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Six Sigma Basics

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  • Greek letter, used for denoting process variationWhat is sigma

  • Specification is necessary to know what is satisfactory.2.30 0.05 mm Meals in hotel room to be served within 30 minutes of orderingSpecification

  • DefectA failure to meet customer/performance standardA leaky gear boxA horn failureA lost reservation at hotelA statement errorA dimension outside the specification limitDinner served beyond the prescribed time limit

  • Any unit which has one or more defects is defectiveDefective

  • Data table

    Sheet1

    2.302.282.302.322.312.322.272.302.312.29

    2.292.282.282.292.292.272.292.302.302.30

    2.302.302.322.302.302.292.322.312.332.29

    2.322.282.312.312.322.302.292.312.302.31

    2.282.292.282.302.302.302.302.332.282.29

    2.272.322.282.292.312.312.312.312.282.29

    2.312.302.292.302.302.312.302.292.322.31

    2.302.312.312.292.292.312.292.282.312.31

    2.332.322.322.302.302.312.302.292.282.31

    2.312.312.302.292.312.302.292.292.292.29

    Sheet2

    Sheet3

  • Pattern of population

    Chart1

    1

    2

    9

    16

    21

    16

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    9

    7

    1

    Frequency

    Sheet1

    2.302.282.302.322.312.322.272.302.312.29

    2.292.282.282.292.292.272.292.302.302.30

    2.302.302.322.302.302.292.322.312.332.29

    2.322.282.312.312.322.302.292.312.302.31

    2.282.292.282.302.302.302.302.332.282.29

    2.272.322.282.292.312.312.312.312.282.29

    2.312.302.292.302.302.312.302.292.322.31

    2.302.312.312.292.292.312.292.282.312.31

    2.332.322.322.302.302.312.302.292.282.31

    2.312.312.302.292.312.302.292.292.292.29

    min2.27

    max2.33

    range0.06

    tbw0.0074298532

    bin

    2.257BinFrequency

    2.264

    2.2712.2640

    2.2782.2712.2671

    2.2852.2782.2742

    2.2922.2852.2819

    2.2992.2922.28816

    2.3062.2992.29521

    2.3132.3062.30216

    2.3202.3132.30914

    2.3272.3202.3169

    2.3272.3237

    2.3342.3301

    Sheet1

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  • Curve spreads from - to +

    100% population lies between - to +Characteristics of normal pattern

    Chart1

    0.000514093

    0.0014772828

    0.003798662

    0.0087406297

    0.0179969888

    0.0331590463

    0.0546700249

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    0.000002482

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    0.0000000885

    0.0000000142

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    400.000514093

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    420.003798662

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  • Measurement of locationMean ()

    Measurement of spreadStandard deviation ()Measurements of location and variation

  • Point to noteSince curve extends to - and + some of the units will have dimensions outside the specification limits

    Chart1

    0.000514093

    0.0014772828

    0.003798662

    0.0087406297

    0.0179969888

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    0.1329807601

    0.1257944092

    0.1064826685

    0.0806569082

    0.0546700249

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    0.0179969888

    0.0087406297

    0.003798662

    0.0014772828

    0.000514093

    0.0001600902

    0.0000446101

    0.0000111236

    0.000002482

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    0.0000000885

    0.0000000142

    0.000000002

    0.0000000003

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    Sheet1

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  • Measuring quality characteristics in terms of distance from target? = 3

  • It is the distance from the target to the upper or lower specification limits (half the tolerance), measured in terms of standard deviation, , the inherent variation of process.Sigma level of quality

  • Target LSLUSLkkA k process

  • USLkTarget A k process for one side specification limit

  • % with in specification = 68.27

    DPMO without shift = 3,17,310One Sigma process ( = 2)

  • % with in specification = 95.45

    DPMO without shift = 45,500A two Sigma process ( = 1)

  • 16171819202128232425262722% with in specification = 99.73

    DPMO without shift = 2,700Three Sigma process (s = 0.667)

  • 16171819202128232425262722LSLUSL% with in specification = 99.9937

    DPMO without shift = 634s4sFour Sigma process ( = 0.5)

  • % with in specification = 99.999943

    DPMO without shift = 0.5216171819202128232425262722Five Sigma process (s = 0.4)

  • % with in specification = 99.9999998

    DPMO without shift = 0.00216171819202128232425262722LSLUSLSix Sigma process ( = 0.333)

  • Sigma processes at A glance

  • DPMO - Best

    Sigma levelDPMOOne 3,17,310Two 45,500Three 2,700Four 63Five 0.52Six 0.002

  • Keeping a process at the target, all the time, is impossible.

    A process shift of 1.5 was observed at Motorola.

    Now widely agreeable.A practical situation

  • LSLUSL1.516171819202128232425262722Allowable shift of 1.5

  • DPMO With shift

    Sigma levelDPMO (with shift)1 697700 2 3087003 668104 62105 2336 3.4

  • Comparison Best VS Worst Possible

    Sigma levelDPMO (without shift)DPMO(with shift)13,17,3106,97,7002 45,5003,08,7003 2,700 66,8104 63 6,2105 0.52 2336 0.002 3.4

  • What is Six Sigma?Six Sigma refers itself to a statistically derived performance target of operating with only 3.4 defects for every million activities or opportunities.

  • Basic Philosophy of Quality Whatever measured must be recorded Records must be analyzed using statistical techniques. Information obtained must be acted upon.

  • An item being processed or the final product or service being delivered to customer.A dimensionA carA house loanA room service for serving dinnerA bank statementUnit

  • Defects per Unit, DPU

  • YieldYield, Y is the measure that tells us the probability that the process would have Zero Failure or will not have any nonconformity.Y is the probability of getting a unit right first time

  • Example - YieldAt station No.1, 5 defects were observed in 487 units produced. What is the yield of the process?

