SPC Simplified Statistical Process Control PDF

SPC SIMPLIFIED STATISTICAL PROCESS CONTROL MADE EASY 1 ©2023 KnowWare International, Inc. SPC Simplified ©2023 KnowWare International, Inc. 2 SPC Simplified SPC Simplified © 2023 by Jay Arthur SPC Simplified Published by International, Inc. Developers of QI Macros 2696 S. Colorado Blvd., Suite 555 D...

SPC SIMPLIFIED STATISTICAL PROCESS CONTROL MADE EASY 1 ©2023 KnowWare International, Inc. SPC Simplified ©2023 KnowWare International, Inc. 2 SPC Simplified SPC Simplified © 2023 by Jay Arthur SPC Simplified Published by International, Inc. Developers of QI Macros 2696 S. Colorado Blvd., Suite 555 Denver, CO 80222 (888) 468-1537 or (303) 756-9144 (phone) (888) 468-1536 or (303) 753-3107 (fax) [email protected] www.qimacros.com © All rights reserved. Permission to reprint quotes and excerpts in company or business periodicals (magazines or newsletters) is given and encouraged with the following credit line: "reprinted from SPC Simplified, by Jay Arthur, (888) 468-1537, qimacros.com." Also by Jay Arthur: Breakthrough Improvement with QI Macros and Excel, McGraw Hill, ©2014 Lean Six Sigma Demystified, A Self Teaching Guide, McGraw Hill, ©2011 Lean Six Sigma for Hospitals, Simple Steps to Fast, Affordable, Flawless Healthcare, McGraw Hill, ©2016 On-Site Workshops with Jay Arthur: QI Macros and data mining: qimacros.com/training/qi-macros-and-data-mining Lean Six Sigma simplified: qimacros.com/training/lean-six-sigma-workshop Agile Lean Six Sigma for healthcare: www.qimacros.com/training/lean-six-sigma-for-healthcare Free Resources: Fully functioning QI Macros 30-day trial: qimacros.com/trial/30-day QI Macros training resources: qimacros.com/free-resources/qimacros-training QI Macros and Lean Six Sigma webinars: qimacros.com/free-resources Lean Six Sigma Yellow Belt training at www.qimacros.com/Moneybelt.com Six Sigma is a registered trade and service mark of Motorola, Inc. Rev:1222 ©2023 KnowWare International, Inc. SPC Simplified ©2023 KnowWare International, Inc. ©2021 SPC Simplified SPC Simplified Table of Contents What is Statistical Process Control (SPC)? Flowcharts Control Plans Control Charts What is Statistical Process Control (SPC)? Once you’ve made improvements you want to sustain (i.e., control) them to ensure that you stay at the new level of performance, otherwise, you’ll gradually slip back to the old levels of performance. That’s why you need SPC. 1 3 4 5 An SPC system of flowcharts, control charts, and/or histograms help you monitor and maintain your new level of performance. Process control systems consist of: Stability Analysis Which Control Chart Should I Use? Why Are There So Many Charts? Control Charts for Special Circumstances 6 9 12 13 Histograms and Process Capability 19 Understanding Distributions Histograms Interpreting the Results to Improve Your Process Histogram Weibull Distribution Frequency Histogram Appendices Appendix A: Control Chart Formulas Appendix B: Capability Metrics Formula Details Appendix C: Capability Metrics Sample Calculation 20 22 23 25 26 27 27 32 36 36 QI Macros Overview 38 QI Macros Chart Overview 43 Prepare Your Data Improvement Project Wizard QI Macros PivotTable Wizard QI Macros Control Chart Wizard Attribute Charts Variable Charts Control Chart Dashboards Histograms and Capability Analysis Charts SPC Simplified DVD Guidebook Laser Focus Your Improvement Story Sustain the Improvement SPC Simplified Introduction Control Charts & Stability Analysis Histograms & Capability Analysis ©2023 KnowWare International, Inc. ©2021 39 40 41 42 43 46 49 50 53 54 55 56 60 63 SPC Simplified The system: suppliers, inputs, process, and outputs Charts of performance: control charts, and histograms Corrective actions: changes to the people, process, machines, materials, measurement, and environment Rework to fix defects in finished products Six Sigma Control is the fifth step in the DMAIC (Define, Measure, Analyze, Improve and Control). SPC is how ongoing performance is controlled. The best a company can hope for without SPC is 3 (three) sigma (6% error). By establishing specifications and targets for your work processes and then defining measurements, you begin to ensure that you deliver what customers require. Continual monitoring lets you know how well you are satisfying your customers and when you need correction. SPC Systematically improves and controls your processes Maintains the gains achieved through improvement projects Sustains the gains from improvement teams Multiplies the gains from one process to other similar processes Increases employee understanding of what is expected SPC Key Tools Flowcharts to define the process flow Control Charts to measure the stability of the process Histograms to measure the capability of the process Control Plans to identify the characteristics of the process or product Use these tools to monitor, sustain, and control virtually any process – service or manufacturing. ©2023 KnowWare International, Inc. 1 SPC Simplified Control Flowcharts Before you can find better, faster, and cheaper ways of serving customers you first have to stabilize the way of doing business. Making existing processes predictable and capable of meeting customer requirements follows the FISH (Focus, Improve, Sustain, and Honor) process. Use Flowcharts to Define and Refine the Process FISH Step Activity 1 Refine the process 2 Refine the quality and process indicators (CTQs or Critical to Quality trees) Improve 3 Implement the process and indicators Sustain 4 Check the process for stability (predictability) and capability (meeting customer requirements) Honor 5 Recognize, review, and re-focus Focus A flowchart uses a few simple symbols to show the flow of a process. The symbols are: What is the Goal of SPC? The goal of SPC is to stabilize the process, reduce variation and meet customer requirements. The first step is to stabilize the process. The second step is to make the process capable of meeting customer requirements. Improvement efforts cannot begin until a process is stable and predictable. Once a process has been improved control charts and histograms can be used to demonstrate improvements. Control Chart Showing Improvement in a Process Instead of writing directly on the flowchart, use small Post-it® notes for both the decisions and activities. This way, the process remains easy to change until you have it clearly defined. Limit the number of decisions and activities per page. Move detailed sub-processes onto additional pages. Across the top of the flowchart list every person or department that helps deliver the product or service. Along the left-hand side, list the major steps in your process: planning, doing, checking, and acting to improve. Even going to the grocery store involves creating a list (plan), getting the groceries (do), checking the list, and acting to get any forgotten item. Histograms Showing Improvement in a Process ©2023 KnowWare International, Inc. 2 SPC Simplified ©2023 KnowWare International, Inc. 3 SPC Simplified Control Plans Control Charts A control plan summarizes the characteristics of a product or process that can be tracked and measured to monitor process variation and performance. These product and process characteristics are often referred to as indicators. A stable process produces predictable results. Understanding variation teaches you how to predict the performance of any process. To ensure that the process is stable (i.e., predictable) you