Viscosity Analysis for Iowa Paint Manufacturing Co.
By
Ruchi Patnaik
Spring 1999
Client
Mark Angerer Technical Director Iowa Paint Manufacturing Company, Inc. 17th & Grand Avenue Des Moines, Iowa 50309 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Executive Summary
The objective of our process-oriented quality improvement class project with Iowa Paint Manufacturing Co. was to improve consistency of viscosity in batches of Satin Acrylic Latex Paint. The company requires final viscosity to be between 95 and 100 Krebs and currently the initial viscosity is between 85 and 95 Krebs. Viscosity of the paint is increased by the addition of Hydroxyethyl Cellulose, also known as A44, and the company currently uses a trial and error method to obtain the required viscosity. For this study, our group analyzed quality control cards given to us by the company and also considered the issue of viscosity measurement precision. Our study of measurement precision involved both an R&R study and a study of the within–tank variability of viscosity measurements. This project gave us insights on the different factors that play a role in viscosity measurement precision. There is a significant difference in measurements if different people do them, and there is also a difference when sampling from different areas of a paint tank. We recommend that a single individual do all the paint viscosity measurement. We also recommend that Iowa Paint sample from different parts of a paint tank and average the viscosity measurements (or mix the samples before testing). This should make measurements more reliable as representing the tank average. These steps may improve measurement precision and allow more effective assessment of initial viscosity (and therefore better perception of the size of viscosity adjustment needed to bring a batch into conformity). A regression analysis was done on historical data in order to infer the average increase of viscosity per pound of A44 added (per 1000 gallons of paint). From this analysis, we found a single representative slope for all measured viscosity increases versus added A44 amounts. We gave our client a solution for ‘x’ in an expression such as “add ‘x’ pounds of A44 in every 1000 gallons of paint to increase the viscosity by amount ‘y’”. Additionally, we provided the client with tables and graphs showing appropriate A44 additions (in pounds) for each tank size used by the company.
2 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Table of Contents
1. Introduction ……………………………………………… 3
2. Procedure ……………………………………………… 3
3. Results ……………………………………………… 7
4. Conclusion ………………………….………………….. 10
5. Recommendations ………………………………………. 11
6. Appendix A ……………………………………………… 12
7. References …………………………………………….... 17
3 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Introduction:
Iowa Paint Manufacturing Company Incorporated, located in Des Moines, Iowa, manufactures paints that are durable, fade resistant, and add lasting beauty. The paints are formulated and manufactured specifically so that they can resist all weather changes in the USA. The company has over 1400 color choices and the paints can be used for interior or exterior purposes to compliment a wide variety of architectural styles. Upon surveying the various processes at the company, our student group was asked to work with the Quality Control department. This department deals with refining paint characteristics such as viscosity, gloss, drying time, and performance under extreme weather conditions. We were asked to help analyze paint viscosity. The company has specifications for final paint viscosity, and their current initial viscosity is below these. To correct this undesirable initial viscosity, Iowa Paint adds A44 (a thickener) in a trial and error method. Our group goal is to help Iowa Paint develop a quantitative method for the addition of A44 in order to obtain a consistent final paint viscosity. This was achieved by analysis (and possible improvement) of viscosity measurement precision and by determining the relationship between the amount of A44 added and the resulting change in viscosity.
Procedure:
Quality control is an important aspect of every manufacturing process. The six- step process-oriented quality assurance cycle presented on page 5 of Vardeman & Jobe (1999) was followed in order to achieve our objective. As our first step, our group attempted a logical analysis of how the paint manufacturing process works. Paint is made in 2000 or 4000 gallon tanks and each batch of paint produced has to go through the quality control department to be checked for appropriateness of all product final quality variables. Quality variables in paint manufacturing include the viscosity, gloss, drying time, etc. After a careful analysis of the manufacturing process, our client seemed to be dissatisfied with initial viscosity values. Initial viscosities tended to be below the required specifications.
