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# Methods & Philosophy Of Statistical Process Control - SPC

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Methods & Philosophy Of Statistical Process Control - SPC

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• I echo GandyDancer's criticism; many of these slides are incorrect, and reflect a naive view of SPC.

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• You do NOT understand control charts!!! READ Shewhart's book (He INVENTED the control chart). Also, read Dr. Donald Wheeler's work. The control chart had NOTHING to do with the normal distribution and the control limits are NOT determined by the standard deviation of the data.

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• I need the Methods & Philosophy Of Statistical Process Control file.

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### Methods & Philosophy Of Statistical Process Control - SPC

1. 1. 4-1. Introduction Chapter 4 • Statistical process control is a collection of tools that when used Methods and Philosophy of together can result in process stability Statistical Process Control and variability reduction Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-2. Chance and Assignable 4-1. Introduction Causes of Quality Variation The seven major tools are • A process that is operating with only chance causes of variation present is said to be in 1) Histogram or Stem and Leaf plot statistical control. 2) Check Sheet • A process that is operating in the presence of 3) Pareto Chart assignable causes is said to be out of control. 4) Cause and Effect Diagram • The eventual goal of SPC is reduction or 5) Defect Concentration Diagram elimination of variability in the process by 6) Scatter Diagram identification of assignable causes. 7) Control Chart Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-2. Chance and Assignable 4-3. Statistical Basis of the Causes of Quality Variation Control Chart Basic Principles A typical control chart has control limits set at values such that if the process is in control, nearly all points will lie between the upper control limit (UCL) and the lower control limit (LCL). Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
2. 2. 4-3. Statistical Basis of the 4-3. Statistical Basis of the Control Chart Control Chart Basic Principles Out-of-Control Situations • If at least one point plots beyond the control limits, the process is out of control • If the points behave in a systematic or nonrandom manner, then the process could be out of control. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3. Statistical Basis of the 4-3. Statistical Basis of the Control Chart Control Chart Relationship between hypothesis testing and Relationship between hypothesis testing and control charts control charts • Control limits can be set at 3 standard • We have a process that we assume the true process deviations from the mean. mean is m = 74 and the process standard deviation is s = 0.01. Samples of size 5 are taken giving a • This results in “3-Sigma Control Limits” standard deviation of the sample average, x , as UCL = 74 + 3(0.0045) = 74.0135 s 0.01 CL= 74 sx = = = 0.0045 n 5 LCL = 74 - 3(0.0045) = 73.9865 Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3. Statistical Basis of the 4-3. Statistical Basis of the Control Chart Control Chart Relationship between the process and the control Relationship between hypothesis testing and chart control charts • Choosing the control limits is equivalent to setting up the critical region for testing hypothesis H0: m = 74 H1: m ¹ 74 Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
3. 3. 4-3. Statistical Basis of the 4-3. Statistical Basis of the Control Chart Control Chart Important uses of the control chart Types the control chart • Most processes do not operate in a state of statistical control. • Variables Control Charts • Consequently, the routine and attentive use of control charts will identify assignable causes. If these causes can be eliminated from – These charts are applied to data that follow a the process, variability will be reduced and the process will be continuous distribution (measurement data). improved. • Attributes Control Charts • The control chart only detects assignable causes. Management, operator, and engineering action will be necessary to eliminate the – These charts are applied to data that follow a assignable causes. • Out-of-control action plans (OCAPs) are an important aspect of discrete distribution. successful control chart usage (see page 160). • Refer to the process improvement cycle, Figure 4-5, page 160. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3. Statistical Basis of the Control Chart Stationary, uncorrelated Type of Process Variability – see Figure 4-6, pg. 162 • Stationary behavior, uncorrelated data • Stationary behavior, autocorrelated data • Nonstationary behavior Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition Stationary, correlated Non-stationary 50 100 150 200 250 12 -5 10 8 -10 6 -15 4 2 -20 50 100 150 200 250 Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
4. 4. 4-3. Statistical Basis of the 4-3. Statistical Basis of the Control Chart Control Chart Popularity of control charts Type of Variability 1) Control charts are a proven technique for improving productivity. 2) Control charts are effective in defect prevention. • Shewhart control charts are most effective 3) Control charts prevent unnecessary process adjustment. when the in-control process data is 4) Control charts provide diagnostic information. stationary and uncorrelated. 5) Control charts provide information about process capability. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3.2 Choice of Control Limits 4-3.2 Choice of Control Limits General model of a control chart “99.7% of the Data” • If approximately 99.7% of the data lies within 3s UCL = m W + Ls W of the mean (i.e., 99.7% of the data should lie Center Line = m W within the control limits), then 1 - 0.997 = 0.003 or 0.3% of the data can fall outside 3s (or 0.3% LCL = m W - Ls W of the data lies outside the control limits). where L = distance of the control limit from the (Actually, we should use the more exact value center line 0.0027) m W = mean of the sample statistic, w. • 0.0027 is the probability of a Type I error or a sW = standard deviation of the statistic, w. false alarm in this situation. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3.2 Choice of Control Limits 4-3.2 Choice of Control Limits Three-Sigma Limits Warning Limits on Control Charts • Warning limits (if used) are typically set at 2 standard • The use of 3-sigma limits generally gives good deviations from the mean. results in practice. • If one or more points fall between the warning limits and • If the distribution of the quality characteristic is the control limits, or close to the warning limits the reasonably well approximated by the normal process may not be operating properly. distribution, then the use of 3-sigma limits is • Good thing: warning limits often increase the sensitivity applicable. of the control chart. • These limits are often referred to as action limits. • Bad thing: warning limits could result in an increased risk of false alarms. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
