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- 1. Statistical Process ControlGreg Swartz // (650) 274-6001 // gregs@opsalacarte.com Ops A La Carte LLC // www.opsalacarte.com
- 2. The following presentation materials are copyright protected property of Ops A La Carte LLC.These materials may not be distributed outside of your company.
- 3. Presenter’s Biographical Sketch – Greg Swartz◈Greg Swartz has worked successfully for over twenty years in the fields of statistics and process improvement, as a Consultant and Trainer. His consulting experience includes working with a number of Biotech, high tech companies, Aerospace, and Defense. His expertise includes analysis of technical data, a hands-on approach towards design of experiments, and Failure Analysis, e.g. with Ops A La Carte for Semiconductor Equipment. Greg was a Sr. Quality Program Manager at Sun Microsystems for 6 years.◈Mr. Swartz has worked in the fields of Applied Data Analysis (ADA) techniques, yield improvement, quality assessments, and reliability studies. Additionally, Greg has a background in software reliability, CMM, and Software Product Life Cycle (SPLC). © 2008 Ops A La Carte
- 4. Metrics and Statistical Process Control Level II for Operations, Engineering and Research Developed and Presented by: Greg Swartz, CQE Ops A La Carte April 11, 2008Gregory Swartz, © 2008 (650) 274-6001 Page 1
- 5. Metrics and Statistical Process Control Learning ObjectivesOverview:This Level II Statistical Process Control (SPC) course presentsa number of valuable tools to assist you in evaluating processvariation and to make sound decisions based on your data.Topics covered included the following: ♦ Pareto Charts and Check sheets for Attribute and Visual Data ♦ Histograms for understanding variation in measurable data ♦ Variables and Attribute Control Charts including p Charts for varying sample sizes ♦ Process Capability (Cp & Cpk) and Sample Size Determination ♦ Interpretation and Corrective Action including Out-Of-Control guidelines ♦ Correlation and Regression Studies with guard-banding techniques.Learning Objectives:Upon completion of this Metrics/SPC Level II course,participants will be able to do the following: ♦ Construct p, NP, and C Charts for attribute process control ♦ Be able to construct Ave. and Range control charts for variables data ♦ Construct 90 and 95% Confidence Intervals for process data. ♦ Distinguish between Process Control and Process Capability. ♦ Perform a Correlation Studies and interpret results.Gregory Swartz, © 2008 (650) 274-6001 Page 2
- 6. Metrics/Statistical Process Control Level II Content OutlineChapter 1: INTRODUCTION TO SPC • Benefits of Metrics and SPC • SPC Tools — Overview • SPC Implementation StrategyChapter 2: PROBLEM SOLVING TOOLS • Cause and Effect Diagrams (Fishbone) • Check Sheets • Pareto Analysis using Excel with ExcelTMChapter 3: DESCRIPTIVE STATISTICS • Measures of Central Tendency and Variation • Histograms and Specification Limits • SPC vs. Process CapabilityChapter 4: PROCESS CAPABILITY AND YIELD STUDIES • "Central Limit Theorem" • Cp and Cpk Indices — A practical approach • “t” Test and Confidence Intervals in Excel * Sample Size DeterminationChapter5: PROCESS CONTROL TOOLS FOR VARIABLES DATA • X Bar & R Chart • X Bar & S Charts (n>10) (for reference) • Short Run Charting TechniquesChapter 6: PROCESS CONTROL TOOLS FOR ATTRIBUTE DATA • NP Charts and • P Charts (fraction defective) • C ChartsChapter 7: INTERPRETATION AND CORRECTIVE ACTION • Interpreting Trends and Shifts in Data • Planning Corrective Action • Implementing Continuous Process ImprovementChapter 8: CORRELATION AND REGRESSIONAppendix Terms and Definitions Formula SummaryGregory Swartz, © 2008 (650) 274-6001 Page 3
- 7. Metrics and Statistical Process ControlChapter One: Introduction to SPC • SPC is a tool that uses analytical techniques to: Investigating Monitoring Improving • SPC measures quality during the production process, using statistics to determine and maintain a state of process control in your area. • SPC ensures that quality is built into the product at each step, as shown in the overview process flow of Genotyping. Sample Combine Auto-Receiving (VI) QC Assays caller BioinformaticsGregory Swartz, © 2008 (650) 274-6001 Page 1
- 8. Metrics and Statistical Process ControlKey Features of ImplementingMetrics and SPC • Baseline Data 1st thing to do: catching abnormal variations where special causes to problems can be identified and corrected! • SPC responds to trends by making changes before reaching an out of control condition. Emphasis is on prevention, versus after the fact. • "Corrective action guidelines" are determined statistically, and are commonly known as Control Limits. • Corrective Action Planning can be performed by cross-functional metric improvement teams.Gregory Swartz, © 2008 (650) 274-6001 Page 2
- 9. Metrics and Statistical Process ControlBenefits of Measuring yourprocess with SPC Improved customer satisfaction, both internal and external % % % % Increased product yield Failure rate = 1-yield % Reduced operating costs Improved product flow Increased profitsGregory Swartz, © 2008 (650) 274-6001 Page 3
- 10. Metrics and Statistical Process Control Value Add of Statistical Process Control Process decisions are made based on ”Fact versus Opinion.” Increases knowledge base regarding analysis of your process data, in-process inspection, and improves your out-going quality! Improves long-term relationships between your company, suppliers, and your customers. Targets critical process, for product optimization and Capability, for example, in meeting Six Sigma criteria. Allows sound decision making, using empirical methods, versus opinions, or whims.Gregory Swartz, © 2008 (650) 274-6001 Page 4
- 11. Metrics and Statistical Process Control Types of Data – Flowchart Raw Fabri- Assembly Test Materials cation TYPES OF DATA Variable Attribute Process Improvement with SPC!Gregory Swartz, © 2008 (650) 274-6001 Page 5
- 12. Metrics and Statistical Process Control SPC Implementation - Overview Initially, Flowchart Your Process Variable Data i.e. measurable - Identify Critical costs, cycle time, or response time Product or Service or Process Parameters Attribute Data e.g. categorical - error types, PPM, defects by type Independent Causes Dependent Effect Use Cause & Effect Diagrams to Brainstorm all Cause Variables Use Pareto Charts to Prioritize $ Key Problem Areas Key Problem Areas Continue To Page 7Gregory Swartz, © 2008 (650) 274-6001 Page 6
