Variability & Statistical Process Control

Variability & Statistical Process Control
Audience: Intel Senior Manufacturing Technicians (SMTs) Prerequisites: none Timing: Section 1-Variation 8 hours Section 2-Process Control 3 hours Section 3-Meas. Cap. 8 hours Class Size: students Preparation: Give CQI Pretest to use as a baseline for assessing end results. 1

Outline Section 1: Understanding the Impact of Variation
Section 2: Process Control Systems Section 3: Measurement Capability Analysis Major Point: The module will be divided into three distinct sections. Variation will consume ~8 hours; PCS will consume ~4 hours; and measurement capability analysis...~8 hours. Other: Credit Walt Flom and Ann Russell with the development of sections 1&2; and Sematech with section 3. 3

What is Variation? ? ? Loss Function
What is the target for a given process? How far away from the target is still OK? ? ? Major Point: Introduce the concept of a Loss Function Ask: Ask the class to identify a particular process in the factory. For the chosen process, ask what the target would be. Mark it as the center of the process diagram. Discuss what happens if the process runs at the extremes, e.g., if the width is 1.4 microns, use 1.4 feet in the example. Ask the class when the shift from OK to BAD occurs. Target 20

A curve representing loss in quality as a function of a measured value
What is Variation? Loss Function Loss in Quality Major Point: There is not a definite point at which an off-target process suddenly becomes unacceptable. Instead, as the process moves further away from the target, it gradually becomes less acceptable and generates greater loss of quality. Discuss: Discuss the construction of a loss function from the information given above. There are two ways to do this: One way is the traditional loss function with cliffs at the switch over point identified above. The other is the quadratic loss function, arrived at by leading questions: Is just in spec much better than just out of spec? Is just off target much worse than on target? target Measurement A curve representing loss in quality as a function of a measured value 21

What is Variation? Traditional “Loss Function”
Spec limits define acceptable and unacceptable quality Loss in Quality Lower Spec Limit Upper Spec Limit Major Point: The traditional loss function is defined by spec limits. Discuss Refer to the class’ example on the previous slides. Point out that specs define the region where the process probably works okay. Ask Is this loss function is realistic? “Just in” vs. “just out” is not really much different. What is management’s job is when using the traditional loss function? Mgmt. should ensure that everything is “in-spec” by inspecting, reworking, or scrapping. How do we continuously improve quality with this loss function? By trying to get everything in spec What happens if specs change? People may have new tasks to perform The inspect-rework-scrap paradigm gives no guidance to improving the process to better meet the new requirements. 22

What is Variation? Modern “Loss Function”
Target: Desired Value or Outcome Loss in Quality Increases as Variation from Target Increases Loss in Quality Major Point The modern loss function is defined by distance from the target. Discuss Refer to the class’ example on the previous discussion. Point out that any deviation from the target degrades performance to some extent. Ask What is management's job when using the modern loss function? Mgmt tries to minimize variation around the target. What happens if the specs change? The tasks stay the same The modern loss function focuses on minimizing variation from the target. Therefore, when a spec change occurs, the efforts are not redirected. Note This idea is from Toguchi Target 23

What is Variation? How the Loss Function Affects Product
Both are within spec Which is more desirable? LSL USL LSL USL Major Point Any deviation from the target degrades performance to some extent Discuss Assuming cost is the same, which nuts would you rather get? Why? There is an optimum size for the hole. Any deviation from that size means a loss in quality and/or functionality. How will a larger deviation from the target impact performance? Record responses on a flipchart Beware of the possible response that “in spec” is okay. Counter with the question about whether “just out of spec” will not work. For example, nut #1 = spec (in spec) and nut #2 = spec (out of spec). Is there a difference? 24

Loss Function for Defects
What is Variation? Loss Function for Defects Loss in Quality Major Point For defects, the target is always zero. Any increase degrades performance. Number of Defects Target 26

Less Variation = Higher Quality What is Variation?
Major Point Quality improvement relies on reducing variation rather than inspect-rework-scrap based on spec limits. This theme forms the basis for the remainder of the module. Discussion Open the class for any discussion, or question and answer that has not taken place yet. 32

Examining Variation Definition A Stable Process has the same normal distribution at all times. A stable process is In Control A stable process still has variation Major Point To establish the definition of a stable process Explain Discuss each element of the definition A stable process has the same distribution at all times. Emphasize that a stable process has the same shape, same spread, and same center at all times with no time trends. Comment: This definition is arbitrary. There are other definitions of stability. This one is chosen because it is more useful than others. Ask Does this definition say anything about how we want the process to behave? This definition of stability is descriptive, not prescriptive: What we’ve got vs. what we want. Discuss Introduce the concept of normal distribution: for this class, and frequently in the factory, a stable process has the same normal distribution at all times. 41

