for the factor D. 3.8. Interpretation and experimental conclusion/Influencing factors Minitab v.15 used for the exploitation of predicted values Predicted values S/N Ratio Mean StDev Ln(StDev) 107,223 54,9995 0,0002395 -8,33716 Factor levels for predictions : A (Ambient Temperature) B (Plain Ring Temperature) D (Humidity) 1 1 2 19.00-19.70oC 19.01-19.70oC Expertise

C

(Operator

Proficiency)

2 43.01-48.00%

Best settings / adjustments: A1B1C2D2 The SN ratios under the optimum and initial conditions, denoted by ηoptimum and ηpresent respectively, are predicted by ηoptimum - ηpresent = 107,22 - 101,12 = 6,1 dΒ were ηopt = 104,3+104,4+104,7+104,2-3Χ103,725=107,22 dΒ and ηpresent = 103,2 + 103,0 + 102,8 + 103,3 - 3x103,72= 101,12 dΒ In addition Minitab v.15 used for the exploitation of Main Effects Plot :

8

3.9. Confirmation of Experiment / Final conclusion Three confirmation experiments running in best settings (A1B1C2D2) Minitab v.15 used for the calculations Taguchi Analysis: Y1; Y2; ... versus A (oC ΑΕΣ); Β (oC Δακτυλ; ... Predicted values S/N Ratio Optimum conditions

107,223 dB

1st Confirmation Experiment 2nd Confirmation Experiment 3rd Confirmation Experiment

106,913 dB 107,012 dB 106,998 dB

A (Ambient Temperature) B (Plain Ring Temperature) C (Operator Proficiency) D (Humidity) 1 1 2 2 19.00-19.70oC 19.01-19.70oC Expertise 43.01-48.00%

Best settings: A1B1C2D2

Performance of Comparative Internal Diameter Plain Ring Process Measurement (dB)

1

2

3

Average

106,913

107,012

106,998

106,974

4. Conclusions The study of the Taguchi experiments results leads the Laboratory’s General Manager to the following decisions:  Continuing Education of Laboratory staff  Annual Review of measurement methods  Introduction of Taguchi methods in QMS as a continues improvement process

9



Systematic evaluation of Taguchi experimental results and comparison with results from participation in Interlaboratory Proficiency Testing schemes and internal quality control methods.

As the study shows, Taguchi methodology can be useful in several metrological applications. Relative importance of various precautions used in dimensional measurements, unknown and potential problems, process improvements, and more competitive uncertainties were identified. Perhaps most importantly, current practices were affirmed as effective and nearly optimal. Taguchi methodology can clearly be used in continuous process improvement, as a tool for the requirement of accreditation quality systems to ELOT EN ISO 17025:2005 (§4.2.1, §4.10, §4.12). References  Genichi Taguchi, Subir Chowdhury, Yuin Wu (2005). “Taguchi’s Quality Engineering Handbook”, Wiley Book Company  Ν. Logothetis (1992). TQM, Prentice Hall UK-Interbooks Hellas  Philip J. Ross (1989). Taguchi Techniques for Quality Engineering McGraw-Hill Book Company  Stein. E (1990). Quality Through Design McGraw-Hill  J.Lyle Bagley, Chair Engineering & Industrial Technology Division, Tidewater Community College. “Taguchi Methods to Minimize Variation and Error : An example with Gage Blocks”, 2002.  AUKOM - Ausbildungskonzept Koordinatenmesstechnik e.V, EUKOM project submitted within the framework of LEONARDO DA VINCI pilot projects  Eddie Tarnow, National Metrology Institute of South Africa, Test and Measurement Conference (2007). Finding, recruiting and retaining laboratory staff – The managers’ nightmare of the 21st century.  P Apps “The Critical Role of Skilled Technicians in Laboratory Measurement”, NLA Test & Measurement Conference, October 2006 .  Aikaterini Poustourli-Vrasidas Leopoulos, “Design and Analysis of a Continuous Improvement Robust Model of QMS with emphasis in Metrotechnics Laboratory processes”, Magazine of the Pan-Hellenic Society of Mechanical & Electrical Engineers, issue 419, April of 2009  Aikaterini Poustourli-Vrasidas Leopoulos, “Continuous Improvement of Measurement and testing systems“, 3rd ο 2nd Pan-Hellenic (National) Congress on Standardization, Protypes and Quality 21-22/11/2008, Thessaloniki  Aikaterini Poustourli, “Quality Optimization in Industrial production with design of experiments», 2nd Pan-Hellenic (National) Congress on Standardization, Protypes and Quality, 26-27/05/2006, Thessaloniki  Aikaterini Poustourli, “Design of Experiments and Quality Optimization of Products and Processes”, “1st Pan-Hellenic (National) Congress on Standardization, Protypes and Quality” in Thessaloniki on November 12-13, 2004  Aikaterini Poustourli “The Mahalanobis Taguchi System method as an enterprise quality optimization tool “,Conference of Hellenic Forum for Quality and Eco-Q, Thessaloniki 23/12/2003.  Aikaterini Poustourli-Vrasidas Leopoulos, ‘Taguchi Methodology: Quality Optimization and Customer Satisfaction with Design of Experiments’, 15th National Conference of HELLENIC OPERATIONAL RESEARCH SOCIETY, Tripolis, 2/11/2002.  Aikaterini Poustourli-Vrasidas Leopoulos, “An Innovative Model for Quality Optimization”, WSEAS, Skiathos 25-28/9/2002.

10