- 13. Metrics and Statistical Process Control Continued Tools of Quality - (Con’t.) from Page 6 Do you 2 have one or Build a Scatter Y two variables Diagram ? 1 X Snapshot Y Do you No wish to display Construct a your data Histogram # over time ? Yes Measurement Scale X UCLPlot data over timeon the chart, then Ave.calculate controls. LCL Time / DateAssign causes toout- of - control points Monitor Charts forwith corrective action ImprovementGregory Swartz, © 2008 (650) 274-6001 Page 7
- 14. Metrics and Statistical Process ControlSymbols Summary Σ To Sum X Individual Score X Mean, or average R Range (max-min) σ or S Standard Deviation UCL Upper Control Limit LCL Lower Control Limit K # of groups n Subgroup sample size p Proportion Defective NP Number of Defects per sample C Number of defects per unit or area Cp Basic Capability Index Cpk Capability Index (including process shifts) t Used to determine yield with n < 30 Z Used to determine yield with large samplesGregory Swartz, © 2008 (650) 274-6001 Page 8
- 15. Metrics and Statistical Process ControlSPC Tools Overview Continuous Quality Improvement Need for Feedback Data based on data Type of Data Attribute Variables Data Data Check Histogram Process Yield Sheets Capability Improvement Pie Charts Two Yes Scatter- Variables grams Pareto Charts No Correlation Run Chart Attribute Charts Control ChartGregory Swartz, © 2008 (650) 274-6001 Page 9
- 16. Metrics and Statistical Process ControlChapter Two:Problem Solving Techniques • Process Flow Analysis • Cause and Effect Diagrams (Fishbone) • Check Sheets • Pareto Analysis with Excel ExampleGregory Swartz, © 2008 (650) 274-6001 Page 10
- 17. Metrics and Statistical Process ControlProblem Solving Tools Flow Chart Start Big Picture Detailed Flowchart Check Sheet Pareto Analysis Determine NO Fishbone root cause?? Diagram YES Take Corrective Action pp. 9-13Gregory Swartz, © 2008 (650) 274-6001 Page 11
- 18. Metrics and Statistical Process Control Process Flow Chart Exercise:PROCESS FLOW STEPS A/V TYPES OF DATAGregory Swartz, © 2008 (650) 274-6001 Page 12
- 19. Metrics and Statistical Process ControlCause and Effect Diagrams(Ishikawa Diagram) • Cause and Effect Diagrams can be used for any service or product problem • Serve as the basis for group discussion and brainstorming • Effect could be a quality, yield or productivity problem • Provide guidance for concrete corrective action People Equipment Methods Effect (Problem) Causes (Independent Variables) Materials Measurement Environment 24-29Gregory Swartz, © 2008 (650) 274-6001 Page 13
- 20. Metrics and Statistical Process ControlHow to Create a Cause andEffect Diagram 1. Identify the problem (effect). 2. Brainstorm several causes — include all ideas generated without evaluating causes. 3. Identify and circle a branch for corrective action. CAUSES EFFECT pg. 24Gregory Swartz, © 2008 (650) 274-6001 Page 14
- 21. Metrics and Statistical Process Control Process Improvement Flow “Plan, Do, Check, Act” PDCA Method. Ca uses Effect Ne ed No Take More Data? Corrective Action Yes Ca use TallyGregory Swartz, © 2008 (650) 274-6001 Page 15
- 22. Metrics and Statistical Process ControlPareto Analysis (The 80-20 effect) Errors in a process are categorical (attribute) in nature where defects can easily be tallied with a check sheet. Pareto charts display the 80-20 effect. Key Advantages: • When you identify the “vital few” you improve your ability to identify the root causes to the majority of the problems. • By solving the largest problem decreases the overall percent defective product. • Cost benefit of product can be determined with the assistance of Pareto Analysis. • Solving major problems often reduces or eliminates the minor problems. 17-23Gregory Swartz, © 2008 (650) 274-6001 Page 16
- 23. Metrics and Statistical Process ControlProcedure for Using Check Sheets for Pareto Charts 1. Rank causes by frequency of occurrence. 2. Calculate both percentage and Cum %. 3. Draw Pareto Diagram. 4. Concentrate corrective action on the "vital few." Pareto Analysis Worksheet Causes Tally Mark Freq. Rank % Smear II 2 Color IIII I 6 IIII IIII IIII IIII IIII Contaminatio IIII I 36 IIII IIII IIII IIII M isc. 24 IIII Misc.2 IIII 4 IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII 78 empty well IIII III Totals 150Gregory Swartz, © 2008 (650) 274-6001 Page 17
- 24. Metrics and Statistical Process ControlProcedure for Creating a Pareto Diagram in ExcelTM 1. Sort your cause categories so they are ranked (highest to lowest). 2. Create an ordered Check Sheet as in page 14. 3. Tabulate both % and Cum. % as in the table below: R a n k in g C auses Count F re q . (% ) C u m . (% ) 1 S c r a tc h e s 77 5 1 .3 0 % 5 1 .3 0 % 2 M is a lig n e d 36 2 4 .0 0 % 7 5 .3 0 % 3 M is c . 25 4 W ro n g # 11 5 6 4. Use the mouse to block off the causes, Frequency in %, and Cumulative %. 5. Use the Chart Wizard to create your Pareto Chart (see below). Partially Completed Pareto Exercise 0.6 100.00% 0.5 80.00% 0.4 60.00% 0.3 40.00% Freq. (%) 0.2 20.00% Cum. (%) 0.1 0 0.00% Scratches Misaligned Misc. Wrong #Gregory Swartz, © 2008 (650) 274-6001 Page 18
- 25. Metrics and Statistical Process Control Procedure for Performing a Cost Pareto Analysis 1. List all possible causes to problem. 2. Tally frequency for each cause. 3. Assign option $ cost value to causes (unit cost). 4. Rank causes by total cost for each category. 5. Derive the cumulative cost. 6. Concentrate corrective action on the most costly cause(s). p.20Gregory Swartz, © 2008 (650) 274-6001 Page 19
- 26. Metrics and Statistical Process ControlCost ($) Pareto Procedure in Excel: 1. Create a new table with your Unit Cost per defect type 2. Determine your total cost by multiplying Unit $ x Freq. 3. Rank your whole table by (total) Cost, and then Create a Cumulative Cost Column 4. Swipe your mouse over the Causes, Cost, and Cumulative Cost. 5. Create a bar and line chart with the Chart Wizard 6. Comment on Leading Cost Issue and compare it with the Freq. Pareto Freq. Unit Cost (total) Cost 2 $ 0.015 $ 0.030 6 $ 0.010 $ 0.060 36 $ 0.030 $ 1.080 24 $ 0.005 $ 0.120 4 $ 0.005 $ 0.020 78 $ 0.010 $ 0.780 150Gregory Swartz, © 2008 (650) 274-6001 Page 20
- 27. Metrics and Statistical Process ControlSPC Tools Integration 1. Use Pareto Diagram to determine the major causes of rejects. 1 1 2. Brainstorm possible causes for the biggest problem. 3. Plan Corrective ActionGregory Swartz, © 2008 (650) 274-6001 Page 21
- 28. Metrics and Statistical Process ControlChapter Three: DESCRIPTIVE STATISTICS Concept Variation Measures of Central Tendency Measures of Variation Histograms and Specification Limits Coefficient of Variation (CV)Gregory Swartz, © 2008 (650) 274-6001 Page 22