Normal distribution at all times
Examining Variation Stable Process Normal distribution at all times Prediction Major Point A stable process has the same center and spread at all times Explain For a stable process to have a normal distribution it must have the same bell-shaped curve (i.e., the same spread, and same center) at all times. Discuss The general definition of stability just says the same distribution at all times. Some distributions, e.g., defects, will NOT be normal. For simplicity, in this class we will assume a stable process has the same normal distribution at all times. Poster Keep the poster of the definition of stability in front of the class throughout the remainder of this session. Time 43

Examining Variation Common Causes The cause of variations in a stable process is called a Common Cause. A common cause is a natural cause of variation in the system. Major Point To introduce the definition of common causes Example Make sure the funnel has been reset and the funnel is centered. Drop a couple of balls through the funnel. Ask What causes the variation in this process? The pins. Do the pins always cause variation? Yes Explain The cause of variation that always acts the same way in a process is called a common cause variation. Variations in a stable process are always caused by common causes. Define Common causes of variation are ever-present sources of variation in a stable process. Exercise Use the following idea to get people thinking about common cause variation Process = Driving from home to work Measurement = time to get from home to work 44

Examining Variation Common Cause Examples Machine vibration
Temperature fluctuations Slight variation in raw materials Human variation in setting control dials Exercise (cont’d) What are the causes of variability? (ANY cause) Record Record the causes the students name on a flipchart Make sure some special causes are included, e.g., accident blocks intersection, car breaks down, you have an accident, etc. Ask Which of these are common causes? Make sure that one-of-a-kind occurrences are omitted from the common cause list. Summarize Common causes of variation are always present in the process, with essentially random effects over time. (Sometimes you hit all the lights “green”, sometimes you hit some red lights, and sometimes you don’t get through any lights without having to stop for red.) Discuss Point out the examples on this slide. Ask students what other common causes of variation exist in the factory. Write down causes on flipchart. Leave any debate for later. When several causes have been written down, analyze the list and identify common causes. 45

Examining Variation Tools for Examining Stability
Trend Chart: A plot showing the behavior of a process over time. 200 180 160 140 120 100 80 60 40 20 Thickness Time Major Point A trend chart is a stretched out histogram. Ask How can a stable process be recognized on a trend chart? The chart doesn’t contain any dramatic changes in the plot pattern (or trend). Discuss A trend chart is a measurement plotted against time. 46

Examining Variation Tools for Examining Stability
Histogram: A barchart showing the distribution of the process. 35 30 25 20 Percentage 15 10 5 Major Point A histogram is a collapsed trend chart. Ask How can a stable process be recognized on a histogram? It has the same normal distribution all the time. Refer to flipchart definition. What is the relationship between a trend chart and a histogram? A histogram results from tipping a trend chart on its side and letting all the plots fall to the bottom. Summarize Both graphs are useful ways to assess process behavior. We will always look at both as a trend chart-histogram pair. 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Thickness 47

Examining Variation Activity: Comparing stable processes
Which process has better quality? 150 150 140 140 130 130 120 120 110 110 Thickness 100 Thickness 100 90 90 80 80 70 70 60 60 50 Major Point The less the variation from the target, the better the quality Ask For each A-B pair which is better? Why? What is meant by on-target? For pair #1 which is on target? Trick question. Both are on target For pair #2 which has less variation from its mean? Vocabulary On target refers to the average, long term behavior 50 Sequence 5 10 15 20 25 Sequence 5 10 15 20 25 B A 49

Examining Variation Activity: Comparing stable processes (cont’d)
Which process has better quality? 150 150 140 140 130 130 120 120 110 110 Thickness 100 Thickness 100 90 90 80 80 70 70 60 60 50 50 Sequence 5 10 15 20 25 Sequence 5 10 15 20 25 B A 50

Examining Variation Unstable Process
Any process that is not stable is called an unstable or out-of-control process. ? ? Prediction Major Point To introduce the definition of an unstable process. Ask What is an unstable process? this one is just stupid enough to be fun Any process that is NOT stable is unstable! Time 51

