Is Process Stable ? The Quality Improvement Model Define Process Select Measures Collect & Interpret Data Is Process Stable? Purpose: Determine the stability of key measures of the product. Is Process Stable ? No Investigate & Fix Special Causes Yes Improve Process Capability No Is Process Capable ? Yes Use SPC to Maintain Current Process 6-1 Is Process Stable ? Types of Variation Common Causes Causes that are inherent in the process over time, and affect all outcomes of the process. Ever-present Create small, random fluctuations in the process Lots of them The sum of their effects creates the expected variability Predictable Run Chart Quality Characteristic Time 6-2 Is Process Stable ? Types of Variation Special Causes Causes that are not present in the process all the time, but arise because of specific circumstances. Not always present in the process Can create large process disturbances, or sustained shifts Relatively few in number Pull the process beyond the expected level of variability Unpredictable Run Chart Quality Characteristic Time Control charts help identify the presence of special causes. 6-3 Is Process Stable ? Control Chart Components Run chart of the data Center Line (CL) UCL A line at the average of the data or target of the process Upper Control Limit (UCL) Control Chart A line at the upper limit of expected variability Lower Control Limit (LCL) CL A line at the lower limit of expected variability LCL 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Run Order The control limits are based on data collected from the process. 6-4 Is Process Stable ? Rules for Separating Common & Special Causes Two commonly used signals of special causes are: Rule 1: Any point above the Upper Control Limit (UCL) or below the Lower Control Limit (LCL) Rule 2: 8 points in a row on the same side of the center line (CL) Note: Additional rules do exist. 6-5 Evaluation of Individuals Data Is Process Stable ? s s T c s R ,n=2 s X • ••• • • • • • • • • • • • • • • • • • • •• • •• • • •• • • • c • • • •• • • • • •• • • • • • • •• • • • • Target •• Order of Production s s Measures Variation in All Data Used to Estimate 'Spread' Does Not Reflect 'Capability' Should Not Be Used for Calculating Control Chart Limits s c Measures Variation in Successive Values Used to Estimate the Potential Capability Should Be Used to Calculate Trial Control Chart Limits 6-6 Estimating Sigma (Standard Deviation) Is Process Stable ? n ss = Xi – X 2 Total s s i=1 n–1 n sc = Xi – Xi–1 i=2 n–1 1.128 = R 1.128 Short-Term sc In existing data, Sigma C is a better estimate of the common cause variability… Since it eliminates variation due to cycles, shifts, etc…(Special Causes). Therefore, Sigma C (from edited moving ranges) is always used to calculate control limits! 6-7 Problem: Individuals Chart Calculations Is Process Stable ? Line 1 - First 25 Points Only CO N TR OL C HA R T F O R X & MR Problem #13 F req ue nc y = D ail y D ate T im e O p e rato r Line 1 Me asur em en t ( X) Mo ving R ang e ( MR ) 87.6 91.2 3.6 1 2 94.0 91.6 81.6 94.0 94.4 91.0 84.2 89.5 86.6 92.9 97.4 94.2 81.6 85.6 2.8 2.4 10.0 89.1 90.9 7.5 1.8 3.1 0.4 3.4 6.8 5.3 2.9 6.3 4.5 3.2 12.6 4.0 88.7 88.8 87.7 1.1 3.1 0.1 79.9 96.6 7.8 16.7 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 22 20 21 23 89.3 7.3 93.2 3.9 24 25 X MR 6-8 Line 1 - First 25 Points Only Control Chart for _______________________________ Individuals Chart Calculations X & MR CHARTS - Calculation Worksheet MR = Current Measurement Is Process Stable ? – Previous Measurement R = Total of MRs Total number MRs X = Total of Measurements Total number of Measurements = = UCL MR = 3.267 R = = LCL MR = 0 = 3.267 = R = s c = 1.128 UCL X = X + 3 sc UCL X = + 3( UCL X = + UCL X = 1.128 = LCL X = ) X – 3 sc LCL X = – 3( LCL X = – ) LCL X = 6-9 Minitab: Creating Individuals Control Charts • Open Minitab Software and the Line 1.MTW Worksheet. • Create an Individuals Control Chart following the commands in the notes. • Your output should look like the charts below: Is Process Stable ? I-MR Chart of X U C L=103.03 Individual V alue 100 _ X=89.66 90 80 LC L=76.30 1 3 5 7 9 11 13 15 O bser vation 17 19 21 23 25 1 U C L=16.42 M oving Range 16 12 8 __ M R=5.03 4 0 LC L=0 1 3 5 7 9 11 13 15 O bser vation 17 19 21 23 25 6-10 Minitab: Creating Individuals Control Charts Is Process Stable ? •Open Problem 14.MTW located in the Minitab Datasets folder. •Use Minitab to create an Individuals and Moving Range control chart for X in column C1. •What do you notice about the X and MR Charts? •What should you do to establish control limits? 