Case Study 4

IE 431 Case Study 4 CUink, Inc. Name: Yash Vardhan Agarwal NetID: yashva2 UIN: 662403304

Agarwal, Yash 2 Define The DMAIC (Define, Measure, Analyze, Improve, Control) process is being initiated by CUink, Inc. to resolve ink delamination issues in their printed products, causing disruptions in the customer's production line. The problem stemmed from the use of ink supplied by a new vendor, leading to around 20% of 25,000 parts exhibiting unacceptable delamination. The objective is to identify the root cause of this delamination and establish effective process control parameters to prevent such defects with the new ink. The identified key process factors include belt speed, jet oven temperature, pot life, oven temperature, oven time, and mesh. The DMAIC process encompasses two main studies: firstly, evaluating the rating capability of three team members regarding delamination based on 30 sample parts; secondly, conducting a factorial experiment using a Resolution IV design with 3 replicates to ascertain significant parameters to achieve a mean delamination rating of 9 or higher. This endeavor aims to optimize process settings, ensuring a high-quality product output meeting customer specifications. Measure Key Output: The key objective of the conducted studies is to determine and standardize the evaluation of ink delamination on printed products. Study 1 focuses on assessing the consistency among three operators in rating delamination, comparing their evaluations against the master ratings. Meanwhile, Study 2 aims to identify crucial factors impacting delamination and recommend optimized settings to achieve a targeted delamination rating of 9 or higher. Both studies aim to establish a reliable and objective assessment method for ink delamination, crucial for effective process control and ensuring product quality in CUink’s production line. Current State: ࠵?࠵?࠵?࠵?࠵? ࠵?ℎ࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? = 25,000 ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵? ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? = ~20% ࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? = 20% ∗ 25,000 = 5,000 ࠵?࠵?࠵?࠵?࠵?࠵? ࠵?࠵?࠵?࠵?࠵? = 5,000 25,000 ∗ 1,000,000 = 200,000 ࠵?࠵?࠵? Study 1 - Evaluation of Delamination Rating by Three Operators: - Objective : Assess the ability of three team members to rate ink delamination on sample parts according to the ratings established by the DOE team (Master Rating). - Procedure : The same 30 sample parts were evaluated by each of the three operators, who provided ratings on a scale of one to ten for delamination. These parts were also rated and judged by the DOE team, serving as the master rating. - Analysis : Utilizing an appropriate statistical analysis technique, the aim is to determine whether the three operators significantly differ in their ratings compared to the master ratings or from each other. The statistical significance level of 0.05 will guide the assessment.

Agarwal, Yash 4 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Factor 2 6.822 3.411 0.39 0.679 Error 87 761.800 8.756 Total 89 768.622 Means Factor N Mean StDev 95% CI Inspector 1 30 5.633 2.871 (4.560, 6.707) Inspector 2 30 5.033 3.011 (3.960, 6.107) Inspector 3 30 5.067 2.993 (3.993, 6.140) Pooled StDev = 2.95911 The results of the ANOVA show that the team fails to reject the null hypothesis implying all three means are similar. As seen in the interval plot above, all three intervals overlap each other which does not allow the team to come to a conclusion about the inspectors. However, the mean values of the Inspector 1 was higher than that of the others. Hence the team concluded that there were latent factors that influenced the data. Therefore, the team cannot use one-way ANOVA and would have to take two-way ANOVA to block out the latent factors. To carry out this Two-Way ANOVA, they reorganized their data and individually compared them to the master rating given by the DOE group. This resulted in the following ANOVA result: Method Factor coding (-1, 0, +1)

Agarwal, Yash 5 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Master Rating 9 719.539 79.9488 147.56 0.000 Subscripts 2 6.822 3.4111 6.30 0.003 Error 78 42.261 0.5418 Lack-of-Fit 18 12.078 0.6710 1.33 0.201 Pure Error 60 30.183 0.5031 Total 89 768.622 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 5.4806 0.0845 64.89 0.000 Master Rating 1 -4.147 0.190 -21.85 0.000 1.57 2 -3.647 0.282 -12.95 0.000 2.18 3 -2.481 0.235 -10.55 0.000 1.84 4 -1.147 0.235 -4.88 0.000 1.84 5 0.297 0.235 1.26 0.210 1.84 6 -0.064 0.208 -0.31 0.760 1.67 7 1.186 0.389 3.05 0.003 3.25 8 2.408 0.235 10.24 0.000 1.84 9 3.408 0.235 14.49 0.000 1.84 Subscripts Inspector 1 0.389 0.110 3.54 0.001 1.33 Inspector 2 -0.211 0.110 -1.92 0.058 1.33 From this ANOVA the team conclude that Inspector 1 is statistically significant (P-Value < a ) and its value would change the output. To confirm this further, the team conducted a Fisher Analysis. The results are: Fisher Pairwise Comparisons: Subscripts Grouping Information Using Fisher LSD Method and 95% Confidence Subscripts N Mean Grouping Inspector 1 30 5.86944 A Inspector 3 30 5.30278 B Inspector 2 30 5.26944 B Means that do not share a letter are significantly different.