Kinds of Instability: Excursions
Examining Variation Kinds of Instability: Excursions 200 200 180 180 160 160 140 140 120 120 Thickness 100 100 80 80 60 60 40 40 20 Major Point To introduce new vocabulary describing different types of instability Vocabulary Discuss characteristics of the following: Excursions/Outliers - occasional spikes appear in trend chart. Histogram contains data that is separate from the main grouping. Cycles - Trend chart contains microtrends that gradually vary from the target and then gradually shift in the other direction. Shifts - Trend chart contains sudden shifts in trend. More dramatic than cycles. Chaos - Trend chart jumps all over the place. Unpredictable. Trends - Trend chart shows gradual shifting away from target. 20 Time 53

Kinds of Instability: Shifts
Examining Variation Kinds of Instability: Shifts 200 200 180 180 160 160 140 140 120 120 Thickness 100 100 80 80 60 60 40 40 20 20 Time 54

Kinds of Instability: Drifts
Examining Variation Kinds of Instability: Drifts 200 200 180 180 160 160 140 140 120 120 Thickness 100 100 80 80 60 60 40 40 20 20 Time 55

Kinds of Instability: Cycles
Examining Variation Kinds of Instability: Cycles 200 200 180 180 160 160 140 140 120 120 Thickness 100 100 80 80 60 60 40 40 20 20 Time 56

Kinds of Instability: Chaos
Examining Variation Kinds of Instability: Chaos 200 200 180 180 160 160 140 140 120 120 Thickness 100 100 80 80 60 60 40 40 20 20 Time 57

Examining Variation Special Causes
Anything that causes variations that are not part of the stable process is called a special cause, assignable cause, or unnatural cause. Major Point To introduce the definition of special cause. Do Display the results of the driving to work example on the flipchart. Ask What are the special causes of variation? accidents, breakdown, road repair, etc. 58

Examining Variation Examples of Special Causes
Batch of defective raw material Faulty set-up Human error Incorrect recipe Blown gasket Earthquake Major Point Special causes also occur in factory processes. Discuss Point out examples that affect the packaging process. Ask the class for others; write them on flipchart. Summarize Special causes result in non-random patterns in trend charts or histograms; they are always associated with unstable processes. 59

Reducing Variation Improving a Stable Process
Two strategies for improving a stable process Centering at Target Reducing Common Cause Variation Major Point There are two strategies for improving a stable process: centering at target, reducing common cause variation. Ask How can you tell which is most appropriate? Examine trend charts 79

Reducing Variation Centering at Target Time Thickness 200 200 180 180
160 160 140 140 120 120 Thickness 100 100 80 80 60 Major Point If the process is off-target and stable, then you must make the necessary adjustments to move toward the target. 60 40 40 20 20 Time 80

Reducing Common Cause Variation
Reducing Variation Reducing Common Cause Variation 200 200 180 180 160 160 140 140 120 120 Thickness 100 100 80 80 60 60 40 40 Major Point If the process is on-target and stable, but has large variation, then you must identify and work to reduce common cause variation. 20 20 Time 81

Reducing Variation Reducing Variation in a Stable Process
Make Permanent Changes Changes are based on the scientific approach Structured problem solving Planned experiments Major Point To improve a stable process, the process must be permanently changed Discuss There are two key concepts on this slide It is important that changes be permanent rather than temporary “let’s see if this will work” changes. Changes must be scientific rather than “seat-of-the-pants” or intuitive Examples New Equipment Upgraded Equipment New Procedure New Machine Settings Higher Quality Materials Examples: new equipment, equipment upgrade, new procedure, new machine settings, better raw material 82

Reducing Variation in an Unstable Process
Do not ignore special causes. Do quickly detect special cause variations. Do stop production until the process is fixed. (Reactive) Do identify and permanently eliminate special causes. (Preventive) Major Point Since unstable processes are characterized by special causes of variation, they can be improved by removing these special causes. Ask How can we avoid tampering? Never make adjustments Discuss Tampering is adjusting a stable process, reacting to a common cause as if it were a special cause. The opposite of this is ignoring special cause variation in unstable processes. This is equally bad. There are two modes of dealing with special cause variation: Reactive (local): Quick detection and response to special cause variation. Preventive (systemic): Identification and permanent elimination of special cause. 85

Improving an Unstable Process
Reducing Variation Improving an Unstable Process Four Step Process Detect the special cause variation. Identify the special cause. Fix the process Remove the special cause, or Compensate for the special cause. Prevent the special cause from occurring again Major Point We must react carefully and appropriately to special cause variation. The four step model is one way to apply a systematic approach. Discuss Point out that fixing is reactive, while preventing is preventive. Both are appropriate. Note the options under fix Remove Compensate Two ways to deal with idiots: idiot proof the process, or fire the idiots. 86