need to develop run or control charts of your indicators. How can you tell if a process is stable? Processes are never perfect. Common and special causes of variation make the process perform differently in different situations. Getting to school or work takes varying amounts of time because of traffic or transportation delays. These are common causes of variation; they exist every day. On the other hand a blizzard, a traffic accident, a chemical spill, or other rare occurrence that causes major delays would be a special cause of variation. Process and Quality Indicators Process indicators measure performance during the process. They help find and fix problems before the customer is affected. Put them at critical hand-offs between functions and decision points – especially ones that require error correction. In the 1920’s, Dr. Shewhart, while at Bell Labs, developed ways to evaluate whether the data on a line graph is common cause or special cause variation (see page 13). Using 20–30 data points, you can determine how stable and predictable the process is. Using simple equations, software can calculate the average (center line), and the upper and lower control limits from the data. 99% of all expected (i.e., common cause variation) should lie between these two limits. Quality (CTQ) indicators are measured after a product or process is complete. They track customer satisfaction with timeliness, accuracy, and value. ©2023 KnowWare International, Inc. 4 SPC Simplified ©2023 KnowWare International, Inc. 5 SPC Simplified Stability Analysis There are several slightly different variations of stability rules depending on the industry and which SPC textbook you use. Here are the most widely accepted options: Unstable conditions can be any of the following: QI Macros identifies unstable points or trends and highlights them in red automatically. Any point outside the upper or lower control limits is a clear example of a special cause. The other forms of special cause variation are called runs. Trends, cycling up and down, or hugging the center line or limits are special forms of a run. ©2023 KnowWare International, Inc. 6 SPC Simplified ©2023 KnowWare International, Inc. 7 SPC Simplified Recalculating Control Chart Limits to Show Process Changes Which Control Chart Should I Use? Generally, you calculate control limits using the first 20 to 25 data points and then use those limits to evaluate the rest of your data. If you have a process change, recalculate your control limits beginning with data after the process change occurred. Many people struggle with choosing the right control chart. The chart is based on the type of data, attribute (counted) or variable (measured), and the sample size. Recalculated limits show the success of process improvement efforts. A change in the average or center line and the reduced variation (difference between the UCL and LCL) show success. In the following chart, the process improvements reduced patient falls per 1000 patient days from 5.9 to 4.7 and significantly reduced variation as evidenced by the distance between the UCL and LCL. Here are some tips on how to choose the right chart: Use np, p, c, and u charts if you are counting defective items (e.g. incorrect orders) and have attribute data (i.e., integer or counted defects). Use an np chart if the sample size is constant. Use a p chart if the sample size varies. If you are counting the number of defects (e.g. number of errors on an order): Use a c chart if the sample size is large or not available. Use a u chart if the sample size varies. If you are using a ratio of defects/period (e.g., patient falls/1000 patient days) use the XmR chart. Use XmR, XbarR, and XbarS Charts for variable or measured data (i.e., decimal) such as time, cost, length, weight, etc. Using Control Charts to Compare Data from Different Processes Use control charts to compare different processes side by side. In healthcare, compare data for different doctors, hospitals, floors, etc. In manufacturing, compare data from different machines, lots, batches, etc. In this example, from https://www.itl.nist.gov/div898/handbook/ppc/section5/ppc521.htm, a machine shop has three automatic screw machines that produce various parts. The shop has enough capital to replace one of the machines. The quality control department has been asked to conduct a study and make a recommendation as to which machine should be replaced. If you run side-by-side control charts you can see that Machine 3 has the most variation (greatest distance between UCL and LCL). Based on the analysis you would replace Machine 3. If the sample size is one use an XmR chart. If the sample size is 2–5 use an XbarR chart. If the sample size is 6–25 use an XbarS chart. When working with data in Excel, follow a simple strategy for selecting the right chart based on the format of the data itself. There are three formats: 1. A single row/column 2. Two rows/columns with a numerator and a denominator 3. Two or more rows/columns containing multiple observations from each sample The QI Macros Control Chart Wizard analyzes your data and selects the right control chart. Highlight your data and select Control Chart Wizard from the QI Macros menu. ©2023 KnowWare International, Inc. 8 SPC Simplified ©2023 KnowWare International, Inc. 9 SPC Simplified Single Row/Column Two or More Rows/Columns of Variable Data If you have only a single row/column of data, there are only three charts you can use: Service industries don't use the XbarR or XbarS charts very often. They are mainly used in manufacturing. If you have two or more rows or columns of variable data (time, weight, length, width, diameter, or volume) then you can choose one of three charts: c chart for attribute or counted data (always an integer, e.g., 1,2,3,4,5) XmR chart for variable or measured data (usually has decimal places, e.g., 33.75) XmR Trend chart for variable data that increases, e.g., rising costs due to inflation So, which one should you choose? If you're counting indivisible things like defects, people, cars, or injuries, then choose the c chart. If you're measuring things like time, length, weight, or volume, choose the XmR chart. Look for these patterns in the data and then select the chart. XbarR (Average and Range, 2–5 rows/columns per sample) XMedianR (Median and Range, 2–5 rows/columns per sample) XbarS (Average and Standard Deviation, 6–25 rows/columns per sample) Your data should look like this: Two Rows/Columns If the data has a varying numerator and a denominator (e.g., defects/batch, errors/transactions), use one of the following: p chart (one defect maximum per piece) u chart (one or more defects per piece) You can run the XbarR, XMedianR, or XbarS on this data. XbarR uses the average as the measure of central tendency. The XMedianR uses the median. If you have more than five samples per period, then the XbarS is perhaps the most robust chart for your needs. You can also use the XbarR or XbarS charts if your data has a varying number of samples per period: How can you tell which one to use? Ask yourself, “Can this widget have more than one defect?” If yes, use the u chart, otherwise use the p chart. Sometimes, you can have more defects than samples; this is another clue. Again, look for these patterns in the data and then select the chart. Look for these patterns in your data and then select the chart. ©2023 KnowWare International, Inc. 10 SPC Simplified ©2023 KnowWare International, Inc. 