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OpEx Statistical Process Control (SPC) Training Module

by Frank G. Adler, Ph.D., Consultant & Managing Partner at Operational Excellence Consulting, LLC on Apr 30, 2010

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Operational Excellence Consulting: Statistical Process Control Training Module including 116 slides covering Introduction to SPC, The Histogram, Measure of Location and Variability, Process Control ...

Operational Excellence Consulting: Statistical Process Control Training Module including 116 slides covering Introduction to SPC, The Histogram, Measure of Location and Variability, Process Control Charts, Process Control Limits, Out-of-Control Criteria, Sample Size and Frequency, Out-of-Control Action Plan, and 6 Workshop Exercises.

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OpEx Statistical Process Control (SPC) Training ModulePresentation Transcript

• OPERATIONAL EXCELLENCEC O N S U L T I N G1 April 16, 2013 – v3.0Operational Excellence – Statistical Process ControlWorkshop Instructor: Frank Adler, Ph.D.Operational Excellence Consulting
• OPERATIONAL EXCELLENCEC O N S U L T I N G2 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control (SPC) – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G3 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G4 April 16, 2013 – v3.0The process and quality control methods and techniques used todaygot their start in the American Civil War at around 1789, when EliWhitney took a contract from the U.S. Army for the manufacture of10,000 rifles at the unbelievably low price of \$13.40 each.At that time most of the products were handmade by small owner-managed shops and product parts were thus not interchangeable.The result of Whitney’s first mass production trail was that the rifles didnot work as well as the handmade rifles. In addition, the copied partsdid not fit as expected.The History of Statistical and Process Thinking
• OPERATIONAL EXCELLENCEC O N S U L T I N G5 April 16, 2013 – v3.0GO - TestNO-GO - TestThe first time that one presented machine produced parts was 1851 at theindustry exhibition in the Crystal Palace in London. An American gun smith took10 working guns, took them apart, mixed all the parts in a box and re-assembledthem again. This was found a quite surprising “experiment”.The History of Statistical and Process Thinking
• OPERATIONAL EXCELLENCEC O N S U L T I N G6 April 16, 2013 – v3.0Process InspectionGoodBadRepairScrap+Monitor/AdjustThe Traditional Production ConceptThe Detection Control Scheme
• OPERATIONAL EXCELLENCEC O N S U L T I N G7 April 16, 2013 – v3.0• The traditional production concept does not help us toproduce only good products.• Every product has to be inspected.• Products have to be repaired or even scraped.• With respect to productivity and efficiency every activityafter the actual production process is a non-value addedactivity.The Traditional Production Concept
• OPERATIONAL EXCELLENCEC O N S U L T I N G8 April 16, 2013 – v3.0Prevention Control SchemeProcess InspectionGoodBadRepairScrap+An Advanced Production ConceptMonitor/AdjustLearn/ImproveSelective measurement• Product• Process
• OPERATIONAL EXCELLENCEC O N S U L T I N G9 April 16, 2013 – v3.0Statistical Thinking - A DefinitionAll work is a series ofinterconnected processesAll processes varyUnderstanding andreducing variation are keysto successASQ
• OPERATIONAL EXCELLENCEC O N S U L T I N G10 April 16, 2013 – v3.0Customer SatisfactionorCustomer DissatisfactionProcess/SystemMaterialMachines MethodsMenEnvironmentThe Variation Management Approach
• OPERATIONAL EXCELLENCEC O N S U L T I N G11 April 16, 2013 – v3.0A defect is any variation of a required characteristic of the product orits part, which is far enough removed from its nominal value toprevent the product from fulfilling the physical and functionalrequirements of the customer.Variation Management – Defect Definition
• OPERATIONAL EXCELLENCEC O N S U L T I N G12 April 16, 2013 – v3.0The key to process control and continuous processimprovement is to understand the meaning and causes ofvariation in the outcome of the process.Variation Management – Continuous Improvement
• OPERATIONAL EXCELLENCEC O N S U L T I N G13 April 16, 2013 – v3.0Remarks or Questions ?!?