4 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Paint manufacturing employs additives and thinners in order to obtain a desired final viscosity. One of the additives that increases viscosity is Hydroxyethyl Cellulose or A44. The company requires final viscosity to be between 95 and 100 Krebs. The group was given quality control cards (Appendix A, pp. 13,14) giving an initial viscosity for each batch of paint produced since June 1998. These cards also give the sizes of A44 additions in pounds for each batch and viscosities measured after these additions. Part of our job was to analyze past data and determine the relationship between amounts of A44 added and the increases in viscosity. But before considering the existing data we considered the issue of measurement precision. This involved both an R&R (repeatability and reproducibility) study and a study of the within-tank variability of viscosity. Repeatability refers to the variation in measurement on a single sample by a single operator and reproducibility refers to the variation between operators on a single sample. The batches of paint analyzed were 98J045 and 98K005. (A batch is represented with a code like ‘98F023' where 98 refers to the year of manufacture, F represents the month, and 023 represents the batch number.) A manual viscometer was used to measure the viscosity of the paint. (See Figure 1.) Each of four group members measured the paint viscosity with the same viscometer and took down two readings. Temperature is a major factor influencing the paint viscosity. At high temperatures, paint tends to be less viscous. In order to be consistent, viscosity is always measured at 77 Fahrenheit. The rotating tool on the viscometer (see Figure 1b) was dipped into the paint up to the line marked on the shaft. Weights were attached to the viscometer and time was kept till the dial on the viscometer rotated 360. A stopwatch was used to record the time. This time was then referred to a standard chart (see Table 1) to calculate the viscosity. The variation in measurements for each group member, and variation which can be attributed to differences between the group members, were calculated using the two-way ANOVA procedure in the Minitab statistical software.
5 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Figure 1a. Paint Viscometer Figure 1b. Rotor
Weight Used (gm)
Secs for 100 revs 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 24 42 52 65 75 83 90 95 99 103 108 25 45 54 66 76 84 90 95 100 104 109 26 47 56 68 78 85 91 96 101 105 110 27 49 57 63 69 74 79 83 86 89 92 95 97 100 102 104 106 109 111 28 51 59 65 70 75 80 84 87 90 93 96 98 100 102 105 107 110 112 29 53 60 66 71 76 81 85 88 91 94 97 99 101 103 105 107 110 112 30 54 61 67 72 77 82 86 89 92 95 98 100 102 104 106 108 110 112 31 55 62 68 73 78 82 86 90 93 95 98 100 102 104 106 108 111 113 32 56 63 69 74 79 83 87 90 93 96 99 101 103 105 107 109 111 113 33 57 64 70 75 80 84 88 91 94 96 99 101 103 105 107 109 112 114 34 58 64 75 84 91 97 102 106 110 114 35 59 65 76 85 92 98 102 106 110 114 36 60 66 76 85 92 98 103 107 111 115 37 61 67 77 86 93 99 103 107 111 115 38 62 68 78 87 93 99 104 108 112 116 39 62 68 78 88 94 100 104 108 112 116 40 63 69 79 88 94 100 104 108 112 116
Table 1. Kreb’s Stromer Chart
In addition to considering repeatability and reproducibility components of measurement precision, the group considered the effects of sampling from different areas of a paint tank. This was done to see if some of the measured variation in viscosity might 6 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568. be attributable to paint inhomogeneity. In this case, five samples of paint from different parts of the tank were obtained for a single batch and were tested for viscosity values. Each group member took two measurements for every sample obtained. An analysis was then done to quantify both repeatability and within-vat variation in measured viscosity. With the establishment of the components of measurement variation, the next step taken was to analyze the historical data given to us. One problem encountered was that the sizes of the batches of paint varied. Some batches were produced in 2000-gallon tanks and others in 4000-gallon tanks. In order to be consistent, the group decided to express A44 additions in terms of pounds per 1000-gallons of paint manufactured. The data on all nine batches are plotted as viscosity versus additions of A44 in Figure 2. (Note that two additions of A44 were made for batches 98J026 and 98K005.)