11 SPC Simplified The np Chart Understanding Control Chart Limits The np chart is like the p chart except that the sample sizes are constant. The data looks like this: Ask yourself this question, "If a simple formula using the mean and standard deviation would work for any data, why are there so many different control charts?" The short answer: To save money by measuring small samples, not the entire population. The long answer: When using small samples or varying populations, the simple formula (using the mean and standard deviation) doesn't work because you don't know the average or sigma of the total population, only the sample. Why are there so many control charts? Because you have to estimate µ and sigma using the average and range of your samples. Summary Variable charts: In variable charts the XmR uses a sample size of 1, XbarR (2–5) and XbarS (6–25). These small samples may be taken from lots of 1,000 or more. Recognizing patterns in your data can make it easier to pick the right control chart. Rows/Columns 1 2 Attribute c chart np chart p chart u chart 2 or more Attribute charts: In attribute charts the c and np chart use small samples and fixed populations. The u and p charts have varying populations. So, you have to adjust the formulas to compensate for the varying samples and populations. Variable XmR chart XmR Trend To reduce the cost of inspection at Western Electric in the 1930s, Dr. Walter S. Shewhart developed a set of formulas and constants to compensate for these variations in sample size and population. That's why they are sometimes called Shewhart Control Charts (see page 5). You can find these formulas in any book on statistical process control (e.g., Introduction to Statistical Process Control, Montgomery, Wiley, 2001, pgs. 207–265). XbarR XMedianR XbarS Why Are There So Many Charts? Control Charts for Special Circumstances Understanding Standard Deviation and Control Charts Many people ask, “Why aren’t my upper and lower control limits (UCL, LCL) calculated as µ + 3σ (where µ is the mean and σ is the standard deviation)?” To answer this question, you have to understand some key, underlying statistics: variation, standard deviation, sampling and populations. Variance (stdev2) is the average of the square of the distance between each point in a total population (N) and the mean (µ). If your data is spread over a wider range, you have a larger variance and standard deviation. If the data is centered around the average, you have a smaller variance and standard deviation. Standard deviation (stdev or σ) is the square root of the variance and it can be estimated using the average range (Rbar) between samples (Rbar/d2) when the number of subgroups is 2–10, or using standard deviation Sbar/c4 when n>10. Rbar = Rave = ΣRi/n Sbar = Average (stdev) = Σσ i/n Besides the four attribute charts (p, np, c and u) and four variable charts (XmR, XmR trend, XbarR, XbarS) there are other charts for special circumstances. Short Run Charts Some processes only produce a small number of products in a single run, not the 20 samples needed for most charts. As companies implement just-in-time inventory and lean manufacturing, short runs become more common. The AIAG Statistical Process Control handbook summarizes guidelines for when to use short run charts. These guidelines are summarized from the book, Short Run SPC, 1991 by D.J. Wheeler: 1. 2. 3. 4. The process must be inherently stable over time. The process must be operated in a stable and consistent manner. The process aim must be set and maintained at the proper level. The natural process limits must fall within the specification limits. Sampling: Early users of SPC found that it cost too much to evaluate every item in the total population. To reduce the cost of measuring everything, they had to find a way to evaluate a small sample and make inferences from it about the total population. To do this, short run charts use the difference between the target value and the measurement as data, not the measurement. QI Macros contains short run versions of the following charts (p, np, c, u, XmR, XbarR). Access them in the Control Chart Templates section of the QI Macros menu. Select a specific SPC chart template like the XmR Five Pack; the regular and short run charts can be found on separate worksheet tabs in the template. ©2023 KnowWare International, Inc. 12 ©2023 KnowWare International, Inc. 13 d2 and c4 are constants based on the sample size. SPC Simplified SPC Simplified Charts for Detecting Small Changes Cumulative Sum (CUSUM) Charts There are circumstances in which normal control charts may not be sensitive enough to detect small changes in a process. When small changes in a process need to be identified quickly, consider one of the following charts. The CUSUM chart plots the cumulative sums of the deviations of the sample values from a target value. It puts equal weight on current and recent data. Compare the XmR chart and CUSUM chart below, created using the same data. The XmR chart identifies the process change by showing the last eight points as unstable. Exponentially Weighted Moving Average (EWMA) Chart The EWMA chart plots moving averages of past and current data. The values being averaged are assigned weights that decrease exponentially from the present to the past. The EWMA puts more weight on recent data. QI Macros contains an EWMA chart. Highlight your data, select EWMA control chart from the QI Macros menu, and enter the weight at the prompt. QI Macros will create the EWMA chart: The CUSUM chart draws attention to the subtle process change much earlier (within 3 or 4 points) and much more drastically (by the steep up-sloping line). You can run a CUSUM chart using the QI Macros menu. ©2023 KnowWare International, Inc. 14 SPC Simplified ©2023 KnowWare International, Inc. 15 SPC Simplified Levey Jennings Standard Deviation Chart Analysis of Means (ANOM) Control Chart Healthcare labs use the Levey Jennings charts to monitor key measures of health like cholesterol and glucose. The Levey Jennings chart, unlike other SPC charts, uses standard deviation as a way of calculating control limits. The ANOM chart is like a control chart with a center line and upper and lower decision limits. Means outside of the decision limits are considered to be statistically different from the overall mean (i.e., average). In the ANOM chart below, seven operators are compared. The means for operator 6 and operator 7 are considered statistically different from the overall mean. Levey Jennings 10-20-30% Chart According to SOFT / AAFS Forensic Toxicology Laboratory Guidelines 9.1.12 standard deviation may represent an unacceptably large percentage deviation from the mean; therefore, a realistic percentage deviation should be used, such as ±20% or ±30%. Using these guidelines, Levey Jennings chart control limits look like this: ©2023 KnowWare International, Inc. 16 SPC Simplified ©2023 KnowWare International, Inc. 17 SPC Simplified Histograms and Process Capability Hotelling T2 Control Chart The Hotelling T2 chart helps evaluate two interacting measurements simultaneously. Imagine you are measuring the location of a hole drilled in a sheet of metal. It could be left or right, up or down. It’s possible that both measurements, taken separately, could be stable and predictable, but the two together could have outliers. Similar to the XmR, the Hotelling chart evaluates the covariances of the ranges between each of the two