- 29. Metrics and Statistical Process ControlVariation defined by Cause There are two types of causes of variation: • Normal causes of variation result from the problems in the system as a whole. • Abnormal causes of variation result from special problems within a system. Normal cause Abnormal cause common special random non-random systematic local expected irregular unidentifiable identifiable One recommended method is to identify abnormal causes of variation, first. And then, to continually reduce variation by effecting both abnormal and normal causes.Gregory Swartz, © 2008 (650) 274-6001 Page 23
- 30. Metrics and Statistical Process Control Measures of Variation Variation: Spread, dispersion or scatter around the Central Tendency Range: Difference between the largest and smallest value (Max. – Min.) Standard Deviation ( σ or S ): A measure of the differences around the average. mean -3 o -2 o -1o X +1 o +2 o +3 o Normal Distribution CurveGregory Swartz, © 2008 (650) 274-6001 Page 24
- 31. Metrics and Statistical Process ControlThe Standard Deviation (Sigma) Sigma % of Distribution X +/- 1σ 68 % X +/- 2 σ (1.96) 95 % X +/- 3σ 99.97 % mean -3 o -2 o -1o X +1 o +2 o +3 oGregory Swartz, © 2008 (650) 274-6001 Page 25
- 32. Metrics and Statistical Process Control Histograms A histogram graphically represents the frequency of an attribute or variable, and displays its distribution of data as a snap shot representation. This visual format shows the variability of your data and can be use for further analysis, e.g. capability analysis. 160 140 N 120 u 100 m 80 b 60 e r 40 20 0 60 65 70 75 80 85 90 95 100 Yield Percentages pp. 36-43Gregory Swartz, © 2008 (650) 274-6001 Page 26
- 33. Metrics and Statistical Process Control Histograms vs. Specs LS US LS US 1 5 2 6 3 7 4 8Gregory Swartz, © 2008 (650) 274-6001 Page 27
- 34. Metrics and Statistical Process Control Standard Deviation Exercise Pick a sequence of seven numbers and list them below in the left column. Units. Determine the standard deviation. 2 X (X - X) (X - X) Σ 0 Σ (X-X)2 Formula: σ= nGregory Swartz, © 2008 (650) 274-6001 Page 28
- 35. Metrics and Statistical Process ControlStandard Deviation for Attribute Data Binomial Standard Deviation or σp = p x (1 – p ) n Where, p is the average fraction defective ∑ np -------------- n is the average sample size Total N Standard Deviation Attribute Exercise: Given the following set of data, determine the standard deviation of the fraction defective, and then create a 95% confidence interval. Sample Sample # Size n np p = np/n 1 45 2 2 50 1 3 60 3 4 40 0 5 35 1 6 70 2 7 30 5 8 65 3 9 55 4 10 50 3 Totals 500 ∑ = 24 ∑=Gregory Swartz, © 2008 (650) 274-6001 Page 29
- 36. Metrics and Statistical Process Control Coefficient of Variation The standard deviation depends on units as a measure of variation. A comparison of relative variation cannot be made using the standard deviation, so a unitless (dimensionless) measure called the coefficient of variation (CV) is used. population standard deviation = σ the population mean = μ sample standard deviation = S __ sample mean = X Sometimes the CV is normally expressed as a percentage. Then, the equation becomes: S CV % = 100 • X The Coefficient of Variation (CV) can be used to signal changes in the same group of data, or to compare the relative variability to two or more different sets of data. The larger the CV, the greater its relative variability.Gregory Swartz, © 2008 (650) 274-6001 Page 30
- 37. Metrics and Statistical Process ControlCoefficient of Variation for Variables DataProcedure: a. Determine the (Grand) Average of ROX at 2 Ul b. Determine the Std. Dev. of ROX c. Divide the Std. Dev. by the Average to obtain CV. d. Now repeat procedure for the .5 ul group e. Label each CV value f. Compare the relative variability between the two groups. 2 ul .5 ulAvg ROX % Genotyped Avg ROX % Genotyped 857.2 100 196.74 0 609.54 100 193.11 0 .5 ul 775.25 100 235.59 0 Ave. 471.18 742.79 100 174.13 0 Std. Dev. 52.61506 834.79 100 300.52 12.5 721.02 100 300.2 12.5 2ul 791.38 87.5 340.55 12.5 Ave. 731.602 834.03 37.5 192.79 0 Std. Dev. 69.75184 791.5 100 260.26 12.5 796.88 100 147.19 0 CV .5ul 0.111667 744.67 100 305.19 12.5 CV 2ul 0.095341 679.79 87.5 226.12 50 722.99 100 266.5 50 CV .5ul% 622.92 100 236.47 12.5 CV 2ul % 654.22 87.5 322.33 12.5 821.46 50 253.65 0 758.24 100 309.33 12.5 781.04 25 202.03 12.5 726.51 100 269.09 25 670.2 100 236.88 25 697.83 100 214.98 12.5 630.47 100 196.84 0 704.11 100 364.15 12.5 815.79 87.5 220.58 0 715.18 87.5 242.1 37.5 755.32 87.5 311.26 0 721.65 87.5 294.34 25 650.83 100 248.83 25 699.65 100 284.14 37.5 620.81 100 225.05 0Gregory Swartz, © 2008 (650) 274-6001 Page 31
- 38. Metrics and Statistical Process Control Attribute Coefficient of Variation Example Now, let’s try applying this concept to attribute data: __ Group one: Sp1 = .00142, P1 = .007 __ Group two: Sp2 = .00178, P2 = .01 Which group has the larger variability? Hint: At first you might be led to thinking that group two has the larger relative variation… CV1 = .00142/.007 x (100) = CV2 = .00178/.01 x (100) =Gregory Swartz, © 2008 (650) 274-6001 Page 32
- 39. Metrics and Statistical Process Control Chapter Four: Process Capability, Yield and Attribute Proportion Tests This chapter includes the following key areas for effectively performing process capability studies, accurate yield determination, and testing for single and two sample proportions: • Central Limit Theorem σx • = σx n • X = X i • Cp and Cpk Indices • Yield Determination • Attribute Proportional TestingGregory Swartz, © 2008 (650) 274-6001 Page 33
- 40. Metrics and Statistical Process ControlCentral Limit Theorem (CLT) The CLT states that the average of individual values (X) tends to be normally distributed regardless of the individual (x) distribution. Individual Data: If you randomly selected 100 four-digit numbers and charted them, the distribution will be somewhat uniform. Each digit shows approximately the same frequency.10 8642 0 0 1 2 3 4 5 6 7 8 9 Phone DigitChart the number 4186 by using one each of 4, 1, 8, and 6.Mean = 4.5225 Standard Deviation = 2.8266Gregory Swartz, © 2008 (650) 274-6001 Page 34
- 41. Metrics and Statistical Process ControlAverages DataThis histogram of average values shows the normaldistribution of the averages. For example, each digitin the number 4286 would be averaged (4 + 2 + 8 +6) = 20/4 = 5. Averages are distributed below: Averages Bar Chart 27 24 21 18 (#) 15 12 9 6 3 0 1 2 3 4 5 6 7 8 9 Phone Digit Midpoint Mean = 4.5225 Standard Deviation = 1.4133 Question: Can you now validate the Central Limit Theorem with the above example?Gregory Swartz, © 2008 (650) 274-6001 Page 35