104
102 Upper Viscosity Specification 100 )
s 98 b e r K (
96 Lower Viscosity Specification y t i s
o 94 c s i 98F117 V
d 92 98G042 e r
u 98G113 s
a 90 98H034 e
M 98H093 88 98J026 98J045 86 98J093 98K005 84 0 2 4 6 8 10 12 A44 Addition (lbs/1000gal)
Figure 2. Plot of viscosity vs. A44 additions for nine batches
From these data one would like to find a single representative slope. In order to do this, the group made use of regression analysis (Appendix A, pp. 15,16) in the
7 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Minitab software. This gives a single representative relationship between amount of A44 added and viscosity increase. (See Figure 3.)
12
10
8 ) s b e r K (
e s a
e 6 r c n I
y t i s o c s i
V 4
2
0 1.19 lb 2.38 lb 3.57 lb 4.76 lb 5.95 lb 7.14 lb 8.33 lb 9.52 lb 10.71 lb 11.9 lb A44 added
Figure 3. Plot of viscosity increase vs. A44 additions for 1000-gallon tank
This graph helps to predict a solution for ‘x’ in an expression such as “add ‘x’ pounds of A44 in every 1000 gallons of paint to increase the viscosity by ‘y’ Krebs”. Table 2 in the Results section also shows the predicted increase in viscosity for each unit of A44 added.
Results:
The Gage R&R study helps to provide an assessment of the sizes of measurement variation from various sources. The estimated standard deviation in viscosity measurements for a particular group member on a single sample is referred to as
repeatability. Similarly, the variation in viscosity measurements that exists among the group members is referred to as reproducibility. The repeatability and reproducibility measures were 8 ^ Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568. ^ ^ ^ obtained by using the Minitab software and Equations (1) and (2) respectively (Appendix A, pp.17).
^ (1) repeatability MSE
^ 1 1 reproducibility max0, MSB I 1MSAB MSE (2) mI m (Vardeman & Jobe 1999, pg.27)
^ Calculation using the data for batches 98J045 and 98K005 resulted in repeatability equal to ^ 0.25 Krebs and reproducibility equal to 0.327 Krebs. This gave us estimates of components of measurement variability both within and between different operators. Similarly, based on the samples from a single new batch of paint (not of the same ^ ^ type as those used in rest of our study), repeatability and locations were calculated to assess the variation in paint viscosity between different areas of the paint tank. During this part of our study we had to switch to a different type of paint due to the unavailability of Satin Acrylic paint on the specific day of this study. Rather than estimating R&R exactly as in Vardeman & Jobe, we concentrated on repeatability and location-to-location (“part-to- part”) variation. That is, variation between operators is quantified as in Equation (3).
2 2 (3) operators for the model (2.1) of Vardeman & Jobe (1999). Variation between locations in the paint tank is quantified as in Equation (4).
2 2 (4) locations
We estimated the within-paint tank variation using Equation (5).