measures and the covariances of the actual data points. This gives two charts that are similar to the average and range in the XmR. Product and Process Variation The primary goals of most process improvement methodologies like Six Sigma are to reduce defects, delays, and variation. The focus of this section is on reducing variation. What is Variation? Every process varies: it takes a little more or a little less time, a product is a little bit bigger or smaller, longer or shorter, wider or thinner, heavier or lighter, or fuller or emptier than its ideal target size, shape, etc. The variation may be large or almost undetectable, but it’s still there. The goal of Six Sigma is to reduce the amount of variation so that your product always fits well inside your customers’ expectations (specifications) and hopefully centers on a target value for that product. Manufacturers get into trouble when they produce products that don’t fit the customers’ requirements. Service businesses get into trouble when they can’t meet the customers’ requirement for timeliness. Process Capability Analysis Requires Stability Before a process can be evaluated for capability, it must be stable. Use a control chart to determine process stability. If there are no unstable conditions (QI Macros show unstable conditions in red), you can proceed to capability analysis. ©2023 KnowWare International, Inc. 18 SPC Simplified ©2023 KnowWare International, Inc. 19 SPC Simplified The goal for all problems associated with variation is to center the distribution over the ideal target value and minimize the amount of variation around that target value. For most products, customers have a target value and some tolerance for parts around the target value. Your ability to produce products centered around the target value with a minimum amount of variation determines the quality of your product. For example, a bolt cannot be bigger or smaller than the nut it screws into; a cap cannot be bigger or smaller than its bottle. In many ways, this is like the goal posts in an American football game: There’s a left and a right post, and the kicker’s job is to kick the ball between the two posts. Anything outside of the posts results in no score (or in Six Sigma terms, a non-conforming part). The left and right post might be considered the game’s “specification limits”. The center is usually the average (i.e., the mean) of all of the data points although other measures of the center can be used (e.g., median, center point or mode, most frequent data value). The spread is the distance between the minimum and the maximum values. And the shape can be bell-shaped, skewed (i.e., leaning) left or right, and so on. There are two outcomes for any improvement effort: Center the distribution over the target value. Customers specify their requirements for these targets and tolerances in one of two ways: Target and a bilateral (i.e., two-sided) tolerance (e.g., 74 ± 0.05) Target and a unilateral (i.e., one-sided) tolerance (e.g., 74 + 0.05) These are used to determine the specification limits (the goal posts). Upper Specification Limit (USL) = 74 + 0.05 = 74.05 Lower Specification Limit (LSL) = 74 - 0.05 = 73.95 Specification limits apply to services too. You may expect to wait 3 minutes in line at the grocery store (the target), and you would be pleasantly surprised if you didn't have to wait in line at all (LSL=0 or no LSL). You might leave the store without buying anything if a line looked like it might take longer than 10 minutes (USL=10). Tip: Don’t confuse specification limits (i.e., USL and LSL) with control limits (UCL and LCL). Customers set specification limits; control charts use your data to calculate control limits. Reduce the spread of the distribution. Understanding Distributions Before you can start to analyze capability, you’ll want to understand the basic concept of distributions (e.g., the bell-shaped curve). Distributions have three key characteristics: center, spread, and shape. These two outcomes can be easily monitored using histograms, which help you determine the capability of your process. ©2023 KnowWare International, Inc. 20 SPC Simplified ©2023 KnowWare International, Inc. 21 SPC Simplified Histograms Interpreting the Results to Improve Your Process Histograms are simply bar charts that show the distribution of your data using the number of times your data points fall into each of the bars on the histogram. When you add the upper and lower specification limits, it’s easy to see how your data fits your customers’ requirements and what improvements might be necessary. Once you have run a histogram to calculate Cp and Cpk, you can decide how to improve. If the process is off-center, adjust your work so that it becomes centered. If the capability is less than 1.33, adjust your process so that there is less variation. In manufacturing, customers require Cp=Cpk greater than 1.33 (4 sigma). If you are producing products for the Asian market, especially Japan, they require Cp=Cpk greater than 1.66 (5 sigma). From a Six Sigma perspective, Cp and Cpk directly correlate with Six Sigma targets: Cp and Cpk Pp and Ppk 1.0 1.33 1.66 2.0 Sigma Level 3 4 5 6 If Cp is greater than Cpk – data fits between the spec limits but is not centered. The corrective action is to center the process. Capability Indices Using the specification limits, there are four key indicators of process capability: Cp – Capability Index: Measures how well your data fits between the upper and lower specification limits. It doesn’t measure whether the process is centered within the limits, only if the data fits. Cpk – Centering Capability Index: Measures how well your data is centered between the upper and lower specification limits. If Cp is less than Cpk, data is centered but does not fit between the spec limits. The corrective action is to improve the process to eliminate non-conforming parts. Cp and Cpk use an estimation of the standard deviation known as sigma estimator to calculate the spread of the data. If the variation (i.e., range or standard deviation) between samples is small, Cp and Cpk often provide better predictors of capability. Pp – Performance Index: Like Cp, it measures how well your data fits within the USL and LSL. Ppk – Performance Centering Index: Like Cpk, it measures how well your data is centered between the USL and LSL. Pp and Ppk use the actual standard deviation of the data, not the estimate. ©2023 KnowWare International, Inc. 22 SPC Simplified ©2023 KnowWare International, Inc. 23 SPC Simplified If Cp = Cpk and both are greater than 1.0 but less than the target value of 1.33 (4 sigma) the corrective action is to improve the process to reduce variation: Histogram Weibull Distribution Not all data is normally distributed (i.e., bell-shaped). Weibull analysis is especially suited to failure rates (e.g.: How long does a TV, PC, ball bearing, etc. operate before failing?). Weibull analysis works well with small samples (fewer than 20). Here is an example of ball bearing failure rates. Failure rates peak at 81.86. Capability Analysis Formulas Formulas for Cp and Cpk use sigma estimator Formulas for Pp and Ppk use standard deviation The shape parameter (slope = 2.10) describes the failure rate: Shape < 1 is a decreasing failure rate (infant mortality). Shape > 1 is an increasing failure rate (wear-out failures). Shape = 1 means random failure rate (independent of age). It approximates the exponential distribution. Shape = 3.6 approximates the normal distribution. The scale parameter (characteristic life) is the age at which 63.2% of units will have failed (81.86 million cycles). Weibull Probability Plot Use the Weibull Probability Plot to determine when a certain percent of parts will have failed. Defects Per Million Because you’re using a small sample to analyze process capability, it may seem difficult to calculate the estimated defects, but statistics make it easy. Since you know the standard deviation and the specification limits, through the magic of statistics you can calculate the actual defect rate in parts per million (PPM) and, using the standard deviation, estimate the defect rate in parts per million for the entire population. ©2023 KnowWare International, Inc. 24 SPC Simplified In this example, 10% of the parts will have failed by time 27. ©2023 KnowWare International, Inc. 25 SPC Simplified Frequency Histogram Appendices Use a frequency histogram when your data falls into predictable sizes such as 0.65, 0.70, 0.75. Like a histogram, a frequency histogram shows the spread or dispersion of data. But, rather than sort the values into bins, a frequency histogram has one bin per value. A frequency histogram uses variable data to determine process capability. The customers’ upper specification limit (USL) and lower specification limit (LSL) determines how well the process meets customers’ requirements. Appendix A Control Chart Formulas c Chart: u Chart: p Chart: pi = number of nonconforming items ni = sample size Where (i.e., there isn’t that much variation in sample size) np Chart: ©2023 KnowWare International, Inc. 26 SPC Simplified ©2023 KnowWare International, Inc. 27 SPC Simplified XmR Chart XmR Trend Chart The XmR (Individuals and Moving Range) chart helps evaluate a process when there is only one column of samples and they are farther apart (i.e., monthly postage expense, time to write a computer program, etc.). UCL and LCL calculations are the same as for the XmR chart. The only difference is how the X center line (CL) is calculated using linear regression to give you the slope of the trend and a y-intercept value: "b," calculated as follows: Moving Range Chart X Chart The XmR Trend then calculates the linear correlation coefficient (Ryx) for the degrees of freedom (df=k2). If Ryx is greater than the probability for this degree of freedom, you have a significant correlation between x and y. (The probability that you will conclude there is no correlation when there is one: alpha = 0.05) If Ryx2 is greater than 0.80, then the correlation indicates a useful fit. What does this mean? Significant correlation. k = number of data points for n=2 observations (moving range is calculated from two samples—the present minus the previous value) D4 = 3.267 D3 = 0 E2 = 2.660 A measure of x versus y: Is the relationship between x and y statistically significant? This is a measure of how well the trend line reflects the relationship between x and y. Useful Fit Calculate, plot, and evaluate the range chart first. If it is out of control, so is the process. If the range chart looks okay, then calculate, plot, and evaluate the X chart. Even if there is a significant correlation above, this asks: “Is it useful? Can you make an assumption or prediction about y based on history?” The variation in x versus the variation in y is a measure of how the points vary within the control limits. df 1 2 3 4 5 6 7 8 9 10 Probability.997.950.878.811.754.707.666.632.602.576 df 11 12 13 14 15 16 17 18 19 20 Probability.553.532.514.497.482.468.456.444.433.423 df 21 22 23 24 25 26 27 28 29 30 Probability.413.404.396.388.381.374.367.361.355.349 df 35 40 45 50 60 70 80 90 100 Probability.325.304.288.273.250.232.217.205.195 (Source: Statistical Methods for the Process Industries, W McNeese and R Klein, ASQ Press, Milwaukee, pg. 280–290) ©2023 KnowWare International, Inc. 28 SPC Simplified ©2023 KnowWare International, Inc. 29 SPC Simplified XbarR Chart XMedianR Chart The XbarR chart is especially useful when you sample a process many times a day. Using a small sample (typically five and as many as 25) you can effectively measure and evaluate the process. The XMedianR works just like the XbarR except that it uses the median instead of the average as a measure of central tendency. Range Chart Average (Xbar) Chart Range Chart XMedian Chart k = number of subgroups n = number of samples in a subgroup A2, D3 and D4 are constants based on n n = number of samples in a subgroup k = number of subgroups used to determine the average median and range XBarS Chart Standard Deviation Chart Average (Xbar) Chart Control Chart Constants k = number of subgroups n = number of samples in a subgroup si = Standard deviation of the samples A3, B3 and B4 are constants based on n ©2023 KnowWare International, Inc. 30 SPC Simplified ©2023 KnowWare International, Inc. 31 SPC Simplified Appendix B Capability Metrics Formula Details Appendix B Capability Metrics Formula Details Formulas for Cp and Pp Cp ( USL-LSL ) (6 * sigma estimator) Use when you have a sample Pp ( USL-LSL ) (6 * standard deviation) Use when you have the total population Between/Within Deviation is an option added to the histogram macro and template in December 2015. Formulas for Cpk and Ppk Cpk Minimum of CpU and CpL Ppk Minimum of PpU and PpL CpU ( USL-Xbar ) (3 * sigma estimator) PpU ( USL-Xbar ) (3 * standard deviation) CpL ( Xbar - LSL ) (3 * sigma estimator) PpL ( Xbar - LSL ) (3 * standard deviation) Use when you have a sample Use when you have the total population Points to note: Xbar is the average of the data points = ∑X /n. Changing the spec limits changes Cp and Pp and may change Cpk and Ppk. Cp and Cpk use sigma estimator because they assume your data represents a sample of the population. Pp and Ppk use standard deviation because they assume your data represents the total population. Sigma Estimator Formulas and Calculations Used in QI Macros Pooled Standard Deviation is the default estimator for QI Macros Cp and Cpk calculations since May 2015. Sbar/c4 and Rbar/d2 can still be used by changing the estimator field on the histogram data sheet. d2 is a constant based on subgroup size c4 is a constant based on subgroup size Rbar = Average(Ri) (Average of the Ranges in samples) sbar = Σ(σi)/n Pp and Ppk Calculations in Weibull Histogram Unlike the Pp and Ppk calculations, which rely on a Normal distribution, the Weibull histogram uses the WEIBULL (or WEIBULL.DIST) function to calculate the Z-scores for the USL/LSL, and from these it calculates Pp and Ppk. No Cp or Cpk calculation is possible in the Weibull Histogram. If there is only a USL or LSL, the Weibull histogram Ppk is either PpU or PpL. ©2023 KnowWare International, Inc. 32 SPC Simplified ©2023 KnowWare International, Inc. 33 SPC Simplified Formulas for One Sided Spec Limits Constants for Sigma Estimator Calculation LSL Only Cp = Cpk = CpL Pp = Ppk = PpL Source: The ASTM manual on Presentation of Data and Control Chart Analysis – Table 16, 2002 Subgroup Size 1 Constant Value Constant Value 1.128 Subgroup Size 26 d2 c4 0.9901 2 d2 1.128 27 c4 0.9905 3 d2 1.693 28 c4 0.9908 4 d2 2.059 29 c4 0.9912 5 c4 0.94 30 c4 0.9915 6 c4 0.9515 31 c4 0.9917 7 c4 0.9594 32 c4 0.992 8 c4 0.965 33 c4 0.9922 9 c4 0.9693 34 c4 0.9925 10 c4 0.9727 35 c4 0.9927 11 c4 0.9754 36 c4 0.9929 12 c4 0.9776 37 c4 0.9931 13 c4 0.9794 38 c4 0.9933 14 c4 0.981 39 c4 0.9935 15 c4 0.9823 40 c4 0.9936 16 c4 0.9835 41 c4 0.9938 17 