5. 5. 4-3.3 Sample Size and Sampling 4-3.3 Sample Size and Sampling Frequency Frequency Average Run Length • In designing a control chart, both the • The average run length (ARL) is a very sample size to be selected and the important way of determining the appropriate frequency of selection must be specified. sample size and sampling frequency. • Larger samples make it easier to detect • Let p = probability that any point exceeds the small shifts in the process. control limits. Then, • Current practice tends to favor smaller, 1 ARL = more frequent samples. p Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3.3 Sample Size and Sampling 4-3.3 Sample Size and Sampling Frequency Frequency Illustration What does the ARL tell us? • The average run length gives us the length of • Consider a problem with control limits set time (or number of samples) that should plot in at 3standard deviations from the mean. control before a point plots outside the control The probability that a point plots beyond limits. the control limits is again, 0.0027 (i.e., p = • For our problem, even if the process remains in 0.0027). Then the average run length is control, an out-of-control signal will be 1 generated every 370 samples, on average. ARL = = 370 0.0027 Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3.3 Sample Size and Sampling 4-3.4 Rational Subgroups Frequency Average Time to Signal • Sometimes it is more appropriate to • Subgroups or samples should be selected express the performance of the control so that if assignable causes are present, the chart in terms of the average time to signal chance for differences between subgroups (ATS). Say that samples are taken at fixed will be maximized, while the chance for intervals, h hours apart. differences due to these assignable causes within a subgroup will be minimized. ATS = ARL ( h ) Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
6. 6. 4-3.4 Rational Subgroups 4-3.5 Analysis of Patterns on Control Charts Selection of Rational Subgroups Nonrandom patterns can indicate out-of-control • Select consecutive units of production. conditions – Provides a “snapshot” of the process. • Patterns such as cycles, trends, are often of considerable diagnostic value (more about this in Chapter 5) – Effective at detecting process shifts. • Look for “runs” - this is a sequence of observations of the same type • Select a random sample over the entire sampling (all above the center line, or all below the center line) interval. • Runs of say 8 observations or more could indicate an out-of-control situation. – Can be effective at detecting if the mean has wandered – Run up: a series of observations are increasing out-of-control and then back in-control. – Run down: a series of observations are decreasing Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-3.5 Analysis of Patterns on 4-4. The Rest of the “Magnificent Control Charts Seven” Western Electric Handbook Rules (Should be used carefully because of the increased risk of false alarms) • The control chart is most effective when integrated into a comprehensive SPC program. A process is considered out of control if any of the • The seven major SPC problem-solving tools following occur: should be used routinely to identify improvement 1) One point plots outside the 3-sigma control limits. opportunities. 2) Two out of three consecutive points plot beyond the 2- sigma warning limits. • The seven major SPC problem-solving tools 3) Four out of five consecutive points plot at a distance of 1- should be used to assist in reducing variability sigma or beyond from the center line. and eliminating waste. 4) Eight consecutive points plot on one side of the center line. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-4. The Rest of the “Magnificent 4-4. The Rest of the “Magnificent Seven” Seven” Recall the magnificent seven Check Sheets 1) Histogram or Stem and Leaf plot • See example, page 177 & 178 2) Check Sheet • Useful for collecting historical or current 3) Pareto Chart operating data about the process under 4) Cause and Effect Diagram investigation. 5) Defect Concentration Diagram • Can provide a useful time-oriented summary of 6) Scatter Diagram data 7) Control Chart Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
7. 7. 4-4. The Rest of the “Magnificent Seven” Pareto Chart • The Pareto chart is a frequency distribution (or histogram) of attribute data arranged by category. • Plot the frequency of occurrence of each defect type against the various defect types. • See example for the tank defect data, Figure 4-17, page 179 • There are many variations of the Pareto chart; see Figure 4-18, page 180 Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition Pareto Chart 4-4. The Rest of the “Magnificent Seven” 40 Cause and Effect Diagram 30 • Once a defect, error, or problem has been identified and isolated for further study, potential causes of this 20 Cylinder Heads undesirable effect must be analyzed. • Cause and effect diagrams are sometimes called fishbone 10 diagrams because of their appearance • See the example for the tank defects, Figure 4-19, page 0 182 Size Surface Other Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition 4-4. The Rest of the “Magnificent Example of Cause and Effect Diagram Seven” How to Construct a Cause-and-Effect Diagram (pg. 181) Activities Stops • Define the problem or effect to be analyzed. Gas Station Band practice • Form the team to perform the analysis. Often the team will uncover potential causes through brainstorming. Tau Beta Pi McDonalds • Draw the effect box and the center line. Arrive late to class • Specify the major potential cause categories and join them as boxes connected to the center line Dog to the Vet • Identify the possible causes and classify them into the Traffic categories in step 4. Create new categories, if necessary. Kids to school Parking • Rank order the causes to identify those that seem most likely to impact the problem. Family Commute • Take corrective action. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition
8. 8. 4-4. The Rest of the “Magnificent 4-4. The Rest of the “Magnificent Seven” Seven” Defect Concentration Diagram Scatter Diagram • A defect concentration diagram is a picture of the unit, showing all relevant views. • The scatter diagram is a plot of two variables that can be used to identify any potential • Various types of defects that can occur are relationship between the variables. drawn on the picture • The shape of the scatter diagram often indicates • See example, Figure 4-20, page 183 what type of relationship may exist. • The diagram is then analyzed to determine if the • See example, Figure 4-22 on page 184. location of the defects on the unit provides any useful information about the potential causes of the defects. Introduction to Statistical Quality Control, 4th Edition Introduction to Statistical Quality Control, 4th Edition Uncorrelated and (Positively) Correlated data x[i-1] x[i-1] 3 12 2 10 8 1 6 -2 -1 1 2 3 4 x[i] -1 x[i] 2 -2 2 4 6 8 10 12 Introduction to Statistical Quality Control, 4th Edition