9 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
1 1 max 0, MSA J 1 MSAB MSE (5) ˆ locations mJ m
This analysis provides us with an important insight into the current situation. ^ ^ repeatability for the second set of measurements was 0.612 Krebs and locations was 0.922 Krebs (Appendix A, pp.18). This implies that contrary to the company’s belief that paint tanks are homogeneous, there may be significant inhomogeneties. These inhomogeneties maybe as much as 1.5 times as large as the repeatability variation (for a single operator re-measuring the same sample). Our next step was to analyze the historical data provided by the company. Recall that the viscosity data for the nine batches of paint given to us are shown in Figure 2. A regression analysis was done, and a value of 1.19lb of A44 was found to be the amount to be added to a 1000-gallon tank for an increase of 1 Kreb in mean viscosity. Formulas were then derived for each size of paint tank used by Iowa Paint Manufacturing Co. and are as below:
In the following equations, y = pounds of A44 and x = desired increase in viscosity (Krebs) Thus, For a 1000 gallon tank: y 1.19* x (6) For a 2000 gallon tank: y 1.19* 2x (7) For a 3000 gallon tank: y 1.19*3x (8) For a 4000 gallon tank: y 1.19* 4x (9)
Table 2 was constructed to give a general idea of the amount of additive for increases of up to 10 Krebs. 10 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Desired Increase (Krebs) A44/1000 gal A44/2000 gal A44/3000 gal A44/4000 gal 1 1.19 lb. 2.38 lb. 3.57 lb. 4.76 lb. 2 2.38 lb. 4.76 lb. 7.14 lb. 9.52 lb. 3 3.57 lb. 7.14 lb. 10.71 lb. 14.20 lb. 4 4.76 lb. 9.52 lb. 14.20 lb. 19.04 lb. 5 5.95 lb. 11.9 lb. 17.85 lb. 23.8 lb. 6 7.14 lb. 14.20 lb. 21.42 lb. 28.56 lb. 7 8.33 lb. 16.66 lb. 24.99 lb. 33.32 lb. 8 9.52 lb. 19.04 lb. 28.56 lb. 38.08 lb. 9 10.71 lb. 21.42 lb. 32.13 lb. 42.84 lb. 10 11.9 lb. 23.8 lb. 35.7 lb. 47.6 lb.
Table 2. Amounts of A44 to be added to produce various increases in viscosity for tanks of various sizes
Table 2 and Figure 3 are easy to understand and the following example illustrates how to read and interpret the table. In a 2000-gallon tank, a desired change of viscosity from 90 to 95 Krebs would imply that there is a desired increase of 5 units. Looking across the 5 Kreb row and down the 2000-gallon column gives a value of 11.9 lb. of A44. Therefore, in order to increase the viscosity by five units, we would add 11.9 lb. of A44. Figure 3 shows a plot of values from Table 2 for the 1000-gallon tank. Similar graphs were plotted for 2000-gallon, 3000-gallon, and 4000-gallon tanks (Appendix A, pp. 19,20). The regression analysis that produced the “compromise slope” value of 1.19 also suggests that Iowa Paint’s current measurements (as measures of mean vat viscosity) have a standard deviation of around 1.524 Krebs. From our analysis of the R&R and within-vat variation, we see that improved measurements would help Iowa Paint make appropriate A44 adjustments. “Repeatability ” can be dealt by taking several measurements per sample and averaging them and “reproducibility ” can be dealt with by elimination of multiple operators in the measurement process. Additionally, “within- vat ” can be dealt with by taking paint samples from several locations in a vat and mixing them.
Conclusion:
11 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Quality of Conformance has to do with living up to the specifications laid down in the design of a product. It is concerned with small variation from what is specified or expected. It is a fact of life that variation tends to make goods and services undesirable. (Vardeman & Jobe 1999, pg.2). The analysis of this project gave an insight into the different factors producing variability in viscosity measurements. From our data and calculations, we can see that there can be a significant difference in measurements if different people do them. Our analysis also points out that there is a difference in measurements when sampling paint from different areas of a tank. As stated before, the goal of this project was to help produce paint viscosity within the specification limits. This project proved to be successful since our group was able to derive the appropriate amount of A44 to be added to achieve a desired viscosity level.
Recommendations: We recommend our client make sure that a single person does the paint viscosity measurement. The client may also consider sampling from different parts of the paint tank and mixing samples before testing to make them more reliable in representing the tank average. Averaging several viscosity measurements can combat repeatability variation. These steps may considerably improve measurement precision and allow better adjustments using Equations (5), (6), (7), (8) and Table 1. This would help decrease time and money wasted in trial and error viscosity adjustments.