c4 0.9845 42 c4 0.9939 18 c4 0.9854 43 c4 0.9941 19 c4 0.9862 44 c4 0.9942 20 c4 0.9869 45 c4 0.9944 21 c4 0.9876 46 c4 0.9945 22 c4 0.9882 47 c4 0.9946 23 c4 0.9887 48 c4 0.9947 24 c4 0.9892 49 c4 0.9948 25 c4 0.9896 50 c4 0.9949 ©2023 KnowWare International, Inc. 34 USL Only Cp = Cpk = CpU Pp = Ppk = PpU Formula for Defects in Parts Per Million Actual (# of non conforming)*1,000,000 (# of parts) Estimated for Population PPMU = NORMSDIST(Z upper)*1,000,000 + PPML = NORMSDIST(Z lower)*1,000,000 Formulas for Z Scores Z scores help estimate the non-conforming PPM. Z scores standardize +/-3* sigma estimator values into +/-3. Z lower Z upper Z bench is the Z score for the expected PPM ZT (target) = Cpk for a target value instead of the USL or LSL. If not defined, use the midpoint between the USL and LSL (LSL-Xbar)/sigest (USL-Xbar)/sigest normsinv(1-(Expected PPM/1,000,000)) (Xbar-Target)/(3*sigest)  SPC Simplified ©2023 KnowWare International, Inc. 35 SPC Simplified Appendix C Capability Metrics Sample Calculation Calculations You can perform calculations using the following sample data from Montgomery’s, Introduction to Statistical Quality Control, 4th Ed., pgs. 353–358. Download this data as part of the QI Macros test data at qimacros.com/testdata/SPCManufacturing.xls. Open the spreadsheet and click on the histogram tab. Sample S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20 Obs 1 265 268 197 267 346 300 280 250 265 260 200 276 221 334 265 280 261 250 278 257 Obs 2 205 260 286 281 317 208 242 299 254 308 235 264 176 280 262 274 248 278 250 210 Obs 3 263 234 274 265 242 187 260 258 281 265 246 269 258 265 271 253 260 254 265 280 Obs 4 307 299 243 214 258 264 321 267 294 283 328 235 263 272 245 287 274 274 270 269 Obs 5 220 215 231 318 276 271 228 293 223 277 296 290 231 283 301 258 337 275 298 251 Value.762 USL - LSL ) (6 *standard dev) ( USL - Xbar ) 3 *( SBar/c4 ) ( 346-200 ) (6 * 31.85) ( 346-264.46 ) (3 * (30.02/.94) 146 191.10 81.54 95.81.764 ( Xbar - LSL ) 3 * ( SBar/c4 ) (264.46-200 ) (3 * (30.02/.94) 64.46 95.81.673 Pp ( CpU CpL PpL Ppk Actual PPM Est PPM Z upper (Zu) ) Minimum of CpU and CpL.851 vs.673 ( USL - Xbar ) ( 346-264.46 ) (3 * standard deviation) 3 * 31.85 ( Xbar - LSL - ) ( 264.46-200 ) (3 * standard deviation) 3 * 31.85 Minimum of PpU and PpL.853 vs.675 (# of non conforming parts) 3 (# of parts) 100 PPM Upper + PPM lower NORMDIST (2.553) = * 1,000,000 NORMDIST(Zu) * 1,000,000 + + NORMDIST (2.019) NORMDIST(Zl) * 1,000,000 * 1,000,000 ( USL - Ave ) 346 - 264.46 ( SBar/c4 ) 31.93 Z lower (Zl) Z bench Target Z target ( LSL - Ave ( SBar/c4 ) ) normsinv(1-(Expected PPM/1,000,000)) Defined by Customer or Midpoint between USL and LSL ABS(Xbar-Target) (3*sigest) 81.54 95.55 64.46 95.55 30,000 1,000,000 21,768.4 + 5334.3.851.673.853.675.675 30,000 27,102.7 2.553 200 - 264.46 31.93 -2.019 normsinv(1-(.0267104) ( 346 + 200 ) 2 normsinv(.97329) 1.93 546 2 273 264.46 - 273 3*(30.02/.94) 8.54 95.81.09 The final calculated amounts are: Since there are 5 subgroups, sigma estimator uses the formula SBar/c4 In the table above, the constant for a subgroup of 5 is 0.94 Other calculations for this data set are: –– Xbar = 26,446/100 = 264.46 –– Standard deviation = 31.85 –– Sigma estimator = ( SBar/c4 ) = (30.02/.94) = 31.93 Use the statistical functions in Excel to calculate standard deviation, normdist, and normsinv if you are recalculating this manually. ©2023 KnowWare International, Inc. 36 Calc 146 191.62 ( Cpk PpU Assume the USL = 346 and the LSL = 200. Calc ( 346-200 ) 6*(30.02/.94) Cp Formula USL - LSL 6*( SBar/c4 ) SPC Simplified Cp Cpk Pp Ppk PPM Est PPM Zbench Z target.762.673.764.675 30,000 27,102.7 1.93.09 Since the standard deviation and sigma estimator were fairly close in value, the Cp and Pp and Cpk and Ppk values were similar. ©2023 KnowWare International, Inc. 37 SPC Simplified Prepare Your Data QI Macros Overview When your data is set up properly, it is much easier to draw the graphs and interpret the results. QI Macros Consists of Four Parts 1. Charting Tools: Macros Control Charts, Histograms, Line, Run, Scatter, Pareto, Bar, Pie, Box Whisker, Multi Vari Worksheet Format: Other software packages make you transfer your Excel data into special tables, but not QI Macros; just put your data in a standard Excel worksheet. The simplest format for your data is usually one column of labels and one or more columns of data (e.g., samples): 2. Statistical Tools: ANOVA, F-Test, t-Test, Chi-Squared, Correlation, Regression, Sample Size Calculator 3. Fill-in-the-blank-Templates: SPC Charts, Dashboards, Flowcharts, Fishbones, DOE, Gage R&R, QFD, FMEA, PPAP, Value Stream Maps 4. Data Mining Tools: Data Mining Wizard, PivotTable Wizard, Count Words, Stack/Restack Tables, Paste/Link Transpose QI Macros Wizards Analyze your data and choose the right chart or statistical test for you. Chart Wizard - runs descriptive statistics and possible charts like pareto charts, control charts, histograms, scatter plots, etc. Improvement Project Wizard - automates the creation of a PivotTable and all of the charts that can be derived from the data. Examines your data, summarizes it, and creates control charts and Pareto charts automatically. Control Chart Wizard - chooses the right control chart for your data from: c, np, p, u, XmR, XbarR, or XbarS. PivotTable Wizard - creates a PivotTable when you select up to four column headings. Statistics Wizard - chooses the right statistical tests for you. Tells you if your data is normal and if the means and variances of two or more samples are the same or different. Learn more: qimacros.com/qi-macros/wizards Works Right in Microsoft Excel Other software packages make you transfer your Excel data into special tables within their application, but not QI Macros; lick and drag over the data in your Excel spreadsheet and click on the chart or analysis you want to run from the QI Macros menu. Sample Data Your data can also be in horizontal format (one row of headers, and one or more rows of data). 1 Pareto Pie,Run c, np, XmR Levey Jennings Moving Avg Dot Plot Required number of columns of data: 1 or more 2 2 or more Line, Bar Scatter Box & Whisker Histogram Multivari Freq Hist u Chart XbarR EWMA p Chart XandS Cusum Xmedian R Hotelling Matrix Plot Select Your Data: Highlight the labels and data you want to graph. (Hint: Don’t select the whole column, just the rows you want to graph.) Select The Chart from the QI Macros menu. QI Macros loads sample data for each chart and statistical tool on your computer. Use this data for examples of how to set up your data and to practice running charts. Access the test data from the QI Macros Help menu. Video Tutorials Watch how-to videos for many QI Macros tools: qimacros.com/qi-macros/video-tour ©2023 KnowWare International, Inc. 38 SPC Simplified ©2023 KnowWare International, Inc. 39 SPC Simplified QI Macros PivotTable Wizard Improvement Project Wizard The Improvement Project Wizard automates the creation of a pivot table and all of the charts that can be derived from the data. It examines your data, summarizes it, and creates control charts, Pareto charts, and a fishbone diagram. If you are like many Excel users, you struggle with creating pivot tables in Excel; however, pivot tables are a valuable tool every quality improvement professional can learn to use. QI Macros makes creating pivot tables easy: Make sure each column in your data sheet has a heading and that no blank rows or columns separate the data you want in the pivot table. 