• OPERATIONAL EXCELLENCEC O N S U L T I N G14 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G15 April 16, 2013 – v3.0A histogram provides graphical presentation and a first estimationabout the location, spread and shape of the distribution of the process.0 10 20 30 40 50The Histogram
• OPERATIONAL EXCELLENCEC O N S U L T I N G16 April 16, 2013 – v3.0Step 1: Collect at least 50 data points, but better 75 to 100 points, and organizeyour data into a table. Sort the data points from smallest to largest and calculatethe range, means the difference between your largest and smallest data point, ofyour data points.The Histogram – How to create a Histogram?Actual MeasurementsPart Hole Size1 2.62 2.33 3.14 2.75 2.16 2.57 2.48 2.59 2.810 2.6Sorted MeasurementsPart Hole Size5 2.12 2.37 2.46 2.58 2.51 2.610 2.64 2.79 2.83 3.1Minimum = 2.1Maximum = 3.1Range = 1.0
• OPERATIONAL EXCELLENCEC O N S U L T I N G17 April 16, 2013 – v3.0Step 2: Determine the number of bars to be used to create the histogram of thedata points. Calculate the width of one bar by dividing the range of your data bythe number of bars selected.The Histogram – How to create a Histogram?Number of Bars:less than 5050 - 100100 - 250over 2505 or 75, 7, 9 or 117 - 1511 - 19Number of Data Points:Minimum = 2.1Maximum = 3.1Range = 1.0Bar Width = 0.2 (5 Bars)
• OPERATIONAL EXCELLENCEC O N S U L T I N G18 April 16, 2013 – v3.0Step 3: Calculate the “start” and “end” point of each bar and count how manydata points fall between “start” and “end” point of each bar.The Histogram – How to create a Histogram?Start EndBar 1 2.1 2.1 + 0.2 = 2.3Bar 2 2.3 2.5Bar 3 2.5 2.7Bar 4 2.7 2.9Bar 5 2.9 3.1Minimum = 2.1Maximum = 3.1Range = 1.0Bar Width = 0.2 (5 Bars)Sorted MeasurementsPart Hole Size Bar5 2.1 12 2.3 27 2.4 26 2.5 38 2.5 31 2.6 310 2.6 34 2.7 49 2.8 43 3.1 5
• OPERATIONAL EXCELLENCEC O N S U L T I N G19 April 16, 2013 – v3.0Step 4: Draw the histogram indicating by the height of each bar the number ofdata points that fall between the “start” and “end” point of that bar.The Histogram – How to create a Histogram?Sorted MeasurementsPart Hole Size Bar5 2.1 12 2.3 27 2.4 26 2.5 38 2.5 31 2.6 310 2.6 34 2.7 49 2.8 43 3.1 5012345NumberofDataPoints2.1 2.3 2.5 2.7 2.9 3.1
• OPERATIONAL EXCELLENCEC O N S U L T I N G20 April 16, 2013 – v3.01. The bell-shaped distribution:Symmetrical shape with a peak in themiddle of the range of the data.While deviation from a bell shape shouldbe investigated, such deviation is notnecessarily bad.The Histogram – Typical Patterns of Variation
• OPERATIONAL EXCELLENCEC O N S U L T I N G21 April 16, 2013 – v3.02. The double-peaked distribution:A distinct valley in the middle of the rangeof the data with peaks on either side.This pattern is usually a combination oftwo bell-shaped distributions and suggeststhat two distinct processes are at work.The Histogram – Typical Patterns of Variation
• OPERATIONAL EXCELLENCEC O N S U L T I N G22 April 16, 2013 – v3.03. The plateau distribution:A flat top with no distinct peak and slighttails on either sides.This pattern is likely to be the result ofmany different bell-shaped distributionwith centers spread evenly throughout therange of data.The Histogram – Typical Patterns of Variation
• OPERATIONAL EXCELLENCEC O N S U L T I N G23 April 16, 2013 – v3.04. The skewed distribution:An asymmetrical shape in which the peakis off-center in the range of the data andthe distribution tails off sharply on oneside and gently on the other.This pattern typically occurs when apractical limit, or a specification limit,exists on one side and is relatively closeto the nominal value.The Histogram – Typical Patterns of Variation
• OPERATIONAL EXCELLENCEC O N S U L T I N G24 April 16, 2013 – v3.05. The truncated distribution:An asymmetrical shape in which the peakis at or near the edge of the range of thedata, and the distribution ends veryabruptly on one side and tails off gently onthe other.This pattern often occurs if the processincludes a screening, 100 % inspection, ora review process. Note that thesetruncation efforts are an added cost andare, therefore, good candidates forremoval.The Histogram – Typical Patterns of Variation
• OPERATIONAL EXCELLENCEC O N S U L T I N G25 April 16, 2013 – v3.0The Histogram – The Bell-Shaped or Normal Distribution
• OPERATIONAL EXCELLENCEC O N S U L T I N G26 April 16, 2013 – v3.0The Histogram – Exercise 1Distribution of Heights of U.S. Population:Use the plot area below to construct a histogram from therandom sample of heights on the right:59 66 63 7060 66 69 7065 62 71 7268 65 67 6965 66 70 6864 64 73 7363 67 71 6863 68 70 6865 67 64 7161 64 70 7270 63 68 6868 63 66 6664 63 67 7463 62 66 6862 62 67 70
• OPERATIONAL EXCELLENCEC O N S U L T I N G27 April 16, 2013 – v3.0Remarks or Questions ?!?
