n the three previous articles we discussed the importance of quality control and the theories of densitometry and colorimetry. In this article we will expand on the application of densitometry as a tool for statistical process control, and on the next we’ll deal with colorimetry.

Measuring the Process
Densitometers and colorimeters are the most commonly used devices for measuring applications. Most of them offer the capability of measuring both density and color with one reading, sampling wavelengths at fixed intervals (5 nm, 10 nm, or 20 nm) across the visible spectrum, and gathering spectral data that are then converted either to one of the status densities or to colorimetric values.

The measuring instruments need to be checked for their accuracy and precision. Each device includes some variation, even when it reads the exact same spot. This is expected, and the degree of variation is specified by the manufacturer. However, the device needs to be periodically calibrated, and its conformance to the manufacturer specifications for density and color needs to be verified. At shops that have more than one device of the same manufacturer, or devices from more than one manufacturer, assuring the proper functioning of each one and, more importantly, the agreement between the measurements of different devices is more complicated. Depending on the optics, the reading might differ from device to device. This means that the same process might be deemed conforming when measured with one device and not conforming when measured with another. To verify the instrument agreement of multiple devices, one common practice is to use standardized patches and measure them with each device to see if they agree. If they do not, then the difference between the devices needs to be determined so that it is not an unknown. If offered by the manufacturer as an option, devices can be calibrated to match the readings of other devices. Finally, each device should be set to the same metrology specifications, in terms of status density, illuminant, and standard observer.

Then, it is important to have measurement targets. It is unlikely that the graphics of every production job will include areas that can be measured for process control. Most commonly, there are areas of the sheet where color patches can be placed, like the edge or trail end or in areas like glue flaps as is commonly done in the corrugated industry. These patches should include solid ink patches, tints, overprints between two colors, and grey balance targets, and they should be placed consistently on the same areas. In this manner, variation due to spatial differences can be eliminated. Apart from the above mentioned targets that refer to color and density, there are other targets that measure other attributes of the production like slurring and doubling. These are equally important in determining whether there is a mechanical problem affecting the process.

The Use of Process Control Targets
In order to be able to manage a process, it is fundamental to be able to establish certain targets values that would provide an aim point and determine the compliance of the production. Lacking such targets allows for a great degree of ambiguity. Let’s assume that a certain operator is trying to match a color proof that is supplied by the customer and has no color or density targets for the individual colorants. The efforts of that operator would then involve a great deal of trial and error, with numerous empirical adjustments to the amount of ink being laid on the paper, until the production results in an acceptable color match. Furthermore, if the particular job is going to be reprinted at a later time, unless there is a process by which the production values are communicated to the press and the operator aims for them, it would take the same amount of trial and error to get to color. This is translated in waste, downtime, and since repeatability depends on empirical adjustments, a fair chance of actually selling product that does not have the desired color.

Target values provide a criterion by which conformance can be evaluated. For this to occur, the process needs to be part of a color-managed workflow that examines all the elements of the production, starting from prepress and ending at the press. The end result of a color-managed workflow is the color of a proof to be matching the color of the press, taking into account the amount of ink that is being laid down by each device, color corrections for the differences in colorants, and the overprinted color of the inks. If all these are set in order, a deviation of the production from the target values would mean that the color is not matching and would provide an indication of a possible non-conformance. In such a case that production deviates from the target values, it would be easy to measure all the elements and determine what the cause of the deviation is. Furthermore, having measurable targets provides the necessary information, that we need 4 percent more cyan on the midtones, than “a little more blue.”

The next question is which target values to set. It would be rare to have an operation that would rely exclusively on its own internal resources for color management. More often than not, a proof that was created externally with specifications unknown to the printer would be brought to press to serve as a color target. Likewise, in a competitive environment, it is also likely that a press sheet printed at another press would provide the color target. If such operations do not conform to the same set of standards or specifications, then matching color would be a problem. For this reason, the industry is working diligently in providing industry-wide specifications and calibration methodologies to which all the printers and prepress houses could conform. If two proofs are generated at two different prepress houses that have adhered to the same specifications, then the color of these proofs would match.

