STATISTICS AND PRINTING: APPLICATIONS OF SPC AND DOE TO THE WEB OFFSET PRINTING INDUSTRY. A Project. Presented. to the Faculty of

Transcription

1 STATISTICS AND PRINTING: APPLICATIONS OF SPC AND DOE TO THE WEB OFFSET PRINTING INDUSTRY A Project Presented to the Faculty of California State University, Dominguez Hills In Partial Fulfillment of the Requirements for the Degree Master of Science in Quality Assurance by Craig P. Paxson Fall 1993

2 Copyright by CRAIG P. PAXSON December, 1993 All Rights Reserved

3 PROJECT: STATISTICS AND PRINTING: APPLICATIONS OF SPC AND DOE TO THE WEB OFFSET PRINTING INDUSTRY AUTHOR: CRAIG P. PAXSON APPROVED: E. Eugene Watson, Ph.D. Project Committee Chair Milena Krasich, P.E. Committee Member William Trappen, P.E. Committee Member

4 iv TABLE OF CONTENTS Page Chapter 1: Introduction...11 TQM/SPC in Printing...11 SPC...12 DOE...12 Process Capability...13 Measurement Science...13 Chapter 2: Statistical Process Control...15 Fundamentals of SPC...15 Basic Theory of Control Charts...15 Terminology...16 Types of Control Charts...17 Rational Subgrouping...17 Steps in Implementing SPC...18 Setting up a Control Chart...19 Reacting to Out of Control Conditions...19 Shewhart Control Charts...20 Pattern Analysis...20 Variables Control Charts...26 Introduction...26 X-bar and R Charts...26 Individuals Charts...34 Attributes Control Charts...36 Introduction...36 Sampling Plans...37

5 v Fraction Nonconforming - p-, np- Charts...37 Nonconformities - u-, c- Charts...42 Advanced Control Charts...46 Short-Run SPC...46 Data Normalization...47 Nominal...47 Target...48 Short Run...48 X-bar and R Charts...49 PRE-Control...55 Introduction...55 Construction...55 Use of PRE-Control...57 Potential Applications...58 Conclusion...59 Chapter 3: Design of Experiments...61 Introduction...61 Fundamentals of DOE...61 Terminology...61 Steps in Design of Experiments...62 Statistical Analysis...65 One Way ANOVA...65 Two Way ANOVA...66 Graphical Analysis...67 Main Effect Plots...68 Interaction Plots...69

6 vi One Factor Experiments...70 Factorial Experiments...72 The Taguchi Methods...73 Introduction...73 Limitations...75 Orthogonal Arrays...75 Linear Graphs...76 Assigning Factors...77 Analysis...79 L12 No Interactions...81 S/N Ratios...82 Parameter Design...83 Conclusion...87 Chapter 4: Process Capability and Measurement...88 Introduction...88 Process Capability...88 Definitions...89 Process Capability Using a Histogram...89 Estimating Natural Process Limits...90 Process Capability Ratios...91 Potential Applications...92 Measurement Science...93 Definitions...93 Gage Repeatability and Reproducibility...94 Conclusion...99 Chapter 5: Conclusion...100

7 vii Appendix 1 - Tables for Control Limits Appendix 2 - Taguchi Experiment Tables Appendix 3 - GR&R Forms Bibliography...108

8 viii LIST OF TABLES Table Page Table 1. X-bar and R Chart Example Data...32 Table 2. Individuals Chart Example Data...35 Table 3. p-chart data...39 Table 4. Holes/Plate Example Data...44 Table 5. Nominal Short Run Example Data...50 Table 6. Short Run Example Data...53 Table 7. One-Way ANOVA Table...65 Table 8. Two-Way ANOVA Table...67 Table 9. One Factor Experiment Example Data...71 Table 10. One Factor Example ANOVA Table...72 Table 11. L4 Array...76 Table 12. Interaction Table...76 Table 13. Sum of Squares example table...80 Table 14. L8 ANOVA Table example...81 Table 15. Parameter Design Arrays...85 Table 16. Parameter Design Example Data...86

9 ix LIST OF FIGURES Figure Page Figure 1. Out of Control Condition # Figure 2. Out of Control Condition # Figure 3. Out of Control Condition # Figure 4. Out of Control Condition # Figure 5. Non-Random Pattern...25 Figure 6. X-bar and R Chart Example...33 Figure 7. Individuals Chart Example...36 Figure 8. Plate Defect p-chart...40 Figure 9. Plate Defect np-chart...42 Figure 10. Holes/Plate Example u-chart...45 Figure 11. Nominal Example X-bar chart...51 Figure 12. Short Run X-bar and R Chart...54 Figure 13. PRE-Control Chart...56 Figure 14. Example PRE-Control Chart...59 Figure 15. Main Effect Plot...68 Figure 16. Interaction Plot...69 Figure 17. Interaction Plot...69

10 ABSTRACT The printing industry has recently had an explosion of interest in Total Quality Management (TQM) and Statistical Process Control (SPC). Printers are beginning to realize the positive effects that statistical tools such as SPC can have on quality and productivity. This paper will present ideas on applying the statistical tools of SPC and Design of Experiments (DOE) to the web offset printing industry. The paper is not intended as a primer on the theory or mathematics involved in the tools; rather it is a treatise on applying SPC and DOE to the printing industry. Hopefully, the reader will garner new ideas for statistics in printing, or be excited at the possibilities of using SPC and DOE in the industry.