• OPERATIONAL EXCELLENCEC O N S U L T I N G28 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G29 April 16, 2013 – v3.0Example: x1 = 5 x2 = 7 x3 = 4 x4 = 2 x5 = 6Measure of Location – The Sample AverageDefinition:Nxxxx N...218.4524562475x
• OPERATIONAL EXCELLENCEC O N S U L T I N G30 April 16, 2013 – v3.0Example 1: x1 = 2 x2 = 5 x3 = 4Construction: Order all data points from the smallest to largest. Then choosethe middle data point if the number of data points is odd, or the mean value ofthe two middle data points if the number of data points is even.Example 2: x1 = 5 x2 = 7 x3 = 4 x4 = 2Example 3: x1 = 5 x2 = 7 x3 = 4 x4 = 2 x5 = 6median = 4median = 4.5?Measure of Location – The Sample Median
• OPERATIONAL EXCELLENCEC O N S U L T I N G31 April 16, 2013 – v3.0Example: x1 = 5 x2 = 7 x3 = 4 x4 = 2 x5 = 6Measure of Variability – The Sample Range),...,,min(),...,,max( 2121 NN xxxxxxRDefinition:527)6,2,4,7,5min()6,2,4,7,5max(R
• OPERATIONAL EXCELLENCEC O N S U L T I N G32 April 16, 2013 – v3.0x3xaverage_x2x1x10Measure of Variability – Sample Variance9)110(...2102221orxxxxxxTimex6
• OPERATIONAL EXCELLENCEC O N S U L T I N G33 April 16, 2013 – v3.0Example: x1 = 5 x2 = 7 x3 = 4 x4 = 2 x5 = 6Measure of Variability – Sample Variance)1(...222212Nxxxxxxs N7.3)15(8.468.428.448.478.45222222sDefinition:
• OPERATIONAL EXCELLENCEC O N S U L T I N G34 April 16, 2013 – v3.0Example: x1 = 5 x2 = 7 x3 = 4 x4 = 2 x5 = 6Measure of Variability – Sample Standard Deviation)1(...22221Nxxxxxxs NLTDefinition:7.3)15(8.468.428.448.478.45222222LTs92.17.3LTs
• OPERATIONAL EXCELLENCEC O N S U L T I N G35 April 16, 2013 – v3.0Time tProcessCharacteristice.g. Hole SizeProcess not in controlaverageSubgroup size n = 5Number of subgroups N = 7Measure of Variability – The Principle of Subgrouping
• OPERATIONAL EXCELLENCEC O N S U L T I N G36 April 16, 2013 – v3.0Whereis the range of subgroup j, N the number ofsubgroups, and d2 depends on the size n of asubgroup (see handout).sST , often notated as s or sigma, is another measure ofdispersion or variability and stands for “short-termstandard deviation”,which measures the variability of a process or systemusing “rational” subgrouping.Measure of Variability – Standard Deviation sST2221 ...dRdNRRRs NSTm inm ax XXRjn2345678910d21.1281.6932.0592.3262.5342.7042.8472.9703.078
• OPERATIONAL EXCELLENCEC O N S U L T I N G37 April 16, 2013 – v3.0Time tProcessCharacteristice.g. Hole SizeProcess not in controlaverageSubgroup size n = 5Number of subgroups N = 7Measure of Variability – The Principle of Subgrouping sST stays the same, even if the process is not in control sLT increases over time because the process is not in control sST and sLT are identical if the process was in control
• OPERATIONAL EXCELLENCEC O N S U L T I N G38 April 16, 2013 – v3.0Long-term standard deviation:Short-term standard deviation:The difference between the standard deviations sLT and sST gives anindication of how much better one can do when using appropriateproduction control, like Statistical Process Control (SPC).)1(...22221Nxxxxxxs NLTMeasure of Variability – Difference between sLT and sST2221 ...dRdNRRRs NST
• OPERATIONAL EXCELLENCEC O N S U L T I N G39 April 16, 2013 – v3.0average average+1*s(igma)average-1*s(igma)average+2*s(igma)average-2*s(igma)average-3*s(igma)average+3*s(igma)34.13 %34.13 %13.60 % 13.60 %2.14 %2.14 %0.13 % 0.13 %Measure of Variability – The Normal DistributionIf your process is under control, over 99.74% of your data points will fall between theaverage ± 3s(sigma) limits.
• OPERATIONAL EXCELLENCEC O N S U L T I N G40 April 16, 2013 – v3.0Measure of Location and Variability – Exercise 2Calculate the Mean Value or Average, Median, Range, andlong- and short-term Standard Deviation of the sample data.You may copy the data into MS Excel and simplify thecalculations.Group1 59 66 63 622 60 66 69 653 65 62 71 724 68 65 67 695 65 66 70 686 64 64 73 737 63 67 71 688 63 68 65 68MeasurementsOverall Mean Value =Overall Median =Subgroup Ranges =Long-term Standard Deviation =Short-term Standard Deviation =Note: The Excel function for the Long-Term Standard Deviation is “stdev()”.
• OPERATIONAL EXCELLENCEC O N S U L T I N G41 April 16, 2013 – v3.0Measure of Location and Variability – Exercise 2 ResultsSubgroup Median Range1 59 66 63 62 63 72 60 66 69 65 66 93 65 62 71 72 68 104 68 65 67 69 68 45 65 66 70 68 67 56 64 64 73 73 69 97 63 67 71 68 68 88 63 68 65 68 67 5Overall Range: 14Overall Median: 66Average Range: 7.1Short-Term Standard Deviation: 3.46Long-Term Standard Deviation: 3.55Measurements
• OPERATIONAL EXCELLENCEC O N S U L T I N G42 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G43 April 16, 2013 – v3.0Attribute Data(Count or Yes/No Data)Variable Data(Measurements)VariablesubgroupsizeSubgroupsizeof 1Fixedsubgroupsizex chartx-barR chartx-bars chartCountIncidences ornonconformitiesFixedoppor-tunityVariableoppor-tunityc - chart u - chartYes/No DataDefectives ornonconforming unitsFixedsubgroupsizeVariablesubgroupsizenp - chart p - chartProcess Control Charts – Types of Control ChartsType of Data