Agarwal, Yash 7 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Master Rating 9 501.992 55.7769 131.13 0.000 Subscripts 1 0.017 0.0167 0.04 0.844 Error 49 20.842 0.4253 Lack-of-Fit 9 5.125 0.5694 1.45 0.200 Pure Error 40 15.717 0.3929 Total 59 522.850 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 5.3225 0.0917 58.07 0.000 Master Rating 1 -4.223 0.206 -20.50 0.000 1.57 2 -3.572 0.306 -11.69 0.000 2.18 3 -2.822 0.255 -11.06 0.000 1.84 4 -1.156 0.255 -4.53 0.000 1.84 5 0.011 0.255 0.04 0.966 1.84 6 0.053 0.226 0.23 0.817 1.67 7 1.678 0.423 3.97 0.000 3.25 8 2.177 0.255 8.53 0.000 1.84 9 3.511 0.255 13.76 0.000 1.84 Subscripts Inspector 2 -0.0167 0.0842 -0.20 0.844 1.00 Fisher Pairwise Comparisons: Subscripts Grouping Information Using Fisher LSD Method and 95% Confidence Subscripts N Mean Grouping Inspector 3 30 5.33917 A Inspector 2 30 5.30583 A Means that do not share a letter are significantly different. Fisher Individual Tests for Differences of Means Difference of Subscripts Levels Differenc e of Means SE of Differenc e Individual 95% CI T- Value P- Value Inspector 3 - Inspector 2 0.033 0.168 (-0.305, 0.372) 0.20 0.844 Simultaneous confidence level = 95.00%

Agarwal, Yash 8 This Fisher Interval Plot confirmed the claim of the team and reiterated that Inspector 1 was out of order and Inspector 2 and Inspector 3 are consistent. Outcomes: • The study revealed acceptable inter-rater agreement among the three inspectors. • This confirmed that all inspectors were rating correctly except Inspector 1 who might need to be trained more to rate more carefully. Study 2 This study aimed to investigate the effects of six process factors on the delamination rating of printed parts using ink from the new supplier. A 2-level factorial design was chosen to efficiently evaluate the main and interaction effects of these factors. Factors and Levels: • Factor A: Belt Speed: Low and High • Factor B: Jet Oven Temperature: Low and High • Factor C: Pot Life (hours): 2 and 4 • Factor D: Oven Temperature (°F): 140 and 160 • Factor E: Oven Time (hours): 2 and 3 • Factor F: Mesh: Narrow and Wide Design and Replications: • A Resolution IV design was chosen to minimize the number of experimental runs while still allowing for the estimation of all main and interaction effects.

Agarwal, Yash 10 Coded Coefficients Term Effect Coef SE Coef T-Value P-Value VIF Constant 6.4792 0.0551 117.55 0.000 A -0.1250 -0.0625 0.0551 -1.13 0.265 1.00 B -0.0417 -0.0208 0.0551 -0.38 0.708 1.00 C -1.4583 -0.7292 0.0551 -13.23 0.000 1.00 D -2.7083 -1.3542 0.0551 -24.57 0.000 1.00 E -1.2083 -0.6042 0.0551 -10.96 0.000 1.00 F 0.0417 0.0208 0.0551 0.38 0.708 1.00 A*B -0.2917 -0.1458 0.0551 -2.65 0.013 1.00 A*C 0.1250 0.0625 0.0551 1.13 0.265 1.00 A*D 0.0417 0.0208 0.0551 0.38 0.708 1.00 A*E 0.0417 0.0208 0.0551 0.38 0.708 1.00 A*F -0.0417 -0.0208 0.0551 -0.38 0.708 1.00 B*D 1.6250 0.8125 0.0551 14.74 0.000 1.00 B*F 0.2083 0.1042 0.0551 1.89 0.068 1.00 A*B*D 0.2083 0.1042 0.0551 1.89 0.068 1.00 A*B*F -0.0417 -0.0208 0.0551 -0.38 0.708 1.00 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Model 15 165.313 11.0208 75.57 0.000 Linear 6 131.292 21.8819 150.05 0.000 A 1 0.187 0.1875 1.29 0.265 B 1 0.021 0.0208 0.14 0.708 C 1 25.521 25.5208 175.00 0.000 D 1 88.021 88.0208 603.57 0.000 E 1 17.521 17.5208 120.14 0.000 F 1 0.021 0.0208 0.14 0.708 2-Way Interactions 7 33.479 4.7827 32.80 0.000 A*B 1 1.021 1.0208 7.00 0.013 A*C 1 0.187 0.1875 1.29 0.265 A*D 1 0.021 0.0208 0.14 0.708 A*E 1 0.021 0.0208 0.14 0.708 A*F 1 0.021 0.0208 0.14 0.708 B*D 1 31.688 31.6875 217.29 0.000 B*F 1 0.521 0.5208 3.57 0.068 3-Way Interactions 2 0.542 0.2708 1.86 0.173 A*B*D 1 0.521 0.5208 3.57 0.068 A*B*F 1 0.021 0.0208 0.14 0.708 Error 32 4.667 0.1458 Total 47 169.979