- 42. Metrics and Statistical Process Control Cp & Cpk: The Inherent Capability of a Process The Cp index relates the allowable spread of the specification limits (USL - LSL) to the actual variation of the process. The variation is represented by 6 sigma. USL − LSL Cp = 6σ If the tolerance width is exactly the same as the 6 standard deviations width, then you have a Cp = 1. 1.333 LSL X USL mean -3σ -2σ -1σ X +1σ +2σ +3σ 12.5% 75% 12.5%Gregory Swartz, © 2008 (650) 274-6001 Page 36
- 43. Metrics and Statistical Process ControlCpk Defined Cpk expresses the worst case capability index — a process that is off-center. Cpk also takes into account the location of the process average. Cpk = the smaller result of the following two formulas: USL − X X − LSL C pu = or C pl = 3s 3s Where: Cpu = Upper Capability Index and Cpl = Lower Capability Index pp. 64-66Gregory Swartz, © 2008 (650) 274-6001 Page 37
- 44. Metrics and Statistical Process Control Process Capability Indices Example:Your boss attended this statistical seminar and isfamiliar with process capability indices. He or shethreatens to take away your new sports car if theprocess capability indices (Cp) from the new oxidemanufacturing process is not greater than 1.0. Tolerances = 250 to 400 μ Average = 300 μ sample S = 35 μ Question: Will you be driving to work in your old car tomorrow?Gregory Swartz, © 2008 (650) 274-6001 Page 38
- 45. Metrics and Statistical Process Control 400 − 250 Cp = =.714 6(35) 6(35) Cratio = =1.4 400 − 250 400 − 300 Cpu = =.95 3(35) 300 − 250 Cpl = =.476 = Cpk 3(35) Your boss has taken away your new sports car.Gregory Swartz, © 2008 (650) 274-6001 Page 39
- 46. Metrics and Statistical Process ControlProcess Capability Index ExerciseGiven the following specifications,determine Cp and Cpk. • Upper Spec. (US) = 100.0 • Lower Spec. (LS) = 24.0 • Mean (X) = • Sigma = Cp = _________ Cpk = _________Gregory Swartz, © 2008 (650) 274-6001 Page 40
- 47. Metrics and Statistical Process Control MEAS MIN MAX 26.81 24 100 26.67 24 100 26.9 24 100 27.04 24 100 26.63 24 100 26.92 24 100 26.73 24 100 26.8 24 100 26.94 24 100 26.85 24 100 27.54 24 100 27.22 24 100 25.84 24 100 25.77 24 100 26.93 24 100 26 24 100 26.96 24 100 25.79 24 100 27.04 24 100 25.98 24 100 27.48 24 100 27.03 24 100 26.92 24 100 27.69 24 100 26.83 24 100 25.38 24 100 25.87 24 100 26.81 24 100 27.36 24 100 27.3 24 100 26.73Gregory Swartz, © 2008 (650) 274-6001 Page 41
- 48. Metrics and Statistical Process ControlInterpretation of Cp and Cpk Indices Cpk < 1.00 Not Capable Cp < 1 Cpk = 1.00 Barely Capable Cp = 1 Cpk > 1.33 Very Capable Cp = 1.33Is the process truly capable of meeting the customerrequirements? _________Why or why not?Gregory Swartz, © 2008 (650) 274-6001 Page 42
- 49. Metrics and Statistical Process ControlCreating Confidence Intervals for Variables DataThe fish and game commission have been feeding robin yearlings a special bird seed.Sample weights of 13 robins are listed below. What are the 95% and 99%confidence intervals?Procedure:1. Determine the Mean and Std. Deviation of the data set.2. Create Lower and Upper Confidence Intervals based on the “t” values provided. Data Set 95% Confidence Interval (Mean) (in Grams) Mean = 12.5 Std Dev.= Tinv(95)= 2.178813 12.3 n= 13 Tinv(99)= 3.05454 12.7 Confidencence Limits 12.5 Lower= 0 Upper= 0 12.4 12.1 12.6 12.7 99% Confidence Interval (Mean) 12.2 Mean = 12.1 StdDev= 11.9 n= 13 12.3 Confidence Limits 12.6 Lower 0 Upper 0 Sum = 160.9Question: Why are we using “t” scores versus standardized “Z” scores?Gregory Swartz, © 2008 (650) 274-6001 Page 43
- 50. Metrics and Statistical Process ControlSample Size Determination for Means and ProportionsDetermining a sample size for means.The formula for determining a sample size for a mean is Ζ 2σ 2 η= (χ − μ ) 2The Ζ -value depends on the level of confidence required. Remembering that: A 99 percent confidence results in a Ζ -value of 2.58. A 95 percent confidence results in a Ζ -value of 1.96. A 90 percent confidence results in a Ζ -value of 1.645.σ is the standard deviation or variance.χ −μ is the difference between the sample mean and the population mean referredto as the error.Sample Size Determination Z-Value = 2.576321008 Std. Dev.= 0.75 error= 0.15 sample size= 165.9357483Gregory Swartz, © 2008 (650) 274-6001 Page 44
- 51. Metrics and Statistical Process ControlDetermining a sample size for proportion:The formula for determining a sample size for a proportion is n = Ζ 2 ( p 1− p ) (ρ − p )2The Ζ -value depends on the level of confidence required.p is the population proportion if known. If the proportion is notknown, π is assigned a value of .5ρ − p is the difference between the sample proportion and thepopulation proportion referred to as the error.The Easy technique for determining sample “n”: np > 5Gregory Swartz, © 2008 (650) 274-6001 Page 45
- 52. Metrics and Statistical Process ControlScenario: You have been selected as the “improvement Expert”in your lab to determine the appropriate “n” size per sample afteryour team has determined an average failure rate of .035. Dueto new equipment in the lab an initial confidence level of 95% isselected, and degree of precision (error) @ .02.Procedure: 1. On a worksheet, key in the following information: Sample Size Determination - Proportion Z-Value= Pop.Prop.= error= sample size= #DIV/0! 2. In cell B3, input the Z value for 95% Confidence 3. In cell B4, input the failure rate 4. In cell B5, input the error. 5. In cell B6, key in =B3^2*B4*(1-B4)/B5^2Questions:Gregory Swartz, © 2008 (650) 274-6001 Page 46
- 53. Metrics and Statistical Process Control 1. What is the required random sample size for a degree of precision of .05? 2. What sample size is required for the same precision, with 99% confidence?Chapter Five: Process Control Tools for Variables Data ♦ X Bar and R Charts ♦ X Bar and S Charts (n>10) for reference ♦ Short Run SPC Charting TechniqueGregory Swartz, © 2008 (650) 274-6001 Page 47
- 54. Metrics and Statistical Process Control Control Limits • Help define acceptable variations of the process. • Are calculated and represent true capability of the target process, or where baseline metrics have been implemented. • Can change in time as the process improves. UCL X LCL 1 2 3 4 5 6 7 8 9 10 11 12 Time or Sample Number General Rule: Don’t apply specification limits on control charts.Gregory Swartz, © 2008 (650) 274-6001 Page 48
- 55. Metrics and Statistical Process ControlX and R Control Chart UCL xMEASURE xMENT LCL x UCL R RGregory Swartz, © 2008 (650) 274-6001 Page 49
- 56. Metrics and Statistical Process ControlControl Limits vs. Spec. LimitsControl limits monitor the performance of theprocess. y UCL XMeasure X LCL X X 1 2 3 4 5 6 7 8 9 10 time or sample number -->Spec. limits monitor the quality of the product as tothe individual distribution below: X LS USGregory Swartz, © 2008 (650) 274-6001 Page 50