• OPERATIONAL EXCELLENCEC O N S U L T I N G44 April 16, 2013 – v3.0 The x - chart is a method of looking at variation in a variable dataor measurement. One source is the variation in the individual data points over time.This represents “long term” variation in the process. The second source of variation is the variation betweensuccessive data points. This represents “short term” variation. Individual or x - charts should be used when there is only one datapoint to represent a situation at a given time. To use the x - chart, the individual sample results should besufficient normally distributed. If not, the x - chart will give morefalse signals.Process Control Charts – The x - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G45 April 16, 2013 – v3.01 0 . 0CHANo kiFr a nton t hOBSERVATIONS791 11 31 51 71 92112EEEEEEEEEEEEEEEEEEEEEEEEALURANGES0123456LUR01.01.8701.02.8701.03.8701.04.8701.05.8701.06.8701.07.8701.08.8701.09.8701.10.8701.11.8701.12.8701.01.8801.02.8801.03.8801.04.8801.05.8801.06.8801.07.8801.08.8801.09.8801.10.8801.11.8801.12.881 00G r oA u t oCL OCu r vK - SA V EPROUCLL CLr e e nProcess Control Charts – x - Chart Example
• OPERATIONAL EXCELLENCEC O N S U L T I N G46 April 16, 2013 – v3.0Regardless of the shape of the distribution of a population, thedistribution of average values, x-bar’s, of subgroups of size n drawnfrom that population will tend toward a normal distribution as thesubgroup size n becomes large.Laplace and GaussProcess Control Charts – The Central Limit TheoremCarl Friedrich GaussPierre Laplace
• OPERATIONAL EXCELLENCEC O N S U L T I N G47 April 16, 2013 – v3.0 The (x-bar / R) - chart should be used if the individual measurements are not normally distributed, one can rationally subgroup the data and is interested indetecting differences between the subgroups over time. The (x-bar / R) - chart is a method of looking at two differentsources of variation. One source is the variation in subgroupaverages. The other source is the variation within a subgroup. The x-bar - chart shows variation over time or long-term variationand the R - chart is a measure of the short-term variation in theprocess.Process Control Charts – The (x-bar/R) - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G48 April 16, 2013 – v3.01 0 . 0CHANo kiFr a n5 -o fAVERAGES. 0. 0. 0. 0. 0. 02112AA*ALURANGES01 02 03 04 05 06 07 0LUR95.01.2095.01.2195.01.2395.01.2495.01.2595.01.2695.01.2795.01.2895.01.3095.01.3195.02.0195.02.0295.02.0395.02.0495.02.0695.02.0795.02.0895.02.0995.02.1095.02.1195.02.1395.02.2095.02.2195.02.22INDIVIDUALS6 . 00 6 . 0G r oA u t oCL OCu r vK - SA V EPROUCLL CLr e e nProcess Control Charts – (x-bar/R) - Chart Example
• OPERATIONAL EXCELLENCEC O N S U L T I N G49 April 16, 2013 – v3.0 The (x-bar / s) - chart should be used instead the (x-bar / R) -chart if the subgroup is larger than 10. In this case, thestandard deviation is a better measurement than the range forthe variation between individual measurements in a subgroup. The (x-bar / s) - chart can be used whenever one can use the(x-bar / R) - chart. The (x-bar / s) - chart is a method of looking at sources ofvariation. One chart looks at variation in the subgroup averagesx-bar. The other chart examines variation in the subgroupsstandard deviation s.Process Control Charts – The (x-bar/s) - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G50 April 16, 2013 – v3.0Process Control Charts – Exercise 3Throw the Dice:Step 1: Throw the dice 30 times and record the results in the table on the right.Step 2: Draw a Histogram #1 of the 30 data points in one of the spreadsheets below.Step 3: Calculate the average to 2 consecutive throws and draw the histogram #2 of the resulting 15 datapoints.What do you see and why?AverageResultsHistogram #1 Histogram #2
• OPERATIONAL EXCELLENCEC O N S U L T I N G51 April 16, 2013 – v3.0The number of defect phones produced per hour were1. hour: 100 phones and 10 defect phones.2. hour: 110 phones and 12 defect phones.3. hour: 90 phones and 9 defect phones.4. hour: 95 phones and 10 defect phones.5. hour: 115 phones and 13 defect phones.6. hour: 120 phones and 15 defect phones.7. hour: 80 phones and 7 defect phones.8. hour: 85 phones and 5 defect phones.9. hour: 100 phones and 8 defect phones.10. hour: 110 phones and 11 defect phones.11. hour: 75 phones and 5 defective phones. Something wrong ???Process Control Charts – Attribute “Yes/No” Data
• OPERATIONAL EXCELLENCEC O N S U L T I N G52 April 16, 2013 – v3.0Number of defective Items10 2 3 4 5 6 7 8 9AverageProcess Control Charts – The Binomial Distribution
• OPERATIONAL EXCELLENCEC O N S U L T I N G53 April 16, 2013 – v3.0 The p - chart is used to look at variation in the yes/no attribute data.It can for example be used to determine the percentage p ofdefective items in a group of items. The number n of items in each group has not to be constant, butshould not vary more than 25 %. Operational definitions must be used to determine what constitutesa defective item.Process Control Charts – The p - Chartnnppitemsofnro.itemsdefectiveofnro.The percentage of defective items is given by