Reducing Variation Improving an Unstable Process Reactive 200 180 160 140 120 100 80 60 40 20 Thickness Time Not Here Detect Here Detect Here Major Point Both local and system efforts can improve an unstable process. Discuss The term reactive is not intended to carry a negative connotation. Rather, it denotes reaction (response) to special causes that occur locally. A trend chart makes timely response possible. 87

Reducing Variation Improving an Unstable Process Preventive 200 180 160 140 120 100 80 60 40 20 Thickness Time Major Point Preventive response is fixing the system, e.g., working with vendors to get uniform quality. Unstable Stable 88

Detecting Variation How can we decide if variation is the result of common or special cause? Major Point To motivate the need for a control chart Ask How can we avoid tampering? Never adjust What is wrong with this strategy? It ignores special cause variation. What is the key to taking correct action (not tampering vs. corrective action) Recognize the type of variation If stable, do not adjust; work on reducing common cause variation If unstable, respond to special cause variation How can we tell if a process is stable or unstable? There is subjective judgment involved 95

Benefit: Prevents tampering or ignoring
Detecting Variation Tool: Control Chart Benefit: Prevents tampering or ignoring 200 180 160 140 120 100 80 60 40 20 Thickness Time Major Point To introduce the control chart as a tool to help distinguish common vs. special causes Discuss A control chart is an augmented trend chart that eliminates the subjective judgment about stable vs. unstable processes. Helps prevent tampering with a stable process Helps avoid ignoring an unstable process 96

Control Chart for Detecting Variation
Observe Variation Common Cause Detect Special Cause Control Chart Don’t Tamper Identify Major Point Control charts make the reduction of variation flowchart operational, providing a tool to guide us down the correct branch. Discuss Review the reduction of variation flow. Point out that the critical juncture is at the top: distinguishing common from special cause. A control chart is the tool for making this distinction Fix Reduce Overall Variation Prevent 97

Control Chart for Detecting Variation
Trend Chart + Center Line + Control Limits Major Point The structure of a control chart = trend chart + center line + control limits Discuss Very briefly go over the structure of a control chart. Emphasize that it is just a trend chart with some extra horizontal lines superimposed. Upper Control Limit Center Line Lower Control Limit 98

Detecting Variation Control Limits
Control limits tell us where the measurements in a stable process should fall Lower Control Limit Upper Major Point Control limits are based on the distribution of a stable process. Ask What is a stable process? A process that has the same distribution all the time Discuss For a stable process we can make a strong prediction about where we expect the next observation to fall. Control limits simply describe this prediction They define where we expect most (>99%) of the observations from the stable process to fall. 99

Also called 6 sigma limits
Detecting Variation Control Limits Calculated statistically, based on: Historical Data Characteristics of the stable process Also called 6 sigma limits -3s +3s Highly Unlikely 1.5 out of 1000 Highly Unlikely 1.5 out of 1000 Major Point Control limits, being based on the distribution of a stable process, are empirical and descriptive. Discuss Briefly discuss the main ideas on the slide Control limits are calculated statistically from historical data based on a stable process Key Control limits are empirical (based on data or experimental results), describing where the process runs most of the time. 100

Detecting Variation Creating a Control Chart
Turn the distribution on its side Upper Control Limit Center Line Major Point Recalling the relationship between histograms and trend charts, control limits can be obtained by superimposing the histogram (turned on its side) on a trend chart. Discuss Briefly review the relationship of a histogram to a trend chart. Discuss the control limits and center line and their relationship to the histogram superimposed on the trend chart. Lower Control Limit 101

Detecting Variation Can we use spec limits as control limits?
Can we compute control limits for an unstable process? Major Point Control limits are different than spec limits. They are based on what we know about a stable process rather than what we want from the process. Ask Can we use spec limits as control limits? No. Spec limits are prescriptive (what we want); control limits are descriptive (what we’ve got) Can we compute control limits from an unstable process? No. An unstable process does NOT have a single distribution at all times, so we do not know where to expect the observations to fall. (Provisional control limits could be computed from a stable portion of the data. The key is that control limits should describe the variation in the stable process.) Control limits are sometimes referred to as 3 sigma limits. 102

Process mean, based on historical data
Detecting Variation Creating a Control Chart What is the Center Line? Process mean, based on historical data or Process Target Major Point To get people thinking about two options for a center line. Discuss Main points on slide Center line = process mean Center line = target Ask Is this choice completely arbitrary? No. In a stable off-target process the center line represents the process mean What are the implications of this choice? What factors are relevant in making this choice? The aim here is simply to get the class thinking about the meaning of the center line. Issues include: Description vs. prescription Ability to control the target Effectiveness of a control chart to drive improvement. 105