11 11 CHAPTER 1: INTRODUCTION TQM/SPC in Printing The printing industry has experienced a Renaissance in the last several years in regards to quality. This growth in interest was spurred on by the intense competition in the industry, and included a growth in interest in Statistical Process Control (SPC). Many printing companies have decided to implement Statistical Process Control, especially Shewhart Control Charts. Unfortunately, in many cases the technical knowledge of statistics was not present, leading to control charts that were invalid or misleading. This project will present statistically correct methods of using SPC and Design of Experiments (DOE) in the web offset portion of the printing industry. Potential applications, examples, and proper use of the tools of SPC and DOE will be presented. The paper will be beneficial to anyone in the industry who is interested in increasing quality and productivity, and decreasing costs. This paper will not thoroughly cover statistics, rather it will show how to use statistics, SPC and DOE for gain in the printing industry. Several good primers for statistics, SPC and DOE are listed in the bibliography.

12 12 SPC Statistical Process Control will be covered from an applications standpoint. Basic introduction to the control chart, including basic theory, subgrouping and pattern recognition will be presented, followed by examples and application for the major control charts. The term SPC has become almost a non-word in the last several years. The addition of other tools besides the control chart, and in some cases a certain style of management, has made the term SPC different to many. In this paper, SPC will be addressed as control charts only. Other problem solving tools, such as Pareto analysis, cause and effect diagrams, etc. and styles of management, such as continuous improvement and TQM, will not be covered as a part of paper. Control charts are a tool that can be used with any style of management, although their effects may be greatly enhanced when combined with other problem solving tools and proper management. Further study and in-depth discussions of control charts may be found in any one of the books listed in the bibliography. DOE The next chapter describes Design of Experiments, a relatively new field in printing. Both the classical and

13 13 Taguchi design will be presented, again with the emphasis on applications of DOE to printing. The Taguchi method, no matter how controversial, is easily implemented and understood, and will be presented as the main experimental tool. The use of inner and outer arrays has great application to printing, where many factors cannot be readily controlled. The theoretical discussion of DOE, and texts on the statistical methods (ANOVA, etc.) may be found in the books listed in the bibliography. Process Capability Process Capability will be addressed in the last chapter. An understanding of the tools presented in the first two sections should enable the reader to use this format to improve and maintain his process. Process capability enables printers to measure how changes in the process compare to internal or external specifications. Measurement Science SPC and DOE are based on measurements, and for these tools to be useful the measurements must be valid. Measurement Science deals with the process of taking measurements so they are accurate and repeatable. The last

14 14 chapter will show easy ways of conducting Gage Repeatability and Reproducibility (GR&R) studies, the main tool of measurement science.

15 15 CHAPTER 2: STATISTICAL PROCESS CONTROL Fundamentals of SPC The term Statistical Process Control can be defined by defining its three component words. The word statistical means "having to do with numbers" or "drawing conclusions from numbers." A process is any system of causes, a combination of conditions which create some output. Control means "to make something behave the way we want it to behave (AT&T, 1984)." Putting these three terms together, and applying it to printing, we find that statistical process control means that with the help of numbers, we study our process in order to make it behave the way we want it to behave (AT&T, 1984). It is this use of numbers that is the key to statistical process control. Making changes to the process is not difficult - but it is the statistics that tell us when to make a change, or how much of an effect our changes are having on the process. Basic Theory of Control Charts The fundamental theory of control charts is based on the fact that everything varies, but varies in some way that is predictable. For instance, solid ink density varies, but it has some point it varies around, and some amount of

16 16 spread from that point. Statistics can provide us with the knowledge of that point, how much spread there is, and the chances that the density will stray from that point. Terminology Chance and Assignable Causes. The factors that affect the set point and the spread are divided into two groups - chance and assignable causes. These terms were coined by Walter Shewhart (the inventor of control charts), and modified by W. Edwards Deming. Chance causes are those causes that randomly appear and make the process behave in some random, unpredictable pattern. Such "chance" variation is relatively stable over time, because it is the result of many contributing factors. Assignable causes are those causes that sporadically appear and have impact on the process. These factors are identifiable, and can be assigned the deviations that they cause. Statistical Process Control charts help us to differentiate between these "chance" and "assignable" causes of variation by using charts that show what the chance variation should look like. Once we have identified variation that is not caused by chance causes, we can learn what caused the variation, and eliminate it from the process, thus improving the process.