• OPERATIONAL EXCELLENCEC O N S U L T I N G54 April 16, 2013 – v3.0 The np - chart, like the p - chart, is used to look at variation inyes/no type attributes data. np - charts are used to determine the number np of defectiveitems in a group of items, while p - chart looked at thepercentage of defective items in a group of items. Because thenp - chart uses the number of defects, it is easier to use. However, the major difference between the np - chart and the p- chart is that the subgroup size has to be constant for the np -chart. This is not necessary for the p - chart.Process Control Charts – The np - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G55 April 16, 2013 – v3.0Process Control Charts – The p – Chart Example0 3C HN oF r a20e P024680PERCENTAGE PLU24681 01 21 41 61 82 02 22 42 62 83 03 23 43 63 84 04 24 44 64 85 0
• OPERATIONAL EXCELLENCEC O N S U L T I N G56 April 16, 2013 – v3.0The number of wrong assembled components in SMD made on 20 PCBs were1 - 20: 10 wrong assembled components21 - 40: 8 wrong assembled components41 - 60: 7 wrong assembled components61 - 80: 5 wrong assembled components81 - 100: 6 wrong assembled components101 - 120: 9 wrong assembled components121 - 140: 7 wrong assembled components141 - 160: 5 wrong assembled components161 - 180: 2 wrong assembled components. Something wrong ???Process Control Charts – The Attribute “Count” Data
• OPERATIONAL EXCELLENCEC O N S U L T I N G57 April 16, 2013 – v3.0Number of Incidences10 2 3 4 5 6 7 8 9AverageProcess Control Charts – The Poisson Distribution
• OPERATIONAL EXCELLENCEC O N S U L T I N G58 April 16, 2013 – v3.0 The c - chart is used to look at variation in counting-typeattributes data. It is used to determine the variation in the numberof defects in a constant subgroup size. For example, a c - chart can be used to monitor the number oninjuries in a plant. In this case, the plant is the subgroup. To use the c - chart, the opportunities for incidences to occur inthe subgroup must be very large, but the number that actuallyoccur must be small.Process Control Charts – The c - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G59 April 16, 2013 – v3.0 A u - chart is used to examine the variation in counting-typeattributes data. For example, a u - chart can be used to monitor the number oninfections in a hospital during a specific time period. The u - chart is very similar to the c - chart. The only difference isthat the subgroup size for the c - chart must be constant. This isnot necessary for the subgroup size of a u - chart. To use the u - chart, the opportunities for incidences to occur in thesubgroup must be very large, but the number that actually occurmust be small.Process Control Charts – The u - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G60 April 16, 2013 – v3.0Yes/NoDefective ItemsCountIncidencesConstantSubgroup SizeVariableSubgroup Sizenp - chart c - chartu - chartp - chartProcess Control Charts – Charts for Attribute Data
• OPERATIONAL EXCELLENCEC O N S U L T I N G61 April 16, 2013 – v3.0Process Control Charts – Exercise 4Black Beads Process:Step 1: Take 15 beads out of the bag and record the number of black beads in thesample.Step 2: Repeat Step 1 20 times until you have 20 data points.Step 3: Draw the histogram of the 20 data points in the left spreadsheets below.Step 3: Select the correct process control chart and draw it in the right spreadsheet.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25HistogramProcess Control ChartDataData # of Black Beads1 42 53 24 05 36 17 58 39 610 211 412 313 114 515 316 417 218 119 020 2
• OPERATIONAL EXCELLENCEC O N S U L T I N G62 April 16, 2013 – v3.0Remarks or Questions ?!?
• OPERATIONAL EXCELLENCEC O N S U L T I N G63 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G64 April 16, 2013 – v3.0Process Control Limit – The Basic Ideaaverage average+1*s(igma)average-1*s(igma)average+2*s(igma)average-2*s(igma)average-3*s(igma)average+3*s(igma)34.13 %34.13 %13.60 % 13.60 %2.14 %2.14 %0.13 % 0.13 %If your process is under control, over 99.74% of your data points will fall between theaverage ± 3s(sigma) limits.LowerControl LimitUpperControl Limit
• OPERATIONAL EXCELLENCEC O N S U L T I N G65 April 16, 2013 – v3.0Upper Control Limit (UCL) = average + 3*sigmaLower Control Limit (LCL) = average - 3*sigma••••• •••averageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigmaProcess Control Limit – Upper & Lower Control Limit
• OPERATIONAL EXCELLENCEC O N S U L T I N G66 April 16, 2013 – v3.0Because the variation of a process is not known in before hand, onecannot calculate or define the control limits in advance.The calculation of the control limits should be based on at least 20 to25 data points from a process that was in statistical control (stable).Control limits are characteristics of a stable process. They bound thevariation of the process that is due to common causes.The limits should not be recalculated and modified unless there is areason to do so (e.g. a process change).Process Control Limit – Upper & Lower Control Limit