Detecting Variation Creating a Control Chart Selecting the Center Line
The center line should be the target, unless we are unable or unwilling to control the process to target. Measurements: Major Point For measurements, first choice should be the center line = the target. For defects, the center line = process mean Discuss Emphasize that choosing the center line = target for measurements directs us to improve the process by moving it to the target. This choice is particularly useful when multiple machines are tracked on one chart; the implication is to move all of them to the target. (Avoid this if at all possible.) Only if moving the process to target is not possible or undesirable should the center line = process mean. For defects, since target = 0, always take the center line = process mean. Ask What about cases where the process has never been “near” target? What about process in which the mean is not significantly different from target? Note Expect this slide to be very controversial Defects: Since the target is zero defects, the center line is the process mean. 106

Control Limits vs. Spec Limits
Detecting Variation Control Limits vs. Spec Limits Control Limits Based on performance of the process. Tell us when to take action on the process. Spec Limits Based on performance of the product. Tell us when to disposition the product. Major Point To introduce the difference between the control limits and spec limits as process performance (CLs) vs. product performance (SLs). Discuss Each point on the slide Highlight the distinction between process-based control limits and product-based spec limits. Control limits describe behavior of a stable process. They tell us when action is needed to remove special-cause variation. Spec limits prescribe performance of the product. They tell us when to disposition the product. Try to get the class involved in discussion. Make sure the distinction between process-based control limits and product-based spec limits is clear. 107

Detecting Variation Control Limits vs. Spec Limits Focus On
Improve Process Quality Spec Limits Improve Product Quality Major Point Modern quality improvement efforts focus on control limits to improve the process rather than spec limits to improve the product. Improving the process quality results in product quality improvements. You cannot inspect quality into a process. Ask Where should your attention be focused for process improvement? Control limits focus our attention on continuously reducing variability from the target. Spec limits do not tell you how to make the process better. You cannot inspect quality into the process. Are spec limits useful for anything? DO NOT use spec limits to manage the process. DO use spec limits to disposition the product. Discuss Recall the loss function Traditional loss function uses spec limits to inspect-rework-scrap without helping to fix the process. Modern loss function focuses on reducing variability in the process. 109

Detecting Variation Uses of a Control Chart
On-Line: Assess the present stability of a process, as part of a process control system (PCS) Off-Line: Assess the historical stability of a process Major Point Control charts can be used on-line to detect local instability (and lead to corrective action); or off-line to assess historical, systematic stability/instability (and lead to improvement). Discuss Briefly discuss the difference between on-line and off-line. Vocabulary On-line: These are control charts in the workstream used to detect local instability. Off-line: These are control charts containing historical data from the workstream. Ask Why would it be useful to have on-line control charts? This leads us down the right hand side of the reduction of variation flowchart during the process. Hence, troubleshooting. Coincidentally, an on-line control chart will tell us when the process is stable, so we will not be tempted to tamper. Why would it be useful to have off-line control charts? These are used primarily by engineering to assess systemic stability/instability. Points to existence of special causes in the system that need to be reduced, but cannot be tackled on the floor. Coincidentally, the magnitude of common-cause variation is highlighted. This can help to: Prioritize improvement activities, and Evaluate the results of improvement activities. 111

A PCS is a subset of the Reduction in Variation flow
What is a PCS? A PCS is a subset of the Reduction in Variation flow Observe Variation Detect Special Cause Common Cause Control Chart Identify Don’t Tamper Major Point A PCS is a subset of the reduction of variation flowchart Discuss Point out the place of a PCS in the reduction of variation flowchart In addition to a PCS, the reduction of variation flowchart includes an extra box at the bottom of each branch: Special cause variation: prevent Common cause variation: reduce Both of these point to system level efforts to reduce variability in the process (as opposed to local). Fix Reduce Overall Variation Prevent 122

What is a PCS? Definition
A process control system is an on-line, real-time system for identifying and responding to process/equipment problems 123

What is a PCS? Elements of a Process Control System Measurements
Calculations Control Chart PCS Rules Response Flow 124

Elements of a PCS PCS Rules
Set of rules applied to the data plotted on the control chart to determine if the process is stable or unstable. 128

Sequence of actions followed to respond to an unstable process
Elements of a PCS Response Flow Sequence of actions followed to respond to an unstable process 129

Elements of a PCS Example: Wafer film thickness
Measure: Thickness in ms Compute: mean thickness Plot: mean thickness Apply PCS rules A single point falls beyond the 3s limit 2 of the last 3 points fall between 2s and 3s 8 points in a row fall on the same side of the center line Response Flow: Check calculations, check settings, ... 130