6-11 Minitab: Creating Individuals Control Charts With Range Edited Limits Is Process Stable ? •As you noticed the moving range control chart for problem 14 has two ranges that are above the upper control limit. •So, a special cause source of variation is included in the limits calculation. •The special cause needs to be removed and the limits re-calculated. •Row 24 is the data point causing the moving ranges to be out of the limits. •Use the brush tool to select and update the control chart or create a new column without data point #24 (Remember to use the Backspace). •These were taught in the Introduction to Minitab Course which is a pre-requisite for the SPC course. •Brush tool – Page 13 Introduction to Minitab book 6-12 Minitab: Creating Individuals Control Charts With Range Edited Limits Is Process Stable ? •The chart below shows the updated control charts without point #24. I-MR Chart of X_1 Individual V alue 66 1 1 U C L=65.261 65 2 64 2 2 2 2 2 _ X=63.528 63 62 LC L=61.796 1 1 5 9 13 17 21 O bser vation 25 29 33 1 37 1 1 M oving Range 2.4 1 1 U C L=2.128 1.8 1.2 __ M R=0.651 0.6 2 2 2 2 0.0 2 2 2 LC L=0 2 1 5 9 13 17 21 O bser vation 25 29 33 37 •The updated moving range chart shows more moving ranges outside of limits. •These are caused by rows 7 and 29. •Remove the data points and update the control charts again. 6-13 Minitab: Creating Individuals Control Charts With Range Edited Limits Is Process Stable ? •The second updated Moving Range chart does not have any points outside of limits I-MR Chart of X_1 65 1 U C L=64.579 Individual V alue 2 64 2 2 2 2 2 _ X=63.411 2 63 62 LC L=62.242 1 1 61 1 5 9 13 17 21 O bser vation 25 29 33 1 37 1.6 M oving Range U C L=1.436 1.2 0.8 __ M R=0.439 0.4 0.0 LC L=0 1 5 9 13 17 21 O bser vation 25 29 33 37 •The objective is to calculate control limits that represent common cause sources of variation only. •However, stop editing data points once 10 to 20% of the data has been edited. •If the initial data has this many special causes, the limits will identify plenty special causes in the future for you to work on. 6-14 Minitab: Obtain Statistics to Calculate Limits for Continuous Process Monitoring Is Process Stable ? Select I-MR Options in the I-MR dialog box Choose Storage and select Means and Standard deviations 6-15 Minitab: Obtain Statistics to Calculate Control Limits Continued Is Process Stable ? Two new columns are created Mean1 – Average of your data STDE1 – Sigma_C 6-16 Process Stability Is Process Stable ? Stable Process A process in which the key measures of the output from the process show no signs of special causes. Variation is a result of common causes only. Unstable Process A process in which the key measures of the output from the process show signs of special causes in addition to common causes. Variation is a result of both common and special causes. 