• OPERATIONAL EXCELLENCEC O N S U L T I N G67 April 16, 2013 – v3.0where the constant d2 depends on the number of items in eachsubgroup used to calculate the range.The LT and ST subscripts represent long-term and short-termvariability.The difference between sLT and sST gives an indication of how muchless variability you can have in your process when using SPC.)1(...22221Nxxxxxxs NLT2dRsSTSTLT ssProcess Control Limit – Two Types of Process Variability
• OPERATIONAL EXCELLENCEC O N S U L T I N G68 April 16, 2013 – v3.0Upper control limit =Lower control limit =Upper control limit =Lower control limit =The x- chartThe R- chart,where x1, x2, ..., xN are the measurements, N the number of measurements,, and .Process Control Limit – The x - ChartRxRxdRx 66.2128.133 2RxRxdRx 66.2128.133 2RRD 267.34003 RRDNxxxx N...211...32NRRRR N1iii xxR
• OPERATIONAL EXCELLENCEC O N S U L T I N G69 April 16, 2013 – v3.0Upper control limit =Lower control limit =The R- chartUpper control limit =Lower control limit =The x-bar - chartwhere x-bar1, x-bar2, ..., x-barN are the averages of each subgroup, n thenumber of items in a subgroup, N the number of subgroups,., andProcess Control Limit – The x-bar/R - ChartRAxndRx 223RAxndRx 223RD4RD3NxxxxN...21NRRRR N...21minmaxiii xxR
• OPERATIONAL EXCELLENCEC O N S U L T I N G70 April 16, 2013 – v3.0n23456A21.8801.0230.7290.5770.483D300000D43.2672.5742.2822.1142.004d21.1281.6932.0592.3262.534Factors for x- and x-bar/R - Charts
• OPERATIONAL EXCELLENCEC O N S U L T I N G71 April 16, 2013 – v3.0Upper control limit =Lower control limit =Upper control limit =Lower control limit =The s- chartThe x-bar - chart, andwhere x-bar1, x-bar2, ..., x-barN are the averages of each subgroup, s1, s2, ...,sN are the standard deviations of each subgroup, n the number of items in asubgroup, N the number of subgroups,.Process Control Limit – The x-bar/s - ChartsAx 3sAx 3sB4sB3NxxxxN...21Nssss N...21
• OPERATIONAL EXCELLENCEC O N S U L T I N G72 April 16, 2013 – v3.0n678910A31.2871.1821.0991.0320.975B30.0300.1180.1850.2390.284B41.9701.8821.8151.7611.716c40.95150.95940.96500.96930.9727Factors for x-bar/s - Charts
• OPERATIONAL EXCELLENCEC O N S U L T I N G73 April 16, 2013 – v3.0Lower control limit =Upper control limit =withandwhere np1, np2, ..., npN are the number of defective items in each subgroupof constant size n, and N the number of subgroups.13)21(npnpnpn13)21(npnpnpnnpnp np npNN1 23...n pnnpnnnpnnnpnNN( )( ) ( ) ... ( )11 1 131 2Process Control Limit – The np - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G74 April 16, 2013 – v3.0Lower control limit =Upper control limit =for i = 1, 2, 3,..., N, where (np)1, (np)2, ..., (np)N are the number of defective items inthe subgroups and n1, n2, ..., nN are the number of items in the N subgroups.Note: The sample sizes should not vary more than 25% around the average samplesize when using control limits for the whole chart.nppnp 13)21(,)...( 21Nnnnn Nwith and,..)(...)()(2121NNnnnnpnpnpp ,3pni3)1( pninppnp 1321nppnp 1321ororControl limitsfor whole processControl limitsfor each subgroupProcess Control Limit – The p - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G75 April 16, 2013 – v3.0Lower control limit =Upper control limit =withwhere c1, c2, ..., cN are the number of defects in each subgroup of constantsize and N the number of subgroups.Process Control Limit – The c - Chartcc 30,3max cc2...21Ncccc N
• OPERATIONAL EXCELLENCEC O N S U L T I N G76 April 16, 2013 – v3.0u u n3Lower control limit =Upper control limit =with anduc c cn n nNN1 21 2....., nn n nNN( ... )1 2where c1, c2, ..., cN are the number of defects in the subgroups and n1, n2, ...,nN are the number of items in each of the N subgroups.Note: The sample sizes should not vary more than 25% around the averagesample size.0,3max nuucc c cNN1 22...Process Control Limit – The u - Chart
• OPERATIONAL EXCELLENCEC O N S U L T I N G77 April 16, 2013 – v3.0Process Control Charts – Exercise 5Task #1: Calculate the average and the upper and lower control limit for exercise #2 and create a ProcessControl Chart.Task #2: Calculate the average and the upper and lower control limit for exercise #4 and create a ProcessControl Chart.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 251 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 251 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
• OPERATIONAL EXCELLENCEC O N S U L T I N G78 April 16, 2013 – v3.0Process Control Charts – Exercise 5 ResultsTask #1Subgroup Range1 59 66 63 62 72 60 66 69 65 93 65 62 71 72 104 68 65 67 69 45 65 66 70 68 56 64 64 73 73 97 63 67 71 68 88 63 68 65 68 5Average Range 7.1Overall Average: 66.4Short-Term Standard Deviation: 3.46Lower Control Limit (LCL): 61.2Upper Control Limit (UCL): 71.6Lower Control Limit (LCL): 0Upper Control Limit (UCL): 16.3Measurementsx-bar Chartx-bar / R ChartR ChartTask #2 c - ChartData # of Black Beads1 4 Overall Average: 2.82 53 2 Lower Control Limit (LCL): 0.04 0 Upper Control Limit (UCL): 7.85 36 17 58 39 610 211 412 313 114 515 316 417 218 119 020 2