17 17 Attribute. Attribute data is characterized by counts, such as number or percentage defective, number of defects, etc. Variable. Variable data is characterized by measurements on a continuous scale, such as length or weight. Subgroup. A sample of more than one individual from a process is called a subgroup. Control limits. Control limits are lines drawn on a control chart that define a band of allowable variation in the process. Statistical Control. A process is in a state of statistical control if it exhibits only random variation. Types of Control Charts Control charts can be divided into two main classes, attributes and variables control charts. Attributes control charts are based on definite numbers, such as percentages or counts. They include p-, np-, c- and u-charts. Variables control charts, such as X-bar and R, are based on measurements. Rational Subgrouping One of the most important concepts in SPC is the concept of subgrouping. Since most of the charts are based on statistics from some set of numbers, how those numbers

18 18 were arrived at is extremely important. This concept is known as subgrouping, and properly chosen subgroups are said to be rational subgroups. Proper determination of sample sizes varies for each type of control chart and will be discussed further in each section. Steps in Implementing SPC Statistical Process Control is a major part of any quality program, including Total Quality Management. Because of its complexity, steps must be taken to ensure it is implemented correctly. Some potential problems that must be addressed are the measuring system, who will plot the chart and calculate the control limits and who will interpret the chart. Training these personnel must be a key part in any SPC program. Generally, steps that need to be taken include the following: 1. Training. Personnel must be trained in their part of the charting process. Calculating control limits, plotting points and interpreting the charts may all be done by different people, but they must understand their part. 2. Measurement. The measurement system must be in good working order. The measuring devices must be appropriate and accurate, the personnel making the measurement must be

19 19 trained properly. Evaluating the measurement system is described in detail in the fourth chapter. 3. Setting up the control chart. Steps in setting up a control chart are described in the next section. Setting up a Control Chart Specific steps must be taken in setting up any control chart. Following these steps will increase the value of the control chart. 1. Determine the characteristic to measure. 2. Choose the type of control chart. 3. Determine sample size and sampling frequency. 4. Collect data for 20 to 25 subgroups. 5. Calculate trial control limits and check for control. 6. Exclude subgroups with assignable causes and recalculate control limits. If an assignable cause cannot be found for a certain subgroup, do not exclude its data. Repeat this process until all out of control subgroups with assignable causes are not used. 7. Plot new data as it is generated and monitor control. 8. React to out of control conditions. Reacting to Out of Control Conditions Once an out of control condition is identified, steps must be taken to identify and eliminate the cause. The true power of SPC in improving processes is by eliminating

20 20 assignable causes. Eliminating these factors will decrease the variation in the process. Once causes have been eliminated from the process, new control limits should be computed and drawn on the control chart, as in step 5 above. Shewhart Control Charts The Shewhart control charts were developed by Walter Shewhart in the 1920's, and published in his book Economic Control of Quality of Manufactured Product (1931). They are intended to show what causes are affecting a process and what changes to the process effect its outcome. Shewhart control charts common characteristics include their parallel centerline, upper and lower control limits. All Shewhart control charts are evaluated the same way, whether they are variable or attribute charts. Pattern Analysis The basis for deciding if a control chart is exhibiting out of control conditions is by examination of possible patterns. With the exception of PRE-Control, the charts have common tests for natural and unnatural patterns. The characteristics of a natural pattern are that the plotted points fluctuate in a random chance pattern. They should follow no pattern or recognizable system. The

21 21 characteristics of a natural pattern can be summed up as follows: 1) None of the points exceed the control limits. 2) A few of the points spread out and approach the control limits. 3) Most of the points are on both sides of the centerline. 4) There appears no pattern or system in the points. An unnatural pattern is marked by points that fluctuate widely, exceeding the control limits, or appearing in non random patterns. These patterns are usually one of the following: 1) A single point exceeding the three-sigma control limit (points 10 and 21 in Figure 1) X UCL CL 9 8 LCL 7 X Figure 1. Out of Control Condition #1

22 22 2) Two out of three points exceeding two-sigma from the centerline or four out of five exceeding one sigma X X X UCL +2 σ σ 10 CL 9 1 σ 8 2 σ 7 LCL Figure 2. Out of Control Condition #2

23 23 3) Eight successive points on one side of the centerline UCL CL 9 8 LCL 7 Figure 3. Out of Control Condition #3

24 24 4) Eight consecutive points within one standard deviation of the center line. 13 UCL σ +1 σ CL 1 σ 2 σ LCL 6 Figure 4. Out of Control Condition #4