- 57. Metrics and Statistical Process ControlShort Run SPCThe Short Run Individual X and Moving RangeCharts can be applied to the following: • Low production volume • Temperature, humidity, concentration of solutions • When data must be obtained at the end of a reporting period (per quarter, month, day) • When the testing is costly or time consumingGregory Swartz, © 2008 (650) 274-6001 Page 51
- 58. Metrics and Statistical Process Control X & R Charts Control Chart Plotting Procedure: 1. Accurately measure the required number of readings for the lot. 2. Calculate the mean. (Add readings together and divide by the number of readings.) 3.Calculate the range. (Subtract lowest reading from the highest reading.) 4. Plot both the mean and range on the SPC chart. Log the lot number and date. pg. 59Gregory Swartz, © 2008 (650) 274-6001 Page 52
- 59. Metrics and Statistical Process ControlExample Data /Analysis for Control Date MEAS 1 Meas. 2 Meas. 3 Ave. Grand AveUCL LCL 1/18/2007 0:00 0.3637 0.3663 0.2118 1/19/2007 0:00 0.1322 0.426 0.2178 1/20/2007 0:00 0.09442 -0.02428 0.02284 1/21/2007 0:00 0.3333 0.1105 0.2807 1/22/2007 0:00 0.04403 0.2663 0.02492 1/23/2007 0:00 0.4842 0.1715 0.0816 1/24/2007 0:00 0.07829 0.1304 0.1919 1/25/2007 0:00 -0.04909 -0.09284 -0.2375 1/26/2007 0:00 0.1948 0.4446 -0.02368 1/27/2007 0:00 0.1614 -0.1326 0.2387 1/28/2007 0:00 -0.206 0.0127 0.2065 1/29/2007 0:00 0.0201 0.1632 0.2199 1/30/2007 0:00 0.04176 0.1323 0.2523 1/31/2007 0:00 0.338 0.09527 0.9097 2/1/2007 0:00 0.2842 -0.05588 -8.97 2/2/2007 0:00 -0.1014 0.04255 0.07366 2/3/2007 0:00 -0.2253 0.3117 0.2042 2/4/2007 0:00 6.543 0.2073 0.000886 2/5/2007 0:00 10.03 -0.1436 9.883 2/6/2007 0:00 0.2127 0.1612 0.4555 2/7/2007 0:00 0.4352 0.1162 0.1387 2/8/2007 0:00 0.744 0.2604 0.5681 2/9/2007 0:00 0.1054 0.2471 0.04124 2/10/2007 0:00 -0.2962 0.05815 0.6354 2/11/2007 0:00 0.4714 9.732 0.2281 2/12/2007 0:00 0.2151 0.0752 0.2977 2/13/2007 0:00 0.2146 0.6519 0.6632 2/14/2007 0:00 0.3294 0.7231 0.1349 2/15/2007 0:00 0.7159 0.2251 0.3108 2/16/2007 0:00 0.5853 0.4141 0.2791Gregory Swartz, © 2008 (650) 274-6001 Page 53
- 60. Metrics and Statistical Process Control Average Control Chart using 2 Sigma Limits Below is an Average Control Chart using the data from the previous page. Limits were generated in Excel at the 95% confidence interval using 1.96 Sigma + Grand Average. Control Chart of Plate Data w ith 2 Sigma Limits 180.0 175.0 170.0 165.0 Average 160.0 UCL 155.0 LCL 150.0 Grand Ave. 145.0 140.0 135.0 4 4 4 4 4 4 4 04 04 04 00 00 00 00 00 00 00 20 20 20 /2 /2 /2 /2 /2 /2 /2 4/ 6/ 8/ 10 12 14 16 18 20 22 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ 1/ Interpretation: There is good reason with the above data set to consider implementing 2 Sigma Control Limits as shown. In this case, data point on 1/09/04 fell just outside the Upper Control Limit. Do you think 3 Sigma Limits would have caught the abnormal cause?Gregory Swartz, © 2008 (650) 274-6001 Page 54
- 61. Metrics and Statistical Process ControlFactors and Control Limits Shewhart Factors n 2 3 4 5 6 D4 3.268 2.574 2.282 2.115 2.004 D3 0 0 0 0 0 A2 1.880 1.023 0.729 0.577 0.483 d2 1.128 1.693 2.059 2.326 2.534Control Limit Formulas UCL X = X + (A2• R) LCL X = X − (A2• R) UCL R = RD4 LCL = RD 3 RGregory Swartz, © 2008 (650) 274-6001 Page 55
- 62. Metrics and Statistical Process ControlExercise - Short-Run Control ChartsKey Points for Plotting the X (individual)Control Charts: • X is the individual measurement to be plotted. • X is the average of the individual plot points. This becomes the center line for the control chart. • UCL is the Upper Control Limit and is calculated by: UCL = [ Average + (2 x σ) ] • LCL is the Lower Control Limit and is calculated by: LCL = [ Average - (2 x σ) ]Gregory Swartz, © 2008 (650) 274-6001 Page 56
- 63. Metrics and Statistical Process ControlCreating a Short-Run Control Chart in ExcelTM 1. Arrange your data from left to right as seen in table below. 2. Assign a # or date for the individual data being collected (see table below). 3. Calculate the average of your data with the function wizard and create separate rows repeating the average across all data points. 4. Determine the Standard Deviation (σ ) with the function wizard. 5. Calculate the Upper & Lower Control Limits (UCL & LCL) by multiplying the Standard Deviation times 2, and then both add and subtract the product from the [X ± (2 xσ )] 6. Repeat the Control Limits across all data points. 7. Use the mouse to block off date, data, average, & control limits. 8. Use the Chart Wizard to create your Control Chart (see below). 9. Interpret Control Chart for shifts, trends, or out-of-control points. pp. 51-63Gregory Swartz, © 2008 (650) 274-6001 Page 57
- 64. Metrics and Statistical Process ControlVariables Data Excel Exercise 1. Determine Averages across date or assay type 2. Create Upper Control Limit = Ave. plus 1.96 Std. Dev. 3. Create Lower Control Limit = Ave. minus 1.96 Std. Dev. 4. Create 3 additional columns for UCL, LCL, and Ave. 5. Swipe Mouse over Dates, Averages, UCL, LCL, and Average 6. Use chart wizard to create a multiple line chart 7. Include Interpretation Section for Out-Of-Control points Date Phred 20 Ave. UCLx LCLx 5/1/2007 351 5/2/2007 375 5/3/2007 368 5/4/2007 364 5/5/2007 321 5/6/2007 289 5/7/2007 325 5/8/2007 366 5/9/2007 378 5/10/2007 347 5/11/2007 339 5/12/2007 335 5/13/2007 389 5/14/2007 348 5/15/2007 354 5/16/2007 368 5/17/2007 356 5/18/2007 392 5/19/2007 373 5/20/2007 352 Sum= Ave. = Std. Dev.=Questions: 1. Since the above Phred scores are individual readings, what might be a realistic lower specification limit? 2. What degree of confidence in % have you created with your control limits?Gregory Swartz, © 2008 (650) 274-6001 Page 58
- 65. Metrics and Statistical Process ControlNow: Let’s try this with another example with min andmax specifications:Date MEAS MIN MAX7/23/2007 26.81 24 1007/24/2007 26.67 24 1007/25/2007 26.9 24 1007/26/2007 27.04 24 1007/27/2007 26.63 24 1007/28/2007 26.92 24 1007/29/2007 26.73 24 1007/30/2007 26.8 24 1007/31/2007 26.94 24 100 8/1/2007 26.85 24 100 8/2/2007 27.54 24 100 8/3/2007 27.22 24 100 8/4/2007 25.84 24 100 8/5/2007 25.77 24 100 8/6/2007 26.93 24 100 8/7/2007 26 24 100 8/8/2007 26.96 24 100 8/9/2007 25.79 24 1008/10/2007 27.04 24 100Gregory Swartz, © 2008 (650) 274-6001 Page 59
- 66. Metrics and Statistical Process Control Control Chart Tools Overview Data Yes/No Measurable Good/Bad Pass/ Fail Variable Data Attribute Data Defects Defects Unlimited Limited X/MR X/R Chart X/S Chart c Chart u Chart p Chart np Chart Chart Sample Sample Fixed Variable Variable Fixed size less size more Individuals Sample Sample Sample Sample than 7 than 6 Size Size Size SizeGregory Swartz, © 2008 (650) 274-6001 Page 60