• OPERATIONAL EXCELLENCEC O N S U L T I N G79 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G80 April 16, 2013 – v3.0Upper Specification Limit (USL)large variation problem existroot cause analysisprocess improvementtrend problem occursroot cause analysiscorrective actionDefectnominal valueOut-of-Control & Process ImprovementLower Specification Limit (LSL)Defectnominal valueUpper Specification Limit (USL)Lower Specification Limit (LSL)
• OPERATIONAL EXCELLENCEC O N S U L T I N G81 April 16, 2013 – v3.050 55 = USLLSL= 45SampleProcess Tempering & OvercontrolLSL USL50 5545Sample LSL USL50 5545LSL USL50 5545LSL USL
• OPERATIONAL EXCELLENCEC O N S U L T I N G82 April 16, 2013 – v3.050 5545LSL USLProcess tampering may substantially increase the product variabilitysince the process average is shifted each time an adjustment is made.Process Tempering & OvercontrolOriginal ProcessTempered Process
• OPERATIONAL EXCELLENCEC O N S U L T I N G83 April 16, 2013 – v3.0Common Causes: Causes that are implemented in the process dueto the design of the process, and affect all outcomes of the process.Identifying these types of causes requires Design of Experiment(DOE) methods.Special Causes: Causes that are not present in the process all thetime and do not affect all outcomes, but arise because of specificcircumstances. Special causes can be identified using SPC.Walter A. Shewhart (1931)Out-of-Control Criteria – Two Causes of Variation
• OPERATIONAL EXCELLENCEC O N S U L T I N G84 April 16, 2013 – v3.0Unstable Process: A process in which variation is a result of bothcommon and special causes.Stable Process: A process in which variation in outcomes arisesonly from common causes.Out-of-Control Criteria – Two Types of Processes
• OPERATIONAL EXCELLENCEC O N S U L T I N G85 April 16, 2013 – v3.0An out-of-control criteria is a signal of a special causes ofvariation:• Is a systematic pattern of the product or processcharacteristic monitored and charted• Has a low probability of occurring when the process isstable and in controlSPC Out-of-Control Criteria – The Types of Signals
• OPERATIONAL EXCELLENCEC O N S U L T I N G86 April 16, 2013 – v3.0What is the “chance”to loose the coin flip11 times in a row?1 =2 =………11 =What is the “chance”to loose the coin flip11 times in a row?1 = 50% or 0.502 =………11 =What is the “chance”to loose the coin flip11 times in a row?1 = 50% or 0.502 = 25% or 0.50*0.50………11 =What is the “chance”to loose the coin flip11 times in a row?1 = 50% or 0.502 = 25% or 0.50*0.50………11 = 0.049% or 0.5011
• OPERATIONAL EXCELLENCEC O N S U L T I N G87 April 16, 2013 – v3.0•••••• ••P = 0.0013 (0.13 %)SPC Criteria #1 – 1 Point above or below 3 Sigmaaverageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G88 April 16, 2013 – v3.0averageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma••••••P = 0.0013 (0.13 %)•••••SPC Criteria #2 – 2 of 3 Points above or below 2 Sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G89 April 16, 2013 – v3.0•••• ••••••SPC Criteria #3 – 4 of 5 Points above or below 1 Sigmaaverageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G90 April 16, 2013 – v3.0•••••••••SPC Criteria #4 – 8 Points on the same Side of the Averageaverageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G91 April 16, 2013 – v3.0averageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma•• •••••SPC Criteria #5 – Trend of 7 Points
• OPERATIONAL EXCELLENCEC O N S U L T I N G92 April 16, 2013 – v3.0••••••••••• ••• •SPC Criteria #6 – 15 consecutive Points in the 1 Sigma Zoneaverageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G93 April 16, 2013 – v3.0averageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma*) The number of runs (crossing the average line) should be about one-halfof the number of points on the control chart.••• ••••••••• ••SPC Criteria #7 – Too few or too many Runs *)
• OPERATIONAL EXCELLENCEC O N S U L T I N G94 April 16, 2013 – v3.0••••••••SPC Criteria #8 – 8 Consecutive Points with none in the 1 Sigma Zoneaverageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G95 April 16, 2013 – v3.0••••••••• ••SPC Criteria #9 – Seasonal Variation Patternsaverageaverage + 3*sigmaaverage + 2*sigmaaverage + 1*sigmaaverage - 1*sigmaaverage - 3*sigmaaverage - 2*sigma
• OPERATIONAL EXCELLENCEC O N S U L T I N G96 April 16, 2013 – v3.0x x / R x / s cunp pCriteria 1Criteria 2Criteria 3Criteria 4Criteria 5Criteria 6Criteria 7Criteria 8Criteria 9•••••••••••••••••••••••••••••••••••••••••••••Chart--SPC Out-of-Control Criteria – Summary
• OPERATIONAL EXCELLENCEC O N S U L T I N G97 April 16, 2013 – v3.0SPC Out-of-Control Criteria – Exercise 6Efficiency Out-of-Control Conditions:Determine why the process control chart below indicates that the efficiency of production line H300 is out-of-control.1 0 . 0 4CHA RNo kiaFr a n k5 - 2o fAVERAGES. 0. 0. 0. 0. 0. 02112AA*AL CUCRANGES01 02 03 04 05 06 07 0L CUCRB95.01.2095.01.2195.01.2395.01.2495.01.2595.01.2695.01.2795.01.2895.01.3095.01.3195.02.0195.02.0295.02.0395.02.0495.02.0695.02.0795.02.0895.02.0995.02.1095.02.1195.02.1395.02.2095.02.2195.02.22INDIVIDUALS6 . 00 6 . 0G r o uA u t oCL OCu r vK - S :A V ERPRO CUCLL CL :r e e n tNotes:
• OPERATIONAL EXCELLENCEC O N S U L T I N G98 April 16, 2013 – v3.0Remarks or Questions ?!?