25 25 5) A non random pattern - i.e. two successive points on one side of the centerline, followed by one point on the other, with the pattern of three repeated several times, or any other pattern that corresponds to some non random phenonoma. In Figure 5, the pattern is constantly up and down. This might correspond to some manufacturing pattern, perhaps a day and night shift. Patterns like this can be a good clue to out of control conditions UCL CL 9 8 LCL 7 Figure 5. Non-Random Pattern

26 26 Variables Control Charts Introduction Shewhart control charts designed for variables data are the X-bar and R chart and the individuals chart. They are the most powerful of the control charts and generally require the smallest sample sizes. X-bar and R Charts X-bar and R measure two characteristics of the process at the same time. The central tendency, or mean of the process is measured on the X-bar chart, with the variability or spread of the chart measured on the R chart. The symbols X-bar and R stand for average and range, respectively. An X-bar and R chart can be constructed for different levels of sensitivity. We will concentrate on the standard level of sensitivity, the three sigma control chart. The basic procedure for constructing an X-bar and R chart is to sample the process at preselected intervals, compute the average and range of the sample, and plot the two points on the chart. After enough samples have been generated, control limits are computed and drawn on the chart. All points are compared to the control limits to detect any out of control conditions, which would signal that something non-normal or out of the ordinary has

27 27 happened to the process. Any out of control conditions should start investigation into causes, and elimination of those causes if they are detrimental to the product. Construction The control lines for the 3σ X-bar chart are: Centerline = X UCL = X + A2 R LCL = X R A2 The control lines for the R chart are: Centerline = R UCL = D R 4 LCL = D R 3 The symbols A 2, D 3 and D 4 are statistical constants that can be found in the tables in the appendix. Their values vary depending upon the sample size. For example, with a sample size of three, A 2 would be 1.023; D 3 would be zero and D 4 would equal

28 28 Sample Sizes The most important aspect of designing an X-bar and R chart is the sampling plan. An improper sampling plan will invalidate the chart, and may cause the chart to be misleading. Points that are out of control on the chart may actually not be and vice versa. When designing a sampling plan one must consider the two types of variation shown on the chart. The X-bar chart shows long term variation - variation that happens between subgroups. The R chart shows short term variation - variation that occurs within the subgroups. This distinction between short term and long term variation is very important. Since the X-bar chart uses the range to set its control limits, essentially using short term variation to predict long term variation, any improper sampling will effect both the X-bar and R charts. It is important to get the short term variation within the subgroup. For instance, on a press we can expect that five consecutive samples will have the same ink density (unless the press is two-around, etc.). Therefore, drawing our sample from five consecutive samples will not give us a true value of short term variation. However, five samples from the folder to evaluate fold skew could very well be a representative sample of short term variation.

29 29 The best approach is to determine what factors influence short term variation and try to capture them in a sample. On a folder, the number of jaws would be a factor; if a press is two around we should try to include both halves of the plate or blanket in the sample. Because web printing is a continuous process, time is a factor in short term variation. Try to determine how much of an influence time is and work with it. For example, pulling one book a minute for five minutes to form a subgroup of five would be a be better alternative than five in a row. Each situation will be different with factors such as the speed of the press and the type of work influencing the sampling plan. Potential Applications There are many potential applications for the X-bar and R chart in printing. Ink density, dot gain, and cutoff are examples. There are however, some advanced charts that may be more applicable in detecting the small shifts that occur in the printing process. One chart that may be more useful in detecting small shifts in the process is the Cumulative Sum, or CUSUM chart. This chart is constructed quite differently than an X-bar and R chart, using a V-shaped mask instead of control lines. It is quite often used in conjunction with an X-bar chart. This control chart is quite advanced, and will not be

30 30 discussed in detail here. Several of the books in the bibliography discuss CUSUM charts in detail. Ink density may be measured throughout a run and plotted on an X-bar and R chart. This would give us two pieces of information; the average ink density and the normal variation for the process. If, once color was set, we plotted ink density on a control chart, and only made adjustments when the chart indicated out of control conditions, we would have used the variation of the process to control the process. Out of control conditions would be investigated - and hopefully eliminated from the process. For example, the ink density dropped below the lower control limit - what is the cause? Did we run out of ink, is there water in the ink, etc. Once these conditions are identified, we can work to eliminate them from reoccurring. In the same way we can track dot gain through a run. In this case an out of control condition might signal some other cause - emulsified ink, piling, etc. Cutoff, being a mechanical condition, is more easily controlled by SPC. Many times operators make adjustment to the cutoff control based on the condition of one book. Use of a control chart would eliminate unnecessary moves, and actually reduce the cutoff variation in the final product. Example: Midtone dot gain. A press operator wished to construct an X-bar and R chart for midtone dot gain. Because he had a two around

31 31 press he chose a sample size of four and a sampling frequency of fifteen minutes. The data for his first twenty subgroups is summarized below. Subgroup X R X R

32 X R X R Table 1. X-bar and R Chart Example Data The operator looked up his constants for a subgroup of size four and found A 2 = 0.729, d 3 = 0, and d 4 = He then calculated his 3σ control limits and came up with the following results:

33 33 X-bar chart R Chart UCL = 24.8 UCL = 8.2 X = 22.2 R = 3.6 LCL = 19.6 LCL = 0 His finished control chart appears below: 28 Dot Gain X-bar Chart UCL CL LCL Dot Gain R Chart 10 8 UCL CL LCL Figure 6. X-bar and R Chart Example Since the charts did not exhibit any signs of out of control conditions, the press operator did not make any

34 34 adjustmens. Any out of control conditions on the charts would prompt the operator to determine and correct the cause. The X-bar and R chart can be a great tool to understand and reduce the variation in a process. Individuals Charts Individuals charts are based on one measurement, rather than a subgroup as with X-bar and R charts. This makes these charts easier to construct, but less powerful. Sometimes it may be necessary to use an individuals chart, such as when it is expensive or time-consuming to collect more than one measurement. Examples might include ink mileage or afterburner efficiency. Construction The control lines for a 3σ individuals chart are: Centerline = X UCL = X R LCL = X 2.88R

35 35 Potential Applications Potential applications include any data that is hard to gather, or takes too long to gather. Examples could include ink mileage, paper waste, etc. An ink manufacturer wanted to track the mileage on his black ink. He decided to use one months data to compute pounds of ink per thousand copies. His data looked like this: Jan Feb Mar Apr May June July Aug Sept Oct Table 2. Individuals Chart Example Data He computed his X to be 1.15 and his R to be His control limits turned out to be: UCL = 1.37 LCL = 0.93 His finished control chart follows:

36 36 Ink Mileage Individuals UCL CL LCL Figure 7. Individuals Chart Example For applications where an X-bar and R chart is not feasible, an individuals chart can be used to get a handle on variation. Attributes Control Charts Introduction Attributes control charts are based on data that is countable rather than measured. Counts may include plate scratches, number of books with skewed fold or number of short skids. Attribute control charts are further divided into two types - those based nonconforming units, and those based on nonconformities. This difference is important, and can be quite confusing.

37 37 A nonconforming piece, or defective part, is a single piece that is not good. It may contain one or more defects or nonconformities that make it so. We can count the defective part or we can count the number of defects on it. An example would be a plate with holes. We can count the defective plate (a nonconforming item) or we can count the number of holes on the plate (nonconformities). Each count has its own type of control chart. Sampling Plans Because attribute charts are not based on measurements, the sample sizes need to be larger to get the same sensitivity. Sampling plans should be put together to capture the normal short term variation in the subgroup. Typical sampling plans for attribute charts include part related plans such as batches, and time related plans such as days or shifts. Fraction Nonconforming - p-, np- Charts P-and np- charts are based on number of defectives. They may be used for monitoring percent defective. P-charts are based on percent defective, if the sample size is consistent np-charts based on number defective may be used.

38 38 p-charts P-charts are so named because they track percentages. The p-chart uses a percent defective as its values. Construction The control lines for the 3σ p-chart are: Centerline = p UCL = p + 3 p( 1 p)/n LCL = p 3 p( 1 p)/n Potential Applications For example, a plateroom wished to track defective plates. The manager decided on a p-chart. His subgroup size would be however many plates were made each day. He would count the number of bad plates and find the percentage. His data is below.

39 d n p d n p Table 3. p-chart data The control limits were calculated: p = UCL = LCL =.009

40 40 His finished control chart looked like this: Plate Defect p-chart 0.14 UCL CL LCL Figure 8. Plate Defect p-chart np-charts The np-chart is just like the p-chart except it uses the number of defective items rather than the percentage. This is only possible if each sample has the same number of units. Construction The control lines for the 3σ np-chart are: Centerline = np UCL = np + 3 np 1 ( p)

41 41 LCL = np 3 np 1 ( p) Potential Applications The potential applications are the same as for p-charts. The same data for the p-chart could be constructed as a np-chart since the sample sizes were the same. If the percent defective remained the same each day, the control lines would be: np = 11 UCL = LCL = 1.43 The control chart would now look like this:

42 42 Plate Defect np-chart UCL CL 5 LCL Figure 9. Plate Defect np-chart Nonconformities - u-, c- Charts The charts based on number of defects are the u- and c- charts. They are used when the number of defective units is not as important as the number of defects. u-charts U-charts are most useful when several types of defects can occur in one unit. The u-chart measures defects per unit.