The most commonly used industry standard has traditionally been density, relying on the work of industry organizations that have provided certain aim values for densities that were gathered from press runs. Lately, however, it has been realized that even if density provides a convenient means of measuring the process, it doesn’t contain any information on the color of the inks being used. If two printers use inks that have been made with different pigmentation and have different hues, their color output on the same stock would not match, even if both achieve the specified density targets.

For this reason, ISO is standardizing both the colors of the inks under the 2846 series of international standards and their reproduction on different substrates based on the 12647 series. The ISO 2846 series for “Graphic technology -- Colour and transparency of printing ink sets for four-colour printing” has the standards for gravure publication and flexographic inks under parts 3 and 5 respectively. ISO 12647 series for “Graphic technology -- Process control for the production of half-tone colour separations, proof and production prints” deals with the standards for gravure and flexography under parts 4 and 6 respectively. The fact that ISO creates international standards for the various segments of the printing industry allows for color conformity to be achieved in every part of the world!

A matter that still remains controversial is how to calibrate the process in order to have a proof-to-press match and then control it. The traditional approach has been to rely on achieving a target density and dot gain. Lately however, the work of GRACoL (General Requirements for Applications in Commercial Offset Lithography) has provided an alternative approach. This methodology relies on achieving the ISO ink color and then making curve adjustments in prepress to achieve grey balance of the cyan, magenta, and yellow overprint. The assumption is that once the colorants are grey balanced, the printed output is optimized for the particular set of colorants, and that two grey-balanced sheets would have a visual match. This means that the industry is using colorimetry both to set target values for the color of the inks and to control the process by measuring the color difference of the reproduced neutral grey. This work that started from offset lithography is finding its way in the flexographic and gravure printing processes.

Density takes a less predominant role, even though it can still be used for process control. Assuming that the conformance of the process has been established through colorimetry and the density that results in the color of the ISO standard has been achieved and measured, it could then be communicated as a process parameter control and be measured throughout the production.

Every printing process has its own inherent variation. Expecting to be able to hit the exact same target values for every impression is impossible. Instead, the process should be able to conform to a range of densities or color for the entire production. The challenge here lies in establishing a compromise between what is achievable by the process and acceptable by the customer. Towards this direction, statistical process control tools should be used in order to gain insight and improve the process.

Defining the Capability of the Process
The capability of the process can be assessed either through densitometry or colorimetry, each offering distinct advantages. Density would provide a one-dimensional set of measurement data that would fit into any statistical analysis, but would not provide information that necessarily correlates with human vision, and, thus, it would not be accurate in terms of specifying compliance to visual standards of acceptability. It would be useful, however, in shedding light into the variation of the process. On the other hand, colorimetric measurement data are on a three-dimensional space, and, therefore, they are not practical in terms of understanding the process. Moreover, color difference data measurements are skewed, and, thus, normal parametric statistics cannot be used without certain assumptions.

Process Control Charts
In this section we will provide examples of charts that allow insight into the process. The measurements come from a random production run on a UV sheetfed press with hybrid inks, but they can be used for the other printing processes. It should be noted that the values are only used as an example, and we will not provide the causes of the displayed variation. The measurements can be see, and variation across the printed sheet.

Table 1: Temporal measurements of process colors

One of the main applications where density can be useful is for charting the temporal variation of the printing process. Sheets are picked from the printed load or the delivery end of the press and measured on the same spot so that no bias due to spatial variation is introduced in the measured population. The sampling process could be either every given number of sheets, or over fixed time intervals. Figure 1 offers an example, with a measurement of a single patch for the cyan, magenta, yellow, and black inks.

Figure 1 is the most basic form of charting temporal variation. It has a main drawback since the density where each ink is running is different, and scaling all the inks in the same plot can be misleading as any variation is obscured. Instead, it would be more useful to get the average of the measurement data and chart density as the variation from the average, as is shown in Figure 2. In this case, the average of the measurements is set to zero, and each subsequent measurement is plotted with a negative or positive value from the average.

Figure 1

In Figure 2 it makes sense to include information regarding tolerances, and this is the purpose of the two red lines set at 0.05 density points above and below the average density of each ink. The definition of the tolerance usually depends on the job or the customer, or there can be a tolerance limit that is used as a default. As noted, density tolerances are not being used for evaluation of conformance of the end product, at least from an industry or acceptability standpoint, since they do not correspond to visual perception. They can still be used, though, for the evaluation of the variation of the process. In this case, a variation of plus-minus 0.05 points means that the density has a range of 0.10 points. Being able to measure the temporal variation over a number of jobs would allow a printing company to realize the common density range of its process, and set density tolerances that correspond to its own production line.