• OPERATIONAL EXCELLENCEC O N S U L T I N G99 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G100 April 16, 2013 – v3.0 Applying the Central Limit Theorem to make the average of thesubgroups normally distributed. Dividing the sources of variation in the process outcomes intotwo different subgroups (short-term and long-term variation). Optimizing the probability of identifying a shift in the processaverage with the next observation.Sample Size and Frequency – Rational Subgrouping
• OPERATIONAL EXCELLENCEC O N S U L T I N G101 April 16, 2013 – v3.0avgSample Size and Frequency – Subgroup Size and SensitivityUSLavg + STs3UCLLCLavg - STs3 avg + EEDefects
• OPERATIONAL EXCELLENCEC O N S U L T I N G102 April 16, 2013 – v3.0If a shift in the process average of “E” units will harm the customer orone of the next process stages, the necessary subgroup sample size(n) can be calculated as:2)28.4( Esn STThe next plotted point will with 90% confidence identify a process shiftlarger than “E” units, that means the next point will be above or below 3sigma control limits.Sample Size and Frequency – Subgroup Size and Precision
• OPERATIONAL EXCELLENCEC O N S U L T I N G103 April 16, 2013 – v3.0 The frequency of sampling of two consecutive subgroups can bedetermined by dividing the average time period between two out-of-control situations by at least 3 but not more than 6.Example: If experience shows that your process produces defectsor goes out-of-control once every 12-hour shift, the you shouldcollect measurements from your process every 2 to 4 hours. However, no general rule can be defined about which time intervalworks best. You have to start with a good (conservative) guessand refine the time interval if necessary.Sample Size and Frequency – Sample Frequency
• OPERATIONAL EXCELLENCEC O N S U L T I N G104 April 16, 2013 – v3.0Remarks or Questions ?!?
• OPERATIONAL EXCELLENCEC O N S U L T I N G105 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G106 April 16, 2013 – v3.0Activators (out-of-control decision rules)Checkpoints (list of possible assignable causes)Terminators (corrective actions)Out-of-Control-Action-Plans (OCAP)An OCAP is a flowchart that guides the operator through a definedand repeatable response to “any” out-of-control situation.
• OPERATIONAL EXCELLENCEC O N S U L T I N G107 April 16, 2013 – v3.0StartCheckpointsActivatorsCorrective ActionsNoNoNoYesYesYesYesYesYesEndNoNoOut-of-Control-Action-Plans (OCAP)
• OPERATIONAL EXCELLENCEC O N S U L T I N G108 April 16, 2013 – v3.01. One point outside the 3-sigma control limits.2. A run of at least seven or eight consecutive points, where the type ofrun could be either a run up or down, a run above or below thecenter line.3. Two out of three consecutive points plot beyond from the 2-sigmawarning level.4. Four out of five consecutive points at a distance of 1-sigma orbeyond.5. One or more consecutive points near a 2-sigma warning or 3-sigmacontrol level.6. …Out-of-Control-Action-Plans – Activators
• OPERATIONAL EXCELLENCEC O N S U L T I N G109 April 16, 2013 – v3.0The checkpoints instruct the operator to investigate specific items aspossible assignable causes for the out-of-control situation.Once a checkpoint has identified a probable assignable cause for theout-of-control situation, the OCAP will flow into a terminator orcorrective action.Out-of-Control-Action-Plans – Checkpoints
• OPERATIONAL EXCELLENCEC O N S U L T I N G110 April 16, 2013 – v3.0The terminator contains a detailed description of the corrective actionthat the operator has to take to resolve the out-of-control situation.Out-of-Control-Action-Plans – Terminators
• OPERATIONAL EXCELLENCEC O N S U L T I N G111 April 16, 2013 – v3.0... typically generate one or more of the following actions: Eliminate the most common assignable causes Analyze the activators Revise the order of the checkpoints and terminators Train the operators to perform more of the corrective actions includedinto the OCAP to resolve out-of-control situations quicklyAn Analysis of Out-of-Control-Action-Plans ...
• OPERATIONAL EXCELLENCEC O N S U L T I N G112 April 16, 2013 – v3.0 The OCAP is a systematic and ideal problem-solving tool forprocess problems because it reacts to out-of-control situations inreal time. OCAPs standardize the best problem-solving approaches from themost skilled and successful problem solvers (experts/operators). The OCAP also allows (and requires) off-line analysis of theterminators to continually improve OCAP efficiency.Some Benefits of Out-of-Control-Action-Plans ...
• OPERATIONAL EXCELLENCEC O N S U L T I N G113 April 16, 2013 – v3.0Remarks or Questions ?!?
• OPERATIONAL EXCELLENCEC O N S U L T I N G114 April 16, 2013 – v3.0Section 1: IntroductionSection 2: The HistogramSection 3: Measure of Location and VariabilitySection 4: Process Control ChartsSection 5: Process Control LimitsSection 6: Out-of-Control CriteriaSection 7: Sample Size and FrequencySection 8: Out-of-Control Action PlanStatistical Process Control – Table of Contents
• OPERATIONAL EXCELLENCEC O N S U L T I N G115 April 16, 2013 – v3.0 People are trained without regard for the need to know orimplementation timing. Once the necessary charts are created, they are rarely reviewed. Charts have characteristics or parameters that do not reallyrepresent the process. Control limits are not reviewed or adjusted, or conversely, theyare adjusted too often. Someone other than the process operator maintains the chart.(This is not always bad, however) The process is not capable or set up well off target. Corrective actions and significant events are not recorded on thechart.When SPC fails, look in the mirror ...
• OPERATIONAL EXCELLENCEC O N S U L T I N G116 April 16, 2013 – v3.0The End …“perfection is not attainable, but if wechase perfection we can catchexcellence.” - VinceLombardi