1. Make sure each column in your data sheet has a heading and that no blank rows or columns separate the data you want in the pivot table. 1. Select two column headings, preferably a date and currency, number, or text. (In this example it's a date and lost time due to some sort of failure.) 2. In the data sheet, use the Ctrl key to select up to four column headings for the data you want in the pivot table. 2. Select the Improvement Project Wizard from the Menu. 3. From the QI Macros menu, choose PivotTable Wizard. The Improvement Project Wizard: 4. The wizard determines the best way to organize your data and creates a pivot table. 1. Analyzes the entire table to determine if the field contains dates, dollars, numbers, text or sentences, and uses Excel's pivot table tool to summarize the data 2. Draws a control chart using the selected fields (one field must be a date, not just Jan/Feb/Mar) 3. Changes the pivot table to create Pareto charts using the remaining columns. 5. Use the Ctrl key to select labels and data in pivot table to draw charts using QI Macros. ©2023 KnowWare International, Inc. 40 SPC Simplified ©2023 KnowWare International, Inc. 41 SPC Simplified QI Macros Control Chart Wizard QI Macros Chart Overview The QI Macros Control Chart Wizard analyzes your data and selects the right control chart. Simply highlight your data and then select Control Chart Wizard from the QI Macros menu. The wizard may prompt you when it is trying to determine between a p and u chart or c and XmR chart. Attribute Charts c Chart Attribute Data (defects) Sample Size Constant A c chart is used to monitor defects when the opportunity is large compared to the actual number of defects (e.g., patient falls, injuries, etc.). The c chart is useful when it's easy to count the number of defects and the opportunity is large, but the chance is small (e.g., injuries/month). Healthcare Example Healthcare Data Special Cause Here’s a quick reference guide for choosing the right control chart: Mfg Data Manufacturing Example Special Cause C Chart Formulas ©2023 KnowWare International, Inc. 42 SPC Simplified ©2023 KnowWare International, Inc. 43 SPC Simplified u Chart Attribute Data (defects), Sample Size Varies np Chart Attribute Data (defective) Samples Constant The np chart is used to monitor and evaluate process stability when counting the fraction defective (i.e., samples are either good or bad) and sample size is constant. Examples include defective parts per 100, restraints with constant number of patients. Mfg Data The u chart is used to monitor and evaluate process stability when there can be more than one defect per unit and the sample size varies. Examples might include: the number of defective elements on a circuit board, the number of defects in a dining experience–order wrong, food too cold, check wrong–or the number of defects in a bank statement, invoice, or bill. Healthcare Data Manufacturing Example Service Example Special Cause u Chart Formulas np Chart Formulas Mfg Data Manufacturing Example p Chart Attribute Data (defective) Sample Size Varies A p chart is used to monitor and evaluate process stability when counting the fraction defective (i.e., samples are either good or bad) and the sample size varies. Examples include defective circuit boards, parts, paychecks, or other products or services. Defects/Samples Special Cause Manufacturing Example p Chart Formulas Special Cause Special Cause ©2023 KnowWare International, Inc. 44 SPC Simplified ©2023 KnowWare International, Inc. 45 SPC Simplified Variable Charts XbarR Chart Variable Data, Sample Size = 2–5/period XmR Chart Variable Data or Ratio, Sample Size = 1/period The XbarR chart is used to monitor and evaluate process performance using time, length, weight, or cost when there are 2–5 samples per period. The XmR chart is used to monitor and evaluate process performance using variable data when there is only one measurement per period. X Chart Formulas Average Chart Example X Chart (Ratio) X Chart Formulas Range Chart Example Moving Range Chart Range Chart Formulas Unstable Condition Range Chart Formulas ©2023 KnowWare International, Inc. 46 SPC Simplified ©2023 KnowWare International, Inc. 47 SPC Simplified XbarS Chart Variable Data, Sample Size = 6–25/period Control Chart Dashboards The XbarS chart is used to monitor and evaluate process performance using time, length, weight, or cost when there are 6–25 samples per period. To show control charts for several measures on the same worksheet, use the QI Macros control chart dashboards. For more detail see: qimacros.com/control-chart/control-chart-dashboard. Each dashboard has an instruction sheet, a data input sheet, and a sheet for each available control chart and a run chart. Open the Xmr or c, p, u, np chart dashboard. Type or paste your data into the data input sheet. X Chart Formulas Data Input Sheet Click on the chart sheet to see charts for the first data set. Click on the arrows to view charts for each data set. These charts show that the process is stable and predictable with no special causes. Chart Sheet Range Chart Formulas Click on the Create Dashboard icon to create a dashboard with each chart. Control Chart Dashboard ©2023 KnowWare International, Inc. 48 SPC Simplified ©2023 KnowWare International, Inc. 49 SPC Simplified Histograms and Capability Analysis Charts Frequency Histogram Evaluate the capability of a process to meet customers’ specifications using measured (i.e., variable) data like time, money, age, length, width, and weight. Evaluate the distribution of your data and capability of your process when the variable data falls into predictable sizes (e.g., 0.65, 0.70, 0.75). Data Data Diameters Diameters Cp, Cpk Cp, Cpk Sigma 3 4 5 6 Sigma 3 4 5 6 Cp/Cpk 1.0 1.33 1.67 2.0 Cp/Cpk 1.0 1.33 1.67 2.0 What can you learn? What can you learn? Cp > 1: Process is capable (products fall between upper and lower specification limits) and between 3–4 sigma (Cp=1.0 to 1.33). Process could be improved by reducing variation and tightening up the production around a target (e.g., 74.0). Cpk > 1: Process is capable and centered. Because Cp = Cpk process is centered between LSL and USL, not shifted either direction. (Don’t shift the process mean, just reduce variation.) Cp > 1: Process is capable (products fall between upper and lower specification limits) and between 3–4 sigma (Cp=1.0 to-1.33). Process could be improved by reducing variation and tightening up the production around a target (e.g., 0.7). Cpk > 1: Process is capable and centered. Because Cp = Cpk (approximately), process is centered between LSL and USL, not shifted either direction. (Don’t shift the process mean, just reduce variation.) Normal: If you look at the chart you can see that the bars are closely aligned to the normal curve: you have a normal distribution. Normal: Use Cp, Cpk when you have a sample; Cp, Cpk use sigma estimator. Use Pp, Ppk when you have the total population; Pp, Ppk use standard deviation. If Cp, Pp are fairly different, you may have an unstable process. Run a control chart on your data to analyze stability. Use Cp, Cpk when you have a sample; Cp, Cpk use sigma estimator. Use Pp, Ppk when you have the total population; Pp, Ppk use standard deviation. If Cp, Pp are fairly different, then you may have an unstable process. Run a control chart on your data to analyze stability. ©2023 KnowWare International, Inc. 50 ©2023 KnowWare International, Inc. 51 SPC Simplified If you look at the chart you can see that the bars are closely aligned to the normal curve: you have a normal distribution. SPC Simplified Cp and Cpk Worksheet Aid the manufacturing of quality products by measuring capability (Cp, Cpk, Pp, and Ppk). Cp (process capability) should be close to Pp (process performance). Similarly, Cpk should be close to Ppk. Otherwise, the process is unstable and should be evaluated with control charts. 