Why Use a PCS? Compare the Control Charts
Which process is more desirable? 150 150 140 140 130 130 120 120 110 110 Thickness 100 Thickness 100 90 90 80 80 70 70 60 60 50 50 5 10 15 20 25 5 10 15 20 25 Ignored Prompt Reaction 131

Why Use a PCS? Compare the Control Charts
Which process is more desirable? 150 150 140 140 130 130 120 120 110 110 Thickness 100 Thickness 100 90 90 80 80 70 70 60 60 50 50 5 10 15 20 25 5 10 15 20 25 Ignored Prevention 132

A PCS aids in reactive and preventive process improvement
Why Use a PCS? A PCS aids in reactive and preventive process improvement Measurements Calculations Control Chart PCS Rules Response Flow Detect Identify Fix Prevent 133

Measurement Capability
Have you ever been bitten by a measurement system? Observed Data True Data METROLOGY SYSTEM Major Point We often assume that a measurement system is valid. Measurement is a process and has variation just like any other process Ask What kinds of problems can measurement systems cause? An off-target measurement system might make you think the process is off-target when in reality it is on-target. Time/money is wasted trying to fix a nonexistent problem. An unstable measurement system might make you think a process is on target when it really isn’t. Others? black box 139

A Measurement Process Measurement tools themselves hardware software All the procedures for using the tools which operators set-up/handling procedures off-line calculations and data entry calibration frequency and technique Major Point Measurement system consists of tools and procedures. Ask What is the definition of measurement? Not just equipment Not just units Process = equipment + procedure Not a production process 140

Why Do Measurements Vary? Work Methods ease of data entry operator training calibration frequency operator technique maintenance of standards standard procedure sufficient time for work Measurement Variation Environment line voltage variation temperature fluctuation vibration humidity cleanliness Tool mechanical instability electrical wear algorithm Major Point Variation in measurement is caused by many things. Some are common causes and some are special causes. Discuss Fishbone diagram helps to identify causal relationships. Understanding these relationships helps to eliminate causes of variation. Discuss each entry in diagram Ask Can you think of other causes of measurement variation? NOTE: Not all of these will necessarily be significant sources of variation for every measurement system. 143

Assumptions We Often Make Metrology tools are perfectly accurate No day-to-day variation in performance No operator-to-operator variation Major Point We often make certain invalid assumptions about the process. Ask Are these assumptions beneficial? Yes, to a degree. At a superficial level we must assume that everything is well in order to get work done. However, at a lower level we must be aware that variation exists and we must continually work to reduce variation. 146

MCA Tells Us: How big is the measurement error? What are the sources of measurement error? Is the tool stable over time? Is the tool capable of making the measurements for this project? Is the tool capable of making the measurements for this process? What needs to be done to improve the measurement process? Major Point A measurement capability analysis helps to answer several questions about the measurement process. Discuss Remind the class that this section is about measurement capability analysis. We are analyzing the capability of metrology systems. This analysis will provide a lot of information. 151

Capability vs. Calibration Calibration Procedure to compare readings from a tool with a standard and then correct for any deviations. Statistically: centering the mean of the distribution of readings on the “true value” (obtained from a standard). Major Point Calibration is one way to improve the measurement process. Ask What are the two ways to improve a process? Move process toward the target Reduce variability Ask What is the target of a measurement process? To give a true measurement Can a measurement process be off-target? How can an off-target measurement process be made on-target? Calibrate the measurement tools Discuss One way to improve a measurement process is by calibrating the tools to ensure that the process is on-target. 152

Capability vs. Calibration (cont’d) Capability Procedure to identify and quantify sources of variation in readings and then eliminate them. Statistically: fitting the model to the readings so that the components of variance can be estimated. Both work together to keep measurement tool performing optimally. Major Point Assessing measurement capability is another way to improve the measurement process. Ask Can a measurement process have variation? How can we reduce measurement process variation? Detect variation Identify variation Fix or prevent variation Discuss Analyzing measurement capability is a way to detect and identify variation in the measurement system. Both capability analysis and calibration are useful for improving a measurement process. 153

Concepts and Vocabulary
Sources Of Variation Process Variation + Measurement Variation Major Point Total variation is a combination of process variation together with measurement variation. Ask If you have variation in your measurement process, would you expect this to impact the variation in the process? Discuss Explain that the total variation is a sum of all variation anywhere in the system. = Total Variation 155