12 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Appendix A
13 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
14 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
15 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Data
Batch A44 added Viscosity 1 0.00 91 1 6.25 102 2 0.00 92 2 6.25 100 3 0.00 93 3 5.00 100 4 0.00 91 4 6.25 98 5 0.00 85 5 10.00 97 6 0.00 88 6 6.00 96 6 7.50 98 7 0.00 86 7 10.00 100 8 0.00 89 8 7.50 96 9 0.00 90 9 7.50 95 9 9.50 97
For i = 1,2, … , 8
1 if measurement is on sample i zi 0 otherwise
16 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Regression Results
The regression equationvisc = 87.3 is + 1.19 - 2.21 added z5 + +
Predictor Coef StDev T P Constant 87.282 1.019 85.620 0.000 added 1.186 0.091 13.040 0.000 z1 5.513 1.410 3.910 0.003 z2 5.013 1.410 3.560 0.005 z3 6.254 1.420 4.400 0.001 z4 3.513 1.410 2.490 0.032 z5 -2.210 1.392 -1.590 0.144 z6 1.383 1.249 1.110 0.294 z7 -0.210 1.392 -0.150 0.883 z8 0.772 1.402 0.550 0.594
S = 1.524 R-Sq = 95.1% R-Sq(adj) =
17 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Data for R&R Batch Batch 98J045Operator Viscosity 98K005Operator Viscosity 1 95 1 99 1 95 1 99 2 96 2 99 2 95 2 99 3 95 3 99 3 95 3 99 4 96 4 99 4 96 4 99
Two-Way Analysis of Variance for R&R Source DF SS MS parts 1 52.5625 52.5625 MSA operator 3 0.6875 0.2292 MSB Interaction 3 0.6875 0.2292 MSAB Error 8 0.5000 0.0625 MSE Total 15 54.4375
MSE 0.25Krebs ˆ repeatability
1 1 max(0, MSB I 1MSAB MSE) 0.327Krebs ˆ reproducibility mI m
18 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Data for Within- Vat Locations Calculatio #1 #2 #3 #4 #5 1 101 100 101 100 101 1 102 100 101 99 102 2 101 100 102 99 103 Operator 2 101 101 100 99 102 3 102 100 101 100 102 3 101 101 101 99 102 4 101 100 100 99 102 4 101 101 101 100 102
Two-Way Analysis of Variance for Within-VatSource DF SS MS CalculationsLocations 4 30.850 7.713 MSA Operator 3 0.275 0.092 MSB Interaction 12 2.350 0.196 MSAB Error 20 7.500 0.375 MSE Total 39 40.975
MSE 0.612Krebs ˆ repeatability
1 1 max(0, MSA J 1MSAB MSE) 0.922Krebs ˆ locations mJ m
19 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Plot of viscosity increase per pound of A44 added for 2000-gallon tanks
12
10 ) s b
e 8 r K (
e s a e
r 6 c n I
y t i s 4 o c s i V 2
0 2.38 4.76 7.14 9.52 11.9 14.28 16.66 19.04 21.42 23.8 A44 added
20 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Plot of viscosity increase per pound of A44 added for 3000-gallon tanks
12
10 ) s b
e 8 r K (
e s a e
r 6 c n I
y t i s
o 4 c s i V
2
0 3.57 7.14 10.71 14.28 17.85 21.42 24.99 28.56 32.13 35.7 A44 added
21 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
Plot of viscosity increase per pound of A44 added for 4000-gallon tanks
12
10 ) s b e 8 r K ( e s a e
r 6 c n I y t i s
o 4 c s i V 2
0 4.76 9.52 14.28 19.04 23.8 28.56 33.32 38.08 42.84 47.6 A44 added
22 Viscosity Analysis By Ruchi Patnaik, 116 ½ Welch Ave. #1, Ames, IA. 50014. Phone: (515)-292-2568.
References: Vardeman S.B. and Jobe J.M. Statistical Quality Assurance Methods for Engineers. John Wiley & Sons, Inc., 1999.
Acknowledgements:
Stephen B. Vardeman, Professor, Iowa State University, Ames, IA. Mark Angerer, Technical Director, Iowa Paint Manufacturing Co., Des Moines, IA. Piyanka Roy, Group Member, Iowa State University, Ames, IA.
Key Words: Gage R&R study, within-tank variation, regression analysis, 2 way ANOVA, Hydroxyethyl Cellulose, quality improvement.
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