43 43 Construction The control lines for the 3σ u-chart are: Centerline = u UCL = u + 3 u / n LCL = u 3 u / n Potential Applications Since holes were a major cause of plate defects, the plateroom manager decided to track the number of holes in a sample of plates. For this, he chose a u-chart. He randomly selected ten plates from ten consecutive shifts to start his control chart. His data looked like this:

44 Holes Plates Holes/plate Holes Plates Holes/plate Table 4. Holes/Plate Example Data He calculated his control lines to be: u = 1.3 UCL = 2.38 LCL = His u-chart looked like this:

45 45 Holes/Plate u-chart 2.5 UCL CL 0.5 LCL Figure 10. Holes/Plate Example u-chart c-charts The c-chart is a chart of counts. It differs from the u-chart in that the defects are not counted by unit. An example would be overall defects in a plate, rather than holes per plate. Construction The control lines for the 3σ c-chart are: Centerline = c UCL = c + 3 c LCL = c + 3 c

46 46 Potential Applications The c-chart relates to the u-chart just as the np- and p-charts relate. The c-chart is good when the sample size is constant. Advanced Control Charts The advanced control charts we will discuss here are short run SPC and PRE-Control. Short run SPC is a technique that can be used when runs are not long enough to use a conventional control chart. Different types of work, or short runs may be kept on the same chart. PRE-Control is a technique that can be used to monitor variables or output to determine if they are within specification. It can be used as a monitoring tool by the operator. Short-Run SPC Short run SPC can be a very powerful form of SPC in the printing industry. Since runs are generally not conducted over a period of months or even weeks, a short run chart can be used where a conventional control charts could not. Data to be used in a short run SPC chart is normalized from existing data before being used. Depending upon the type of process being charted, different data normalization techniques should be used.

47 47 Data Normalization The three types of data normalization are nominal, target, and short run. The first two only take into account deviation from nominal or specification, the second both deviation and variation. For processes using data from similar setups, such as same paper stock and press, either the nominal or target normalization may be used. For processes where variation is very different from setup to setup, the short run normalization is preferred. This normalization takes into account the differences in variability between setups. Nominal The data may be normalized by measuring the deviation from the nominal of the specification. The range chart will be unaffected but the centerline of the X-bar chart will be very close to zero.

48 48 Target The data in this case are coded by measuring the deviation from an historical process average. The centerline of the X-bar chart will again be very close to zero. Short Run This technique takes into account the differences in variability between different parts by dividing by the historical average range for each part. The normalization formulae are: R Coded R = Historical R X Historical X Coded X = Historical R The control limits for the coded data, for a three sigma control chart, appear below: R Chart X-bar Chart Centerline = 1 Centerline = 0 UCL = D UCL = + 4 A2 LCL = D LCL = 3 A2

49 49 X-bar and R Charts Once data are coded, they may be plotted and interpreted just like any other X-bar and R chart. For example, if the data from the X-bar and R chart example above are used, we can construct a nominal short run chart. The data would be normalized to look like this: Subgroup X R X R

50 X R X R Table 5. Nominal Short Run Example Data The new control limits are calculated to be: X = 2.18 UCL = 4.79 LCL =

51 51 The control chart looks like this: Dot Gain Short Run X-bar Chart UCL CL LCL Figure 11. Nominal Example X-bar chart The R-chart is unaffected by the normalization and would look the same as the previous R-chart. The data could also be normalized with both the historical average and range. This would account for both centering and variability. The data would look like this:

52 X R X R

53 X R X R Table 6. Short Run Example Data The new control lines are calculated to be: X-Chart R-Chart X = 0.44 R = 0.72 UCL = 0.96 UCL = 1.63 LCL = LCL = 0

54 54 The charts appear as below: Dot Gain Short Run X-bar Chart 1 UCL CL LCL Dot Gain Short Run R Chart UCL CL Figure 12. Short Run X-bar and R Chart

55 55 PRE-Control Introduction Once control of a process is established, and specifications are set it may be necessary to transfer control charts to line personnel. In some cases control charting may be too complicated, time consuming or unnecessary. In these cases, a simple technique call PRE- Control may be used. PRE-Control compares parts not to statistically calculated limits but to the specifications. PRE-Control is not meant for establishing statistical control, but for maintaining the process between a set of specifications. Construction A PRE-Control chart appears on the following page:

56 56 PRE-Control Red Zone Yellow Zone Green Zone Yellow Zone Red Zone USL LSL Figure 13. PRE-Control Chart The red bands in the chart represent out of specification measurements. The process must be adjusted for no more out of specification product to be produced. The yellow bands are cautionary zones where the process may have to be adjusted. The green band is a zone of good product. The line marking the boundary between the green and yellow zones is one half the distance between the nominal of the specification and the tolerance limit. The line marking the boundary between the yellow and red zones is the specification limit. With these lines the chart will have a green zone equal to one-half the specification, two yellow zones each equal to one-quarter the specification, and two red zones.