Figure 2

In doing so, however, an important consideration needs to be made. There are two types of variation—systematic and unsystematic. Systematic variation refers to inherent variation, to variables that are constant and expected to affect every production run. Unsystematic variation refers to causes that occur due to a reason external or unexpected throughout a production run and can and should be avoided. These types of variation should be distinguished when analyzing measurement data and any unsystematic causes should be excluded from the definition of tolerances. Rather, they should be investigated so that the causes of the variation are found and eliminated.

Once the density tolerances are set, the information in figure 2 would allow us to determine if the overall process was conforming or not. In this case, the nine sheets that were measured are for the most part within tolerance. However, during the first two measurements we can see that the densities of the magenta and cyan inks are overall higher and then they gradually decrease. This appears to be normal as the measurements follow a trend. The cyan ink reaches equilibrium and stabilizes throughout the rest of the process. However, the magenta ink has a significant drop in density towards the end of the process and then it comes back within tolerance. Such a drop in density can only be attributed to an unsystematic cause; something happened during that time on the magenta unit that caused the magenta density to drop.

Figure 3

Even if figure 2 can be useful in providing insight into the variation of the process, the average density of the run might not be within the tolerances of the target density. This can be determined by subtracting the target density from the measured densities, as seen in Figure 3. Even if the production run was for the most part within acceptable tolerances, it didn’t meet the target densities. The black ink was printed at a higher density, and the yellow at a lower density. The cyan ink fell within the target density range, and the magenta would have been within tolerance if not for that unsystematic cause that affected its reproduction.

The question now becomes how much of a problem is it that the process doesn’t conform to the target densities. Are the densities set at the wrong target value, or was there something related to the particular job? It is possible that there was something affecting the press that didn’t allow the production to run at target densities; maybe the pH of the inks was not optimized, or the cleanup of the unit was not proper. This is an example of having known and measurable operating conditions that, if measured systematically, can be assessed to determine if there is an unsystematic error. Usually, such factors should be examined first, as they introduce bias to the system that need to be eliminated. If, however, no non-conformances are found, it is likely that the graphics of the job in question didn’t allow the production to be within normal density range or that the operator needed to run at different densities in order to match the proof color. In such a case, the job can be adjusted through editing the digital file or applying different plate curves that would accommodate between the differences of the production run and the proof.

These considerations, though, lead to corrective actions that affect the color management of the workflow in its entirety. If the majority of the jobs are found to be within the same densities, then either the target can be adjusted to match the usual production targets or the amount of compensation applied through prepress can be adjusted to shift the achievable densities to the known target values. If, on the other hand, it is found that each production run falls within different densities, then either the tolerances need to be widened or it means that there are a number of different causes that affect each production run, resulting in a moving target.

Dot gain is another metric that provides insight into the process, and it can be found useful for an evaluation of the compensations of prepress as well as the inks’ rheology. Figure 4 displays the measurements of dot gain associated with each reading. It can be seen that dot gain is within tolerance even if density, at the same impression, was out of tolerance. This could mean that, since dot gain is a relative measure that doesn’t include an absolute value but a percentage of the solid patch, its increases and decreases were stable relative to density fluctuations, but the rheology of the inks remained stable.

Figure 4

The other type of variation present in a printing process is spatial variation, relating to the difference in the amount of ink being laid down across the sheet. Temporal variation can be assessed by measuring patches from the far left to the far right of the sheet. It is useful to measure more than one sheet, because differences in density from left to right can be corrected throughout the run, but for our purposes one example of such a graph would be enough.

Observing Figure 5, we can see that the inks have a different behavior. Black and cyan are balanced, but the magenta is printing unevenly on the left position, and the yellow is uneven from left to right. Depending on the process, there might be different reasons for either of these effects. It is likely for example, that the anilox rolls of the yellow unit in flexography are out of parallel. Similar information can be measured and plotted for dot gain.

