C & u charts
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The document discusses the concepts of process stability and capability, emphasizing that a stable process yields predictable results and can meet customer requirements. It outlines the use of control charts to determine stability and differentiate between common and special causes of variation. Essential metrics include upper and lower control limits, and a fully capable process aims for zero defects.
C & u charts
- 1. Stabilize the Process Understanding Stability Stability A stable process produces predictable results consistently. Stability can be easily determined from control charts. The upper control limit (UCL) and lower control limit (LCL) are calculated from the data. Example How long does it take you to commute to work each morning? Daily Commute (minutes) Daily Commute Time 29 min. Stable LSL USL Trips To Work = 22 min. Predictable 15 min. Capable Stable 15 30 Daily Commute (minutes) Daily Commute Time 29 min. LSL USL Trips To Work Your Requirements 22 min. 1. Get to work in 30 minutes or less. 2. Get to work safely 15 min. Capable (no faster than 15 Unstable Trend minutes). 15 Minutes 30 Daily Commute (minutes) Snow Storm Daily Commute Time UCL 32 min. LSL USL Trips To Work 24 min. LCL 18 min. Not Point Unstable Capable 15 Minutes 30 A process does not have to be stable to be capable of meeting the Stability and customer's requirements. Similarly, a stable process is not necessarily Capability capable. A managed process must be both stable and capable. Interpreting stability with control charts and capability with histograms will be discussed in more detail on the following pages. © 2001 Jay Arthur 81 Six Sigma Simplified
- 2. Check Stability Interpreting The Indicators Purpose Verify that the process system is stable and can predictably meet customer requirements Variation A stable process produces predictable results. Understanding variation helps us learn how to predict the performance of any You cannot step process. To ensure that the process is stable (i.e., predictable) twice into the same we need to develop "run" or "control" charts of our indicators. river. Heraclitus 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 from your home 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. A blizzard, a traffic accident, a chemical spill, or other freak occurrence that causes major delays would be a special cause of variation. In the 1920s, Dr. Shewhart, at Bell Labs, developed ways to evaluate whether the data on a line graph is common cause or special cause variation. Using 20-30 data points, you can determine how stable and predictable the process is. Using simple equations, you 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. Control limits are not to be confused with specification limits. Specification limits are defined by the cus- Example tomer. Control limits show what the process can deliver. Your Requirements: 1. Get to work fast! Upper Control Limit (UCL) 2. Get to work safely. Daily Commute (minutes) 68.3% 95.5% 99.7% of all 29 min. Center Line (average) data points 22 min. Lower Control Limit (LCL) 15 min. 1 5 10 15 20 25 30 Stable © 2001 Jay Arthur 82 Six Sigma Simplified
- 3. Check Stability Interpreting The Indicators Special Processes that are "out of control" need to be stabilized before they can be improved using the problem-solving process. Cause Special causes, require immediate cause-effect analysis to Variation eliminate the special cause of variation. Evaluating The following diagram will help you evaluate stability in any control chart. Unstable conditions can be any of the following: Stability Any point above UCL UCL 2 of 3 points in this area Daily Commute (minutes) Snow Storm 4 of 5 points in this area or above 29 min. 8 points in a row in this area or above CL 22 min. 8 points in a row in this area or below 4 of 5 points in this area or below 15 min. 2 of 3 points in this area Point Unstable LCL Any point below LCL 1 5 10 15 20 25 30 Points and Any point outside the upper or lower control limits is a clear example of a special cause. The other forms of special cause Runs variation are called "runs." Trends, cycling up and down, or "hugging" the center line or limits are special forms of a run. Point outside UCL UCL 2 above A 8 above CL A Daily Commute (minutes) 29 min. B CL 22 min. Trend B 15 min. 4 below B 6 ascending A Unstable Trend or descending LCL Any point below LCL © 2001 Jay Arthur 83 Six Sigma Simplified
- 4. Step 4 - Check Stability c and u charts c and u The c and u charts will help you evaluate process stability when Charts there can be more than one defect per unit. Examples might include: the number of defective elements on a circuit board, the (Attribute data) number of defects in a dining experience–order wrong, food too cold, check wrong, or the number of defects in bank statement, X X invoice, or bill. This chart is especially useful when you want to X know how many defects there are not just how many defective items there are. It's one thing to know how many defective circuit Defects boards, meals, statements, invoices, or bills there are; it is another thing to know how many defects were found in these defective items. The c chart is useful when it's easy to count the number of defects and the sample size is always the same. The u chart is used when the sample size varies: the number of circuit boards, meals, or bills delivered each day varies. The c chart below shows the number of defects per day in a uniform sample. Number Defects Per Day n=28 7 Point Outside Limits To automate all of 6 UCL your control charts Number of Defects 5 using Microsoft® 4 Excel, get the QI Macros For Excel. 3 Download a FREE 2 Run Below CL CL limited demo from: 1 www.quantum-i.com Approach to Limits Approach to Limits 0 LCL 10-Feb 11-Feb 12-Feb 13-Feb 14-Feb 15-Feb 16-Feb 17-Feb 18-Feb 19-Feb 20-Feb 21-Feb 22-Feb 23-Feb 24-Feb 25-Feb 26-Feb 27-Feb 28-Feb 1-Feb 2-Feb 3-Feb 4-Feb 5-Feb 6-Feb 7-Feb 8-Feb 9-Feb Stability Given this information, we would want to investigate why February 11th was "out of control." We would also want to understand why we were able to keep the defects so far below average in the other circled areas. What did we do here that was so successful? Capability A fully capable process delivers zero defects. © 2001 Jay Arthur 90 Six Sigma Simplified
- 5. Step 4 - Check Stability c and u charts X X = More Than X One Defect Title Number or Percent of Defects 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Measurement or Sample c 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Defects (c) u 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Defects (u) Sample Size (n) Percent UCL LCL C Chart U Chart UCL: c + 3*sqrt(c) u + 3*sqrt(u/n )i CL: c = ∑ci/n u = ∑ui/∑ni LCL: c - 3*sqrt(c) u - 3*sqrt(u/n ) i © 2001 Jay Arthur 91 Six Sigma Simplified