- 67. Metrics and Statistical Process ControlChapter Six: Process Control Tools For Attribute Data NP Charts - # of defective in a sample (sample size is constant P Charts - fraction defective (sample size can vary C Charts - # of defects per unit SPC Charting GuidelinesGregory Swartz, © 2008 (650) 274-6001 Page 1
- 68. Metrics and Statistical Process ControlAttribute Control ChartsAttribute Control Charts consist of primarily threebasic types of charts following the binomial andpoisson distributions: • np Charts - used for monitoring the # of defects per sample when the sample size is constant, for example, n = 50. • p Charts - can be used either with a constant sample size or variable sample (n) size. (variable control limits or average control limits may be imposed) • c Charts – is applicable for the number on defects per sample unit, e.g. # of defects on a car. Sample unit size is constant. • u Charts – is used in the same way as a c Chart, but the sample unit size may vary.Gregory Swartz, © 2008 (650) 274-6001 Page 2
- 69. Metrics and Statistical Process Controlp Chart Formulas NP Chart Formulas ( p 1− p )UCL p = p + 3. n ( UCLnp = np + 3. np 1 − p ) ( p 1− p )LCL p = p − 3. n ( LCLnp = np − 3. np 1 − p ) C Chart Formulas UCLc = c + 3. c LCLc = c − 3. cGregory Swartz, © 2008 (650) 274-6001 Page 3
- 70. Metrics and Statistical Process ControlBenefits of an “Attribute P Chart” Allows for accurate monitoring of fraction defective. Control Limits act as guidelines when your process is producing bad product. The average fraction defective is a good indicator of “Failure Rate.”Attribute P Chart Procedure 1. Determine fraction defective for each sample in adjacent column 2. Calculate the average fraction defective (Ave. p) into additional column 3. Determine the Std. Dev. Of the proportion defective. 4. Create Upper and Lower Control Limits based on 1.96 Sigma 5. Drag mouse over p, Ave. p, UCLp, and LCLp 6. Create multiple line chart in Chart Wizard 7. Interpret Results and comment on OutliersGregory Swartz, © 2008 (650) 274-6001 Page 4
- 71. Metrics and Statistical Process ControlP Chart Exercise with variable sample sizes in ExcelInstructions: Using the data set below with varying sample n, construct a P Chart inExcel, using +/- 2.58 standard deviation limits.Question: What confidence Interval am I generating? sample n np (defects np/n =p Ave. p UCLp LCLp 1 50 2 0.040 2 35 4 0.114 3 45 3 0.067 4 65 5 0.077 5 75 1 0.013 6 35 3 0.086 7 45 2 0.044 8 75 3 0.040 9 50 2 0.040 10 45 5 0.111 11 58 8 0.138 12 25 5 0.200 13 40 3 0.075 14 60 1 0.017 15 80 0 0.000 16 65 1 0.015 17 46 4 0.087 18 50 3 0.060 19 25 4 0.160 20 85 5 0.059 Totals 1054 64 Average P 0.060721Questions: 1. Is the average fraction defective a good indicator of the failure rate? 2. What processes would lend themselves to p charts in your lab areas?Gregory Swartz, © 2008 (650) 274-6001 Page 5
- 72. Metrics and Statistical Process Control Process Control Tools Overview Flowchart Data Attribute Variable Display Display Data Over Data Over Time? Time? No Yes No Yes Check Data X and MR P, NP, or Sheet Collection Run Chart C Charts Sheet _ Pareto X and R Chart Histogram Control Chart Pie Process Chart Capability ToolsGregory Swartz, © 2008 (650) 274-6001 Page 6
- 73. Metrics and Statistical Process ControlChapterSeven: INTERPRETATION & CORRECTIVE ACTION • Interpreting Trends and Shifts in Data • Planning Corrective Action • Implementing Continuous Process ImprovementGregory Swartz, © 2008 (650) 274-6001 Page 7
- 74. Metrics and Statistical Process Control Control Chart Interpretation • Detecting "Out-of-Control" Conditions • Assigning Causes to Problems • Guidelines for Control and Stability Corrective Action • Assigning Causes to Problems • Selecting SPC Tools • Corrective Action Plan • SPC Report FormGregory Swartz, © 2008 (650) 274-6001 Page 8
- 75. Metrics and Statistical Process ControlDetecting Out of Control ConditionsBonnie Smalls guidelines for interpreting controlchart data • Points beyond the control limits usually indicate: - The process performance is sporadic - Measurement has changed (inspector, shift, gage, etc.) • Runs indicate a shift or trend. Runs include: - 7 points in a row on one side of the average - 7 points in a row that are consistently increasing or decreasing • Non-random patterns may indicate: - The plot points have been miscalculated or misplotted. - Subgroups may have data from two or more processesGregory Swartz, © 2008 (650) 274-6001 Page 9
- 76. Metrics and Statistical Process ControlDetermine whether Bonnie Small rules werebroken: • One average (mean) above or below control limit. • Seven consecutive averages (means) above or below the center line. • A trend of seven consecutive points in an upward or downward trend.Now, take corrective action as follows: 1. Circle the point or group of points 2. Comment on the cause(s) of the unstable point(s). 3. Detail Corrective Action Plan.Gregory Swartz, © 2008 (650) 274-6001 Page 10
- 77. Metrics and Statistical Process ControlTaking Corrective Action • Implementing change in the process • Identify key problem area(s) • Determine root cause(s) • Document causes and Corrective Action • Implement SPC Team Action PlanGregory Swartz, © 2008 (650) 274-6001 Page 11
- 78. Metrics and Statistical Process Control SPC Report Form Name: Date: Department: Extension: Statement of the Problem: Corrective Action Objective: Method: Results: (attach charts, data analysis to form) Corrective Action/Recommendation:Gregory Swartz, © 2008 (650) 274-6001 Page 12
- 79. Metrics and Statistical Process ControlChapterEight: Correlation and RegressionProcedure for Creating a Scatter Diagram in ExcelTMArrange your paired (X and Y) data in table format.Assign a # for each pair of data being collected (see table below). Conc. % Genotype 1.50 72 1.00 65 2.50 87 1.00 63 3.00 92 4.00 95 1.00 60 2.00 80 1.50 68 3.00 90Use the mouse to block off the X and Y data columns.Use the Chart Wizard to create your Scatter Diagram.Gregory Swartz, © 2008 (650) 274-6001 Page 13