Relationship Of These Distributions Averages mtotal = mproduct + mmeasurement error or, if the measurement tool is calibrated mtotal = mproduct Variabilities s2total = s2product + s2measurement error Never Add Standard Deviations. Note: These Relationships Are True Regardless Of The Distribution (Normal, Skewed, Bimodal, ...). Major Point When a measurement tool has been calibrated, the total variation is dominated by the process variation. Discuss Each point on this slide and point out that a calibrated tool is expected to reduce process variation. 156

Activity Suppose you have a process which has been operating for a significant period of time and has a s of 10 units. Then a measurement capability study is done and the measurement error (sms) of the metrology system is found to be 6 units. What is the true variability of the product? How could you confirm that? Major Point To give students a chance to assess their understanding of the concepts presented. Activity Have students work in teams to answer these 2 questions. Answers s2T = s2P + s2MS = 100 = s2P + 36 s2P = 64 sP = 8 Confirm: Calibrate the measurement tools and reduce measurement variation. Experiment to see if process variation drops to 64. 157

Introduction Total Variation Product Measurement System Accuracy
Major Point Total variation is product variation combined with measurement system variation. Measurement system variation is dependent upon accuracy and precision Purpose To establish a framework for how accuracy and precision relate to variation. Accuracy Precision 158

Accuracy The degree to which a process mean is on target Related Terms True Value Bias Major Point Accuracy describes how on-target a process is. Ask Is it possible for a process to be on-target but have a lot of variability? Discuss The degree to which a process is on-target is called accuracy. Ask What is the target of a measurment process? To measure the true value of a parameter. Discuss The actual value of a parameter is called the true value. 159

Precision The degree of variability in a process Related Terms Repeatability Reproducibility Major Point Precision describes how much variability a process has regardless of its accuracy. Ask Is it possible for a process to have very low variability without being on target? Discuss A process can be precise but not accurate, or accurate but not precise. Goal Accurate and precise process 160

Bias Distance between the average value of all the measurements and the true value. Can be positive or negative. Bias = m - True Value Measures the amount by which a tool is consistently off target from the truth. Bias is the numerical value we use to measure accuracy. Synonyms: systematic error, offset. Major Point Bias is the measure of accuracy. Discuss The concepts in each bullet 167

Bias bias Major Point To show a graphical depiction of bias Observed Average True Value 168

Precision Says Nothing About How Close The Measurements Are To The Truth. Accuracy Says Nothing About How Close Measurements Are To Each Other. Major Point Comparison of precision and accuracy. Demonstrates the importance of both. Discuss The differences between precision and accuracy. Both are important. 172

Precision Can be separated into repeatability and reproducibility Total Variation Product Measurement System Accuracy Precision Major Point Precision (measurement variability) is determined by repeatibility and reproducibility Discuss The overall variation components. Especially focus on repeatabilty and reproducibility. Repeatability Reproducibility These characteristics have the relationship: s2ms = s2rpt + s2rpd 180

Repeatability Variation that results when repeated measurements are made of the same parameter under absolutely identical conditions. Same operator Same set-up procedure Same part Same environmental conditions Repeatability (s2rpt) is usually much smaller (better) than the precision of the system. Major Point Define repeatability Ask Suppose you take several measurements under identical circumstances. Would you expect to see variation? Yes. There is variation in everything. Ask Would you expect that variation to be very large? No. s2rpt is usually very small. 181

Reproducibility The variation that results when different conditions are used to make the measurement. Different Operators Different Set-Up Procedures Different Measurement Tools Different Environmental Conditions Different Days Reproducibility (srpd), is approximately the standard deviation of the averages of measurements from different measurement conditions. Major Point Define reproducibility Ask Suppose you took several measurements under different circumstances. Would you expect to see variation? Yes. There is variation in everything. Ask Would you expect this variation to be large? Maybe. Certainly larger than srpt 182

Repeatability vs. Reproducibility sms measurement srpd srpt Major Point To develop a practical understanding of repeatability and reproducibility Discuss This dot plot represents 5 operators taking 10 measurements each on 1 part. The variation for each operator represents repeatability. The variation across operators represents reproducibility. 1 2 3 4 5 operator 183

Suppose the results of your measurement capability study show that srpt is 2.4 Units and srpd is 1.1 Units. What Is The Precision? Major Point To help develop a better understanding of the components of precision. Activity Ask students to use the data given to determine precision Answer s2ms = s2rpt + s2rpd = = 6.97 sms = 2.64 192

Summary of Concepts observed value bias Major Point The impact of bias and measurement error can be severe Discuss This image is designed to reflect how variation can be compounded by accuracy and precision problems in a measurement system. sms true value 195