Figure 5

It is also frequent that both density and dot gain information should be evaluated as they deal with different aspects of the process. It is frequent that a production run might be meeting the specified target densities, but failing to match the color of the visual target. It might well be that the ink rheology, or some other factor, impacts exclusively dot gain affecting solely the reproduction of the midtones, highlights, or shadows, while the solid coverage areas are matching. Relying only on density would not provide the necessary information to achieve color.

A more general approach to evaluate the entire process would be to plot the inks’ densities as a histogram, counting the frequency of each occurrence over a specified range. In Figure 6, the example is of a single ink measured throughout a production run. As we can see, more than half of the measurements are within the 1.36 – 1.40 density range, with an average of 1.38 density points.

Figure 6

A numeric approach to evaluate a process would be to measure its standard deviation. In this case (example from Ink A in Table 2), the standard deviation is 0.04. This means that 68.2 percent of the measurements are within 0.04 density points of the average, 95.45 percent was within two standard deviations of the process, or 0.08 density points, and 99.73 percent within 3 standard deviations, or 0.12 density points. As we can see from the histogram or Table 2, the lowest density was 1.26, 0.12 points from the average. Another important consideration is that standard deviation measures the spread of the variation in either direction of the mean. This means that unless examined more analytically, the nature of the variation cannot be understood. In our example, the variation is mostly towards lower density values, information that would be lost by this general approach.

Finally, our discussion on densities should include the analysis of statistical measures that attempt to provide an overall measure of variation in the measured data. Since density has a normal distribution, standard deviation and other normal distribution statistics become very useful. For our example, we are going to use two inks (Table 2), that both were printed with the same average density (1.38 points), and their tolerance was ± 0.05 points. It is obvious that ink B had less deviation than ink A; the question is whether the amount of variation and deviation from the average density of 1.38 indicates a consistent process. The standard deviation metric differs significantly between the two inks. 68.2 percent of ink A was printed within 0.04 points from the tolerance limit; this means that the rest of the production didn’t meet the specified tolerances. Ink B on the other hand, had a much smaller spread during its reproduction, with 68.2 percent of the measurements being within 0.01 density points, as indicated by its standard deviation.

Some useful metrics that are commonly used in statistical process control applications and are based on standard deviation are Cp and Cpk. Cp measures the precision of the process, focusing on the variation of the measured data and disregarding the target value (in this case the average of the process is the same as the target density). Cpk measures the accuracy of the process, taking into account both the target density and the established tolerance limits. A value of 1.33 for either metric is usually thought to signify a very capable process, but a process with a Cpk higher than 1.00 can also be considered acceptable. Cp and Cpk are estimated by the following equations.

Cp = (USL - LSL)/6*Std.Dev
Cpl = (Mean - LSL)/3*Std.dev
Cpu = (USL-Mean)/3*Std.dev
Cpk = Min(Cpl,Cpu)

As we can see in Table 2, Cpu and Cpl provide insight as to the nature of the deviation from the mean, with the lower value indicating a less capable process. Ink B has been reproduced far more consistently, both in terms of variation from its average, and deviation from a target density. A Cpk measure of 1.25 indicates a very capable process. Ink A, on the other hand, was printed inconsistently, having a Cp value of 0.4 and a Cpk value of 0.36.

Table 2: Average, standard deviation, Cp and Cpk

Conclusion
Hopefully we have provided a good number of examples on how density can be used to provide insight on a process. The graphs, tables, and statistics discussed are the basic tools for statistical process control, but any number of other tools can be used for more complicated evaluations. The fact that density is normally distributed around an average is indeed helpful in that manner. in the next article, we will cover the use of colorimetry for the same purposes and see the manner it can be utilized for statistical process control, as well as the added value it offers.

About the Author:
Dimitri Poumidis finished his Master of Science in Print Media from the Rochester Institute of Technology, with a concentration on Color Science. His thesis dealt with the consistent reproduction of spot colors. During his studies, he worked in the Color Management System’s labs at the School of Print Media and did an internship with Graphics Microsystems. Upon graduation, Dimitri moved to California to work for Pacific Southwest Container as a Color Assurance Engineer (www.teampsc.com). Prior to his studies at Rochester, he completed a Bachelor’s of Science in Marketing in Greece, and worked as a printer, designer, and photographer.

Please, submit any comments, questions, or topics you would like to discuss on printcolor.blogspot.com under the post of the respective article. Dimitri can also be contacted on dxp3756@gmail.com.

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