- 80. Metrics and Statistical Process ControlAppendix: Terms & Definitions:Acceptance Criteria -the amount of acceptable rejects before a lotwill be rejected based on the sample. Used in sampling plans as thecriteria for passing or failing a lot of items inferred from the sample.Acceptable Quality Level (AQL) - a coordinate point for the fractiondefective on the x axis of the Operating Characteristic Curve of anattribute sampling plan. This point is the region of good quality andreasonably low rejection probability - 5% alpha error.Accuracy - how close a measurement comes to its actual value. In aparticular process, accuracy could be a function of calibration. SeePrecision.Alpha Error - the probability of error in making an assumptionincorrectly. In sampling plans, it is the probability of rejecting a lotwhich is truly good. In Control Charts, it is the assumption that aprocess point is out-of-control, when in fact it is not, and is due tostatistical chance alone. Therefore, the smaller the alpha error in anycase, the more confidence there is in the result(s) we‘ve obtained.Analysis - implies some conclusion based on statistical results inorder to interpret some meaning from the statistical test(s) performed.Interpretation.Ambient -certain intervening variables in a environment that havesome effect on the result being measured. Generally, ambientvariables or factors in an industrial environment are those which arenot wanted, such as dust particles, temperatures, or sources of light.Arithmetic Average - the mean of the distribution. It is a measure ofCentral Tendency indicating the center weight of a distribution ofscores.Assignable Causes - those causes to problems which are sporadic innature and not due to statistical chance alone. Assignable causes canbe assigned a reason as to why that problem point exists. Usually,points outside of control chart limits are associated with anassignable cause and this cause can be identified.Attribute Data - qualitative data based on the absence or presence ofa characteristic, usually determined by a specification. Commontypes of attribute data would include: go no-go data, pass-fail,Gregory Swartz, © 2008 (650) 274-6001 Page 14
- 81. Metrics and Statistical Process Controlaccept/reject, yield/reject. Attribute data is based on binomialpopulation of mutually exclusive events designated by P and Q= (1-P).Average Outgoing Quality (A.O.Q.) - based on the fraction defective(P) and the probability of acceptance (PA) for that fraction defective.Also takes into account the characteristics of an attribute samplingplan, that is, its sample size and decision criteria. A.O.Q. = P.A. x P.Average Outgoing Quality Limit (A.O.Q.L.) - the threshold point onthe A.O.Q. curve. It is the worst possible case outgoing quality, and isgenerally derived from the area of indifference off the OperatingCharacteristic Curve.Awareness - attention to the relationships between quality andproductivity. Directing this attention to the requirement formanagement commitment and statistical thinking leads towardimprovement.Beta Error - In sampling plans, beta error is associated with theL.T.P.D. point and implies a 10% risk in accepting a lot which is trulyrejectable. In hypothesis testing, it is the error made in rejecting analternative hypothesis when in fact, it is true. In control charts, betais the error made in assuming the process is in control when in fact, itis not.Bimodal Distribution - a distribution having two modes depicted bytwo distinctive humps in the curve. The presence of two frequentlyoccurring scores, or groups of scores is noticeable.Binomial Distribution - A discrete probability distribution forattributes data that applies to the conformance and non conformanceof units. This distribution also is the basis for attribute control chartssuch as p and np charts.Capability - whether or not product is truly capable of conforming tospecifications. This capability can only be determined after theprocess is in statistical control. A process may be defined as beingtruly capable when the aim of the process is well centered and thevariance or spread of the process on an individual unit basis does notexceed the specification limits.Cause and Effect Diagram - a simple tool for individual or groupproblem-solving that uses a graphic description of the various processelements to analyze potential sources of process variation. Also calledGregory Swartz, © 2008 (650) 274-6001 Page 15
- 82. Metrics and Statistical Process Controla fishbone diagram (because of its appearance) and developed byIshikawa.Capricious Data - the natural occurring chaos in all things, or theunexpected results one derives from attempting to sort out dirty data,like sudden shifts or abnormal changes.Central Limit Theorem (C.L.T.) - when collecting a distribution ofaverages or subgroup scores, the distribution will tend to centralizearound the center value. The distribution will be evenly distributedabout the mean or average. This is true if the averages are sampledfrom an abnormal distribution (skewed, bimodal, etc.).Control - in Statistical Quality Control, control means to get ahandle on the process and be able to manipulate it in a desirablefashion.Control Charts - a tool one uses to visualize a particular processover time and/or across units. It is a way to graphically represent aparameter in an unbiased manner. The various types of control chartsare as follows: C Charts - used to depict the number of defects per unit. Forexample, the number of defects per automobile. An average numberof defects per automobile can also be obtained - (C bar). P Charts - used when the Percent or Fraction Defective isgraphically desired. It depicts the fraction defection per sample, andan average can be obtained. NP Charts - used to the depict the number of defects persample. Similar to a C Chart, NP easily counts the number of defectswhich makes charting fairly simple. The main requirement for a NPChart is the sample size must remain constant. R Charts - used to monitor the range variation when collectingaveraged or subgroup data. Usually seen in conjunction with an XBar Chart, the range chart gives information to the variance of aprocess over time, across units, or across samples.S Charts - similar to R charts and measure the process variation viathe sample standard deviations. The S Chart is especially applicablewith larger sample sizes.Gregory Swartz, © 2008 (650) 274-6001 Page 16