6-17 Is Process Stable ? Process Stability STABLE v s. UNSTABLE PROCESSES ST ABLE s Constant Constant s Constant Sustained Shift s Constant Irregular Shift s Constant Trend s Increase Constant s Irregular Irregular UNST ABLE 6-18 A Stable Process UCL LCL Is Process Stable ? • • • • • • • • • • • • • •• • • • • • • • • • •• • • • • • • • • • • • • • •• • • • • • • • • • •• •• • • • • • • • • • • • • • • • • • • • • • •• • • • Common Causes Alone Are At Work: • Behaves in a Random Manner • No Cycles • No Runs • No Trends • No Shifts • No Defined Patterns 6-19 A Stable Process: Sigma S = Sigma C Lower Spec Upper Spec Is Process Stable ? Centering O.K. Capability Adequate No Action Needed 3sc X 3sc CAPABILITY SPREAD Lower Spec Upper Spec Centering Off Capability Adequate Shift Centering By Altering Aim of Process Lower Spec Upper Spec Centering O.K. Capability Inadequate Change Process 6-20 Un-Stable Process UCL LCL Is Process Stable ? • •• •• • • • • • • • • • • •• • •• • • • • •• • • • •• • • • • • • • • •• • • • • • • • • •• • • •• • •• • • • • • • • • •• • • •• • • • • • • • • • Assignable Cause(s) Are Present In Addition To Common Cause Variation Look For: • Points Outside the Control Limits • Shifts • Cycles • Runs • Trends 6-21 Un-Stable Process: Sigma S Not Equal to Sigma C Lower Spec Upper Spec Spread Within Specifications Determine Cause of Instability and Correct If Economically Feasible CAPABILITY SPREAD Lower Spec Is Process Stable ? Upper Spec Spread Outside Specifications Capability Adequate Determine Cause of Instability and Correct Lower Spec Upper Spec Spread Outside Specifications Capability Inadequate Change Process Attempt to Achieve At Least Partial Improvement 6-22 Is Process Stable ? Advantages of Stable Processes Are: 6-23 Is Process Stable ? Polymer Manufacturing Data Control Chart b* Histogram LS 5 4 US 3 UCL=2.2 2 Avg=1.4 1 LCL=0.5 0 0 1 2 3 4 b* 5 20 40 60 80 Sample 100 120 140 Note: b* is a measure of yellowness Histogram does not show whether the process is stable! 6-24 What’s Wrong With Putting Specification Limits on Control Charts? Is Process Stable ? Case 1: (Specifications wider than Control Limits) USL x UCL x x x CL x LCL x x LSL Case 2: (Control Limits wider than Specifications) UCL x USL x x x CL x x LSL LCL In both cases, specification limits on control charts cause you to take the wrong action. 6-25 Histograms & Control Charts Histograms Plot past data Cannot tell if process is stable Only useful for prediction if the process is stable Is Process Stable ? Control Charts Real-time evaluation Help identify presence of special causes Assess past and present stability of process 6-26 Is Process Stable ? Pump Maintenance Data 20 18 16 Number 14 12 of Failures 10 UCL=11.4 8 6 Avg=4.8 4 2 0 LCL=None 2 4 6 8 10 12 14 16 18 20 22 24 Week Are there any signals of special causes? Circle them. 6-27 Is Process Stable ? Driving to Work Data 55 UCL=51.6 Time (Minutes) 50 Avg=45.9 45 LCL=40.2 40 35 5 10 15 20 25 30 35 Day The next 5 observations are: 47, 46, 43, 52, 45. Plot them. Are there any signals of special causes? Circle them. 6-28 Is Process Stable ? Purchase Order Data 14 13 12 11 Time 10 (Days) 9 8 7 6 5 4 3 2 1 0 UCL=9.5 Avg=5.0 LCL=0.5 2 4 6 8 10 12 14 16 18 20 Week Sample Taken Are there any signals of special causes? Circle them. 6-29 Is Process Stable ? Shipping Data 0.30 0.25 p (fraction nonconforming) UCL 0.20 0.15 Avg=0.123 0.10 0.05 0.00 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 LCL Week Are there any signals of special causes? Circle them. 6-30 Quality Improvement Is Process Stable ? Types of Control Charts Counting Measures p charts np charts c charts u charts Instrument Measures x (X-bar) charts Individuals (x) charts Range (R) charts Moving Range (MR) charts Arithmetic Moving Average charts Exponentially Weighted Moving Average charts Cusum charts “When you have a problem to solve, you want to choose the right tool.” 6-31 Is Process Stable ? Exercises Circle any signals of special causes you find in the following control charts. Example 1 % of Customers Ranking Eastman as #1 Supplier • Example 2 • • •• • •• • • • • • • • • • • • Time Monthly Sales • ••• • • • • • • • • • • Time 6-32 Is Process Stable ? Skill Check - Continued Example 3 • • % Defective • • • • • • • Example 4 • • • • Number of LostTime Accidents • • • • • • • • Time • • • •• • • • • • • • Time 6-33 Exercises Is Process Stable ? 1.) Your Catapult Team should complete page 9 of the “Catapult Process” handout. 2.) Be ready to present your results in PowerPoint Limit yourselves to 10 minutes for this exercise. 6-34