57 57 Use of PRE-Control There are only three steps that need be done in using a PRE-Control chart: Qualify the setup. Every piece must be measured until five greens in a row are produced. If one yellow or red is encountered, restart the count. Make any adjustments necessary during this period to produce five greens in a row. Run. Once the process is qualified, sample and measure two consecutive pieces periodically. Plot both pieces on the PRE-Control chart in the appropriate band. The measurements do not need to be precisely plotted, they just need to be in the appropriate band. If one of the following conditions occur the process must be stopped or adjusted: One red: The process is already producing bad product and must be stopped and corrected. Two yellows: The process should be adjusted back to the center. If the yellows are in opposite zones a more sophisticated investigation might have to be undertaken. If the process is adjusted, it will need to be requalified. That is five greens in a row will have to be produced to ensure the setup is correct. A big advantage of PRE-Control is that it is much easier to use than control charts. If gages are made that have the

58 58 appropriate colors on them the operators need not even worry about precise measurements. Potential Applications PRE-Control is applicable whenever product can be sampled and specifications can be set up. It is important to remember it is not a tool to monitor statistical control, but to keep product within the specifications. Applications could include fold, plate burning, etc. An example, the plateroom manager wished to monitor the consistently of his light sources. Since he had specifications set, he decided to use a PRE-Control chart. His specifications were on a continuous scale. He first burned several plates until he got five greens in a row. He then started his PRE-Control chart. His PRE-Control chart was set up as follows: Red Zone - > 35 Yellow Zone Green Zone Yellow Zone Red Zone - < 30. At the beginning of each shift, a platemaker would burn a scale on two consecutive plates. The chart for ten shifts was as follows:

59 59 The chart looked like this: Plate Exposure PRE-Control Red Zone USL Yellow Zone Green Zone Yellow Zone LSL Red Zone Figure 14. Example PRE-Control Chart The first points out violating the PRE-Control rules occur at shift ten. Both points are below the red line, so the exposure unit should be adjusted back toward the center. Once this is done, the setup will need to be qualified again. Conclusion Statistical Process Control can be a major factor in process improvement. It can be used to monitor any process characteristic, input or output. A good SPC program can put processes in control, which is generally great improvement

60 60 by itself, and from there other methods of improvement, such as Design of Experiments, explained in the next chapter, can improve it even more.

61 61 CHAPTER 3: DESIGN OF EXPERIMENTS Introduction Design of Experiments is a name for a set of methods that aid in determining the outputs that occur for a given set of inputs. The inputs are purposely varied to determine their individual and collective action on the output. Terminology will be discussed, along with the different types of experiments, how to design and apply them, and how to interpret the resulting data. Taguchi methods will be discussed as the major tool for use in experimental design. Fundamentals of DOE Terminology Designed Experiment. An experiment where variables are manipulated according to a predetermined plan, and the resulting data are analyzed statistically to determine the effects of any variable or combination of variables. Response Variable. The output variable, or the variable being investigated, also called the dependent variable.

62 62 Factors. The input variables or the variables that are intentionally varied, also called the primary or independent variables. Random Variables. Variables which, although identified, either cannot or should not be deliberately held constant. Experimental Error. The variables that are not identified or controlled. They are analogous to the "common cause" variables of SPC. Because the term "error" has a negative connotation, the term "all others" will be used here, since this is really the contribution of all factors not controlled. Sometimes these factors are called "noise" factors, since they obscure the true effects of the factors. Replication. Repeating a set of conditions in an experiment. Interaction. Condition in which the effect of one factor depends upon the level of another factor. Level. The values of a factor being studied in the experiment. Steps in Design of Experiments In order to be successful, the designed experiment must follow some logical sequence and meet some specific criteria. A poorly planned experiment, no matter how well it is carried out, will not have the statistical validity necessary to come to a conclusion. The following are steps necessary in using a designed experiment.

63 63 1. Clearly identify the problem. The problem (what we wish to measure) must be clearly identified. It also must be specific, e.g. "Too much dot gain on Press 1" would be a specific problem. 2. Determine the response variable and how to measure it. The response variable is the variable that will be measured to determine the effects of the factors. It must be measurable. Stating the response variable and how it is measured is a good idea, e.g. "The response variable will be dot gain, measured by densitometer." 3. Identify factors of interest and possible interactions. This step determines the variable that will be used in the experiment. It is sometimes a good idea to use a group brainstorming session to come up with appropriate factors. Factors should be weighed against each other for possible interaction before picking the experimental design. The number of factors chosen will determine the cost of the experiment. 4. Select representative levels of each factor. Levels for each factor should be chosen that a representative of normal conditions. For example, if blanket packing is a factor, representative levels might be.008" and.012", not.05". In the Taguchi methods, two level experiments are generally favored.

64 64 5. Pick an appropriate experimental design. The experimental design chosen is determined by the number of factors and interactions chosen in step Run the test and gather the data. The test must be ran according to the design, and the response variable measured. 7. Graph and interpret the results (graphical analysis). Graphical analysis is relatively easy, and may show responses and interactions harder to see in the statistical analysis. 8. Determine confidence and each factors contribution (statistical analysis). Graphical analysis does not calculate the contribution of each factor or interaction, and will not show the confidence in the results. Generally, statistical analysis is done using Analysis of Variance. 9. Run addition tests for confirmation or refinement, as necessary. Once results have been formulated, a confirmation test should be run to eliminate the possibility of a wrong conclusion. 10. Implement the improvements. Once confirmed, the results must be implemented on an ongoing basis.