- 83. Metrics and Statistical Process ControlX Bar Charts - used to monitor variables data (continuous variables)over time. Generally, X Bar Charts, graphically represent averages orgroups of data over time. They serve as a good indication of anyprocess which has been identified as a problem area or formonitoring purposes.Control Limits - c the boundary lines set up on any control chart forthe purpose of determining whether a process is in or out of control.Typically, the area between the control limits account for 99.7% of thedistribution of scores making up the control chart. When controllimits are set plus and minus three sigma (standard deviations), itwill accommodate again 99.7% of the distribution.Control Limits for Averages - when taking average or subgroupdata, these limits are used for averages on an X Bar Chart. They alsoserve as a boundary parameter for a majority of the scores beingmarked on the chart (99.7%), but in this case it applies for averagesand not individual scores.Control Limits for Individuals - also known as the natural processlimits help determine, with 99.7% confidence, where the expectedprocess will go. Because these limits are for individual scores, theyassist in determining the yield for a particular process.Cost-Effectiveness - The reduction of quality costs, such as rework,and waste, makes any operation more cost-effective. By being cost-effective, savings and efficient operations will ensue. Quality is reallyfree, it only cost money when you don’t have it.Fault-Tree Analysis - is a brainstorming and communication tool inorder to figure out all the possible causes to any particular yield,productivity, or quality problem. This tool uses a fish-bone diagramto analyze all the possible causes to an identified problem in thecategorized areas of People, Equipment, Specifications, Flow, RawMaterials, and Measurement.Kurtosis - Refers to the height of a distribution of scores. Platykurticmeans a flat and very dispersed distribution, whereas leptokurticmeans a tall and very tightened distribution.L.T.P.D. - Lot Tolerance Percent Defective. Let Them Pay Dearly.This particular defective level is guaranteed with 90% confidence ofmeeting the plan, and a 10% Beta Error or probability of rejection. SeeBeta Error.Gregory Swartz, © 2008 (650) 274-6001 Page 17
- 84. Metrics and Statistical Process ControlMean - arithmetic average.Measure - the dictionary defines measure as the dimensions,quantity, or capacity of anything ascertained by a scale or by thevariable condition. In S.Q.C., measure could be a reference standardor sample used for the quantitative comparison of properties.Median - is the middle score when the scores are ranked from highestto lowest or lowest to highest. When the median is resolved half of thescores will be on one side, and the other half will be on the other side.Methodology - the systematic way in which an application isaddressed to a problem. S.Q.C. methodology involves a logicalapproach with statistical tools to effectively solve problems.Midpoint - in reference to cell intervals, it is the middle point of anyparticular cell.Modified Control Limits - are generally performed when the processis well within the Specification Limits, and both the upper and lowerspecification limits are outside the natural limits of the process.Mode - a measure of central tendency indicating where the mostfrequently occurring score or group of scores lies in a distribution.Motivation - the impetus influencing the use of S.P.C. to itsmaximum potential.Participation.Normal - a continuous, symmetrical, bell-shaped frequencydistribution for variables data which is the basis for control charts forvariables. The mean, median, and mode are approximately the same,and a standard deviation (S) exists where plus and minus one S =68%, plus and minus two S = 95%, and plus and minus three S =99.7% which is a standard setting for control charts limits.Pareto Chart - A simple tool for problem-solving that involves makingall potential problem areas or sources of variation. Pareto was anItalian economist who resolved that a majority of the wealth resides inGregory Swartz, © 2008 (650) 274-6001 Page 18
- 85. Metrics and Statistical Process Controla few elite or upper class. In relation to a process, this means a fewcauses account for most of the cost (or variation).Poisson Distribution - Another discrete probability distribution forattributes data used as an approximation to the binomial. It can beused when p<.1 and np<5. It is the basis for C charts usingattributes data.Prevention - a strategy for maintenance of a process. This implies anawareness of potential problems that can occur in the process and toact on those problems before an “out-of-control” situation happens. Apreventative maintenance program (PM).Process - a series of events leading to a desired result or product. Aprocess can involve any part of a business.Process Control - having a process behave under an expectedfrequency of occurrence or within the limits which have beenstatistically derived. It is a state in which all the points fall in andaround the average in a random manner and very few of theseapproach the limits of the distribution.Quality - usually determined by the customer, quality is a currentissue today that challenges U.S. companies to surpass itscompetition. Quality gives a product a characteristic of customersatisfaction. If we care for good quality we should have the priority ofpleasing our customer.Randomness - the state of collecting individual data values withoutany expected frequency or basis. They may become defined once adistribution is perceived.Range - the difference between the minimum and maximum score.Sample - a known quantity designated by (n) or the size of thesample. It is randomly pulled from a population parameter in order toprovide statistical data.Statistics - derived from a sampled population, the information isarranged to make interpretation of the data easy and to infersomething about the population from thesample which has been randomly drawn.Gregory Swartz, © 2008 (650) 274-6001 Page 19
- 86. Metrics and Statistical Process ControlSpecial Cause - cause attributable to an assignable item off the x axisof a control chart. Special Causes are People, Machine, Materials, etc.Specification - These may be quality specs. or product specs. Theyare set by engineering or determined by the demands of the customer,keeping in mind Deming’s philosophy: “The customer is King”.Spread - variability in a distribution of data. Can also be thought ofas the dispersion of data around the measures of Central Tendencysuch as the mean.Stable Process - a process which is under statistical control as wellas lacking in assignable or special causes of variation.Standard Deviation - the main statistic to measure the spread ordispersion of a distribution or of a process when applied with the useof Control Charts.Student’s t Distribution - used when the sample size is less than 50or the variance of the distribution is unknown. This distributioncompensates for smaller sample sizes, and is used primarily for meancomparisons or process capability studies.Type I Error - see Alpha Error.Type II Error - see Beta Error.Variables Data - continuous data obtainable via measurable resultssuch as dimensional data (heights, widths), or electrical data(resistance, current).Variation - the degree of change in the spread of a distribution ofscores. Many things built by man and nature have some inherentnatural variability. This variation shows up graphically in adistribution of scores.Gregory Swartz, © 2008 (650) 274-6001 Page 20

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