Agarwal, Yash 11 These coefficients and ANOVA table values provided the team with enough information to identify the statistically significant factors and their interactions. This allowed them to further refine their model and led them to run a Two-Way ANOVA (General Linear Model) on the significant terms only. The results of this ANOVA are given below: Factor Information Factor Type Levels Values C Fixed 2 -1, 1 D Fixed 2 -1, 1 E Fixed 2 -1, 1 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value AB 1 1.021 1.0208 6.91 0.012 BD 1 31.688 31.6875 214.37 0.000 C 1 25.521 25.5208 172.65 0.000 D 1 88.021 88.0208 595.47 0.000 E 1 17.521 17.5208 118.53 0.000 Error 42 6.208 0.1478 Lack-of-Fit 10 1.542 0.1542 1.06 0.422 Pure Error 32 4.667 0.1458 Total 47 169.979 Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 6.4792 0.0555 116.76 0.000 AB -0.1458 0.0555 -2.63 0.012 1.00 BD 0.8125 0.0555 14.64 0.000 1.00 C -1 0.7292 0.0555 13.14 0.000 1.00 D -1 1.3542 0.0555 24.40 0.000 1.00 E -1 0.6042 0.0555 10.89 0.000 1.00 After running the ANOVA with the significant factors only, the team saw that the degrees of freedom for error increased by 10 and the SS E only increased ~1.5. This resulted in a very minimal increment in MS E (or predicted value for variance). Hence, the team concluded that the model is better and more streamlined with the significant factors only. Therefore, they continued with a Response Optimization of these factors resulting in the following:

Agarwal, Yash 13 Variable Ranges Variable Values AB (-1, 1) BD (-1, 1) C 1 D -1, 1 E -1, 1 Solution Solution AB BD C D E Rating Fit Composite Desirability 1 -1 1 1 -1 -1 8.66667 0.944444 Data Collection: • The InkSimulator2023 spreadsheet was used to simulate the printing process and generate delamination ratings for each experimental run. • This allowed for controlled experimentation and eliminated the need for actual production runs. Outcomes: • The data from the 48 experimental runs provided valuable insights into the relationships between the process factors and the delamination rating. • This information served as the foundation for the subsequent analysis and optimization phases of the project. Improve Based on the analyses conducted by the team, they recommended that only the optimal setting for the factors be used while using the products from the new supplier. The setting was:

Agarwal, Yash 14 • Factor A: Belt Speed: High • Factor B: Jet Oven Temperature: Low • Factor C: Pot Life: 4 hours • Factor D: Oven Temperature: 140°F • Factor E: Oven Time: 2 hours • Factor F: Mesh: Narrow or Wide The team utilized the optimal setting for the factors (while constraining the Pot Life to be maximum) and produced another 30 ratings from the InkSimulator2023. Further, CUink had agreed with the customer to have a Lower Specification Limit to be of Rating 7. Hence, to consolidate that their optimal setting for the factors would get them ratings within the specification limits, the team conducted a Distribution Identification and Capability Analysis on the simulated values. The result of this was: Goodness of Fit Test Distribution AD P LRT P Normal 1.442 <0.005 Box-Cox Transformation 1.449 <0.005 Lognormal 1.491 <0.005 3-Parameter Lognormal 1.484 * 0.550 Exponential 11.082 <0.003 2-Parameter Exponential 3.076 <0.010 0.000 Weibull 1.484 <0.010 3-Parameter Weibull 1.551 <0.005 0.163 Smallest Extreme Value 1.569 <0.010 Largest Extreme Value 1.680 <0.010 Gamma 1.511 <0.005 3-Parameter Gamma 1.856 * 1.000 Logistic 1.486 <0.005 Loglogistic 1.516 <0.005 3-Parameter Loglogistic 1.486 * 0.594