65 65 Statistical Analysis One Way ANOVA Analysis of Variance (ANOVA) is the statistical tool used to determine the probability that values from two samples come from different populations. In other words, it measures the probability that levels of a certain factor actually create different results. An ANOVA compares the variation between levels of a factor against variation within those levels. The greater the ratio of "between level" versus "within level" the higher the probability there is actually a difference between the levels. Results from an ANOVA are summarized in an "ANOVA table" which is shown below. The terms are explained below the table. Source of Degrees of Variation Variance F4 α5 Variation Freedom1 (SS)2 (MS)3 Between Level Within Level Total Table 7. One-Way ANOVA Table

66 66 1. The Degrees of Freedom depicts the assurance the variance is close to the true population variance It is generally one less than the number of values used to compute the sum of squares. 2. The variation is the Sum of Squares. 3. The variance is the Mean Square - the Sum of Squares divided by the Degrees of Freedom. 4. F is the ratio of the between level variance divided by the total variance. This is used as a lookup to find the probability. 5. Alpha is the probability that there is a difference between the levels. Two Way ANOVA The two way ANOVA is similar to a one way ANOVA, but compares the effects of more than one variable. For instance, if an experiment had factors of plate and fountain solution, a two way ANOVA would be appropriate. The table is similar, but has rows for each variable, plus one for all other variables.

67 67 Source of Degrees of Variation Variance F α Variation Freedom (SS) (MS) Factor One Factor Two... Factor n All Others Total Table 8. Two-Way ANOVA Table Analysis of Variance is a complicated subject and will not be covered here. Several good textbooks are listed in the bibliography. A table for finding α is included in the appendix. Graphical Analysis Results from experiments may be analyzed graphically by plotting them on main effect plots and interaction plots. As their names suggest, these plots analyze the effects of the main factors and the first level interactions. Graphical plots may make it easier to visualize the effects of the factors and may lead to quick conclusions about the experiment.

68 68 Graphical analysis is not a substitute for statistical analysis, but a supplement to it. Both graphical and statistical analysis should be performed on each experiment. Main Effect Plots Main Effect Plot A1 A2 A3 Figure 15. Main Effect Plot The main effect plot shows the responses of each of the main variables. It is simply plotted like a horizontal histogram for each factor level.

69 69 Interaction Plots Interaction Plot B1 B2 A1 A2 Figure 16. Interaction Plot In Figure 2, the interaction plot shows an interaction. That is, the effect of A changes depending upon the level of B. This is demonstrated by the crossed lines. The more nearly perpendicular the lines, the greater the interaction. Interaction Plot B1 B2 A2 A1 Figure 17. Interaction Plot

70 70 In Figure 3, the interaction plot shows an absence of an interaction. This is demonstrated by the parallel lines, indicating the effects of A and B do not change because of the others level. One Factor Experiments The most common type of experiments are one factor experiments, in which only one variable is of interest. An example would be a plate test, in which one variable (the type of plate) is varied. This type of experiment would use a one-way ANOVA. If a printer wanted to test two plates for midtone dot gain, a one factor experiment would be in order. The data from such a test could look like this:

71 71 Run Plate 1 Plate 2 Run Plate 1 Plate Table 9. One Factor Experiment Example Data

72 72 A one-way ANOVA should be performed on the data. The ANOVA would look like this: Level Count Sum Average Variance Plate Plate Source SS df MS F Alpha Between Groups Within Groups Total Table 10. One Factor Example ANOVA Table The low Alpha (zero) shows that there is a big difference between the two plates. Factorial Experiments A factorial experiment is one where more than one factor is under control, and all are varied at the same time. A full factorial is where at least one result is taken from each combination of levels that can be formed from the different factors.

73 73 These experiments are the most revealing of any designs, but with this comes the penalty of complexity, and cost. Taguchi designs, discussed later, offer many of the advantages, at a cheaper cost, than full factorial designs. Full factorial experiments could be used when several factors, each at several levels, are to be tested to find the optimum settings. The Taguchi Methods Introduction Perhaps the most effective of all the DOE tools is a relative newcomer, the Taguchi methods. It is increasingly being accepted by quality professionals across the United States, and is in widespread use in Japan. It is not the most statistically correct of methods, and many statisticians invalidate it for that reason, but it is a very effective tool, and translates well to use in all industries. It is for this reason that this paper will emphasize its use above all others. The concepts, tables and terms can be daunting, but they have been simplified as much as possible, with several tables not found anywhere else included.