Capability Indices Now that we understand the impact that measurement has on variation, how can we determine its impact on the product and process? Two Approaches Compare measurement error to specs Compare measurement error to process variability Major Point To help clarify what we already know and how to apply that knowledge Discuss We now understand the impact of measurement variation on overall variation. How do we assess the impact of measurement variation on the product and the process? Compare measurement error to spec limits Compare measurement error to control limits Compare measurement error to process variability 196

Capability Indices Compare Measurement Error To Specs
"How much of the specs window is eaten up by measurement error"? s2p Major Point To help students understand what it means to compare measurement error to spec limits Ask Suppose your measurement variation is very large. What must be true in order for the product to be acceptable? It must be very high quality. Process must have very little variation Discuss The measurement distribution is not necessarily centered. An inaccurate & imprecise measurement system may err toward one spec limit more than another. s2ms s2ms LSL USL 197

Capability Indices Compare Measurement Error to Specs
P/T = Precision/Tolerance Ratio = 6 * sms /(USL - LSL) Tolerance = Upper Spec Limit - Lower Spec Limit You Want P/T To Be Small. The position of the measurement distribution relative to the product specs does not matter! Major Point Understanding how to quantify the comparison of measurement error to spec limits. Discuss The precision of the measurement system is described as 6sms . This is 3sms above and below the mms. The tolerance is defined by the difference between the spec limits If the tolerance is large and the precision is small, the P/T ratio is small. This is good. It means that less of the spec window is consumed by measurement error. 198

Capability Indices Compare Measurement Error To Specs
P/T is designed to measure how much of the spec window is lost to measurement error. P/T uses only the standard deviation of the measurement error distribution. Recall that s2total = s2p + s2ms Major Point To assess capability you must understand the impact of measurement error on variation, irrespective of product variation. Discuss Key points on slide 200

Capability Indices Interpretation of P/T
Large P/T Increases the Probability That We Will Misclassify Product As Defective When Really It Is Good, or Misclassify the Product As Good When It Is Really Defective Major Point Understanding what P/T really means. Discuss Larger P/T --> larger s2ms since s2total = s2product + s2ms , if s2ms dominates s2total the chances increase that we will misclassify a product. LSL USL LSL USL True Value True Value 206

Compare Measurement Error To Process Variability
Capability Indices Compare Measurement Error To Process Variability “How well can we discriminate where in the product distribution a measurement error came from?” s2p Major Point To develop an understanding of the potential impact of metrology noise on distribution. Ask What happens to the distribution when you have a lot of metrology noise? It may become less “normal” It may become wider It may be skewed ? ? s2ms s2ms LSL USL 201

Capability Indices Compare Measurement Error To Process Variability
SNR = Signal-To-Noise Ratio = sproduct / sms You want SNR to be big. Major Point SNR is a means of quantifying the impact of metrology noise on the total variation Discuss The more sproduct dominates sms, the larger SNR gets The larger SNR is, the more the distribution represents product variation rather than metrology noise. For 1-sided spec limits you cannot calculate tolerance. Therefore, use SNR. 202

Capability Indices Interpretation of SNR
Small SNR Increases The Time Before An Out-Of-Control Process Is Detected By A Control Chart. 200 180 160 140 120 100 80 60 40 20 Thickness Time small SNR small SNR Major Point Understanding what SNR really means Discuss Small SNR means that the measurement error is very large relative to the product error. This may make you think that the process is in control when it is really out of control. This may also make you think the process is out of control when it is really in control, causing you to tamper with a stable process. 207

Capability Indices Typical Target Value for P/T P/T: <= 0.30
Typical Target Value for SNR SNR: > 10 Major Point To provide some heuristics for determining whether you have acceptable levels of metrology noise. Discuss Relationships on this slide. 205

Capability Indices Cautions
Poorly developed spec limits imply meaningless P/T. Large P/T does not mean that engineering effort should be expended on improving metrology. The process may be so poor that improving metrology won't help in the short run. P/T and SNR do not indicate where the problem exists in the measurement system (operator, tool, repeatability). Major Points To develop an understanding of the issues in P/T and SNR Discuss If spec limits have no basis, then neither does P/T P/T and SNR only give you knowledge about the impact of measurement noise on total variability. They do not tell you the cause of the variation. 203

Capability Indices Caution (cont’d)
Poor P/T performance may be partially overcome by increasing the sample size. Need to look at both P/T and SNR to get the full story. Confidence intervals for P/T and SNR can be calculated. Major Point (cont’d) Discuss P/T and SNR provide complementary information. Both together tell you how much of the spec window is filled with measurement error and what impact measurement error has on total variation. 204

Variability & Statistical Process Control

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