1. Identify characteristics of each part to be measured. 2. Specify Upper and Lower Specification Limits. 3. Enter measurements in the data section as they are selected. ©2023 KnowWare International, Inc. 52 SPC Simplified Video Particpant Guidebook SPC Simplified ©2023 KnowWare International, Inc. 53 SPC Simplified Video Participant Guide Laser Focus Your Improvement Story Sustain the Improvement Your Million Dollar Money Belt Improvement Strategy 1. Create a Master Improvement Story 2. Track Key Indicators 1. Refine the Process Good Fast Cheap Monitor and Sustain New Levels of Performance in Mission Critical Systems Control Chart 3. Define the Problem Pareto's Rule Less than 4% of any business creates over 50% of the waste, rework, and lost profit. Like a crime scene investigator reviewing forensic evidence, you can use data you already have to find and fix these root causes, and save a ton of money. 80% 4-50 Rule 2. Analyze Stability 64% Control Charts 4% 20% 20% 20% 20% Attribute (defects) np, p c,u 20% 4. Analyze Parts of the Problem Simultaneously Variable (time, length, weight, temp) XmR XbarR XbarS 3. Analyze Capability Histogram 5. Prevent The Problem ©2023 KnowWare International, Inc. 54 SPC Simplified Video Participant Guide ©2023 KnowWare International, Inc. 55 SPC Simplified Video Participant Guide SPC Simplified Introduction SPC Simplified Introduction Focus the Improvement Statistical Process Control Goals Know when:  Defects 4-50 Rule  Deviation Improve the Process A process is working predictably and smoothly to avoid tampering Something has gone wrong and needs to be corrected Statistical Process Control Outline Define the Process  Choose the Right Chart: Countermeasures - Control Chart Histogram  Analyze the Chart Verify Results Sustain the Improvement Universal Process Flow Order Histogram ©2023 KnowWare International, Inc. 56 Fulfill Bill Pay Manual Error Correction SPC Simplified Video Participant Guide ©2023 KnowWare International, Inc. 57 SPC Simplified Video Participant Guide SPC Simplified Introduction Choosing the Right Chart SPC Simplified Introduction Stability and Capability Cycle Time (X Charts & Histograms) Order Fulfill Bill Stability Pay Capability Manual Error Correction Is the output of the process predictable and consistent? Does the process meet customer specifications? Choosing the Right Chart X Charts & Histograms Weight, Length, etc. Order Fulfill Bill Pay Manual Error Correction Choosing the Right Chart Order Fulfill Bill Manual Error Correction Pay Attribute Charts c, np, p, u Defects (Good/Bad) Pareto Charts ©2023 KnowWare International, Inc. 58 SPC Simplified Video Participant Guide ©2023 KnowWare International, Inc. 59 SPC Simplified Video Participant Guide Control Charts & Stability Analysis Control Charts & Stability Analysis X Charts - Stability X Charts - Stability Special Cause Variation 99.7 % of the data points Upper Control Limit Average Mean or Median Lower Control Limit Stability Analysis Rules 99.7 % of the data points X Charts - Stability Common Cause Variation 1 point above 3 sigma Upper Control Limit 2 of 3 points above 2 sigma 4 of 5 points above 1 sigma 8 points above the average 8 points below the average Average Mean or Median 4 of 5 points below 1 sigma 2 of 3 points below 2 sigma Lower Control Limit 1 point below 3 sigma X Charts - Stability Special Cause Analysis  Determine root cause Special Cause Variation - Use 5 Whys? Use Ishikawa or Fishbone diagram  Eliminate special cause variation  Then use problem solving methods to eliminate common cause variation ©2023 KnowWare International, Inc. 60 SPC Simplified Video Participant Guide ©2023 KnowWare International, Inc. 61 SPC Simplified Video Participant Guide Control Charts & Stability Analysis Histogram - Capability Stability and Capability Stability Capability Histograms & Capability Analysis Is the output of the process predictable and consistent? Does the process meet customer specifications? Measurements Control Limits Control Chart Limits calculated based on the data Specification Histograms – Specification Limits set by the customer Limits Histograms Cp ≥ 1 Does the process fit between the USL and LSL? Cpk ≥ 1 Is the process centered between the USL and LSL? If both Cp and Cpk ≥ 1 then the process is capable ©2023 KnowWare International, Inc. 62 SPC Simplified Video Participant Guide ©2023 KnowWare International, Inc. 63 SPC Simplified Video Participant Guide Histograms & Capability Analysis Free Webinars and Training Money Belt, Green Belt and Champions Training: www.qimacros.com/Moneybelt Pre-Recorded QI Macros Webinar: qimacros.com/webinar Email Lessons, Tips, and Tricks: qimacros.com/free-resources/newsletter Capability and Six Sigma Cp = 1 3 Sigma Cp = 1.33 4 Sigma Cp = 1.66 5 Sigma Cp = 2.0 6 Sigma Online Articles: qimacros.com/free-resources/excel-tips QI Macros Video Tour: qimacros.com/qi-macros/video-tour Other Products and Services Most manufacturing customers require 1.33 minimum. We offer books, training videos and on-site training on Lean, Six Sigma, and SPC. Products Page: qimacros.com/store Product Brochure: qimacros.com/qiflyer.pdf On-Site Training Options: qimacros.com/training/lean-six-sigma-training Reduce Deviation Off Target LSL USL Too Much Variation LSL USL Cpk < 1 Ordering Options Cp < 1 LSL Online: qimacros.com/store USL Center Process Fax PO’s: (888) 468-1536 or (303) 756-3107 Reduce Spread By Phone: (888) 468-1535 or (303) 757-2039 Centered on Target Email PO’s: [email protected] Tech Support: Mon – Fri 8:30am to 5:00pm Mountain Time Call: (888) 468-1537 or (303) 756-9144 Email: [email protected] ©2023 KnowWare International, Inc. 64 SPC Simplified Video Participant Guide ©2023 KnowWare International, Inc. 65 SPC Simplified SPC SSIMPLIFIED IMPLIFIED The key to sustaining higher levels of quality and productivity reside in the control charts and histograms of statistical process control. Unlike other courses that burden the learner with all of the statistics behind these charts and graphs, this video focuses on analyzing the information in the graphs, because that's all that's really important — to understand what the graphs are telling you. The video also demonstrates how to use the QI Macros to create all of these graphs: Attribute Charts (defects/sample):  c, u, np, p Variable Charts (time, length, width, weight, volume, etc.):  XmR (Individuals and Range)  XbarR (Average and Range)  XbarS (Average and Standard Deviation) Jay Arthur, the KnowWare Man, teaches employees how to use the QI Macros and Excel to eliminate the three silent killers of productivity and profits: delay, defects and deviation. Jay conducts one-day, on-site SPC Simplified trainings tailored to your company and industry. ISBN 1-884180-24-8 59900> KnowWare International Inc 2696 S Colorado Blvd #555 Denver, Colorado 80222 (888) 468-1537 www.qimacros.com ©2023 KnowWare International, Inc. 66 9 781884 SPC Simplified 180248 ©2023 KnowWare International, Inc. 67 SPC Simplified