  • Rolled throughput yield, YRTIf focus only on the defect rate at the end, we lose sight of the rework that occurs within the process.

    Rework means having a Hidden Factory

  • Calculation - Rolled throughput yieldY1Y2Y3Yn-1Yn

  • Most products and services have multiple customer requirements and therefore there can be several chances or opportunities for a defect to appear.Defect opportunity

  • A room service can be defective on account of:Dishes coldDirty cover on food articlesDinner served lateItem served that was not orderedBland taste.There are 5 opportunities for a customer to be unhappyExample defect opportunity

  • Defects per Opportunity

  • Example - # of units = 330 - # of opportunities(type of defects)= 7 - # total number of defects= 59 Defects per Opportunity

  • Defects per Million OpportunitiesDPMO = DPO 106

  • DPMODefects per Million Opportunities

    It simply indicates how many errors would show up if there are one million of activities where defect can occur. This way it can equate a car with simple pin.Performance measures

  • Example DPMO, late coming Number of participants= 32Number of breaks= 6 per dayCourse duration = 6 daysTotal number of opportunities= 32 x 6 x 6Not coming at the agreed time (late)> 5 minutesNumber of occasions participants= 183failed to come in time (defect)

  • SL= 1.5 + normsinv(success rate) = 1.5 + normsinv(1-failure rate)Formulae for Sigma level performance

  • Example

    Situation Baggage handling at airportNumber of passengers traveled in week40, 000Average number of baggage per passenger 2Total number of baggage not arrived with flight per week160Calculate DPMO and Sigma Performance Level

  • Solution

  • SolutionSigma level = 1.5 + normsinv(1-0.002) = 4.378

  • Level of Competition

    Sigma

    DPMO

    Cost of poor quality

    (% of sales)

    Competitive level

    6

    3.4

    40

  • Times improvement

    From sigma levelTo sigma level3456255514851,02,46531129720,4934271863569

  • Improvement times

  • 3 VS 6 Supplier Performance Gap

    Event

    3-Sigma

    6-Sigma

    Wrong drug prescription

    54,000/year

    1 in 25 years

    Unsafe drinking water

    2 hours/month

    1 sec in 25 years

    Incorrect surgical operation

    1,350 / week

    1 in 20 years

    Lost article in post

    54,000 per hour

    35 in a year

  • Bill SmithSix Sigma Born 0n 15 January 1987Father of Six Sigma sigma

  • Number of repairs in factoryField FailuresDiscovery of bill smith

  • To reduce field failures, much higher level of internal quality is required.Done right, improving quality will reduce cost.Cost of correcting poor quality ranged $800-$900 million per year.Realization at Motorola

  • 100 times4 yearsDesire of Bob Galvin

  • Before manufacturing a product determine:The product characteristics that will satisfy customer.Decide whether product characteristics can be met with:Product designManufacturing processesMaterial usedSix Sigma approach at Motorola

  • Six Sigma approach at MotorolaDevelop design tolerance to satisfy customer.Have measurements to establish process variation.Hone product design and manufacturing to get desired results.

  • Six Sigma at MotorolaTodays existence due to Six SigmaInvented for survivalMethod for tracking companys performance vis a vis customer requirementImprovement 10X in two years or 100X in four years

  • Five fold growth in salesAnnual increase of profit 20%Cumulative saving $14 BillionAnnual stock price gain 21.3 %Results of Six Sigma at Motorola

  • Launched Six Sigma in 1995Profit by 1998$750 MillionProfit by 1999$ 1.5 BillionCutting invoice defect by 98%Streamlining of contract review - $1 Million/yearGE Medical body scan time 3 minutes to 1 minuteGE Mortgage Call reaching person 76% to 99%Bottom Line Improvement at GE

  • The best Six Sigma project begin not inside the business but outside it.Focused on answering the question how can we make customer competitive?Knowing what is critical to customer and providing it.Explanation of Jack Welch

  • One thing we discovered with certainty is that anything we do that makes the customer more successful, inevitably results in financial return to us.Jack Welchs Important Discovery

  • Savings of $600 million per yearReduction in time from drawing to certification of aircraft engines from 42 months to 33 months.Increase in productivity by 6 %Increase in market share 27% annually Results at Allied Signals

  • Redefine Six Sigma

  • Six Sigma provides companies with a series of interventions and statistical tools that can lead to breakthrough profitability and quantum gains in quality, whether the product of a company are durable goods or services.Six Sigma

  • Six SigmaThe Six Sigma strategy involves the use of statistical tools within structured methodology for gaining the knowledge to achieve better, faster, and lower-cost products and services.

  • Another Way of Defining Six SigmaSix Sigma is a sweeping Cultural Change effort to position a company for greater customer satisfaction, profitability, and competitiveness.

  • More than just numbers it is a statement of our determination to pursue a standard of excellence using every tool at our disposal and never hesitating to reengineer the things we do.Six Sigma at Allied Signals

  • Six sigma is driven by close understanding of the needs of customer, disciplined use of factual data, and statistical analysis while paying diligent attention to managing, improving, and reinventing business processes.Driving Force Behind Six Sigma

  • Six Sigma is a business initiative, rather than quality initiativeHow Six Sigma is Different?

  • With traditional approachQuite often Quality ImprovedyetBottom line did not

  • Provide quality in such a way that creates economic worth for: customer employees share holders corporationall at the same timeWith Six Sigma Approach

  • Forces organisations to Re-examine how the work gets doneSimplify the system and processImprove the capability of the processFind ways to control systems and process permanently.What Six Sigma Does?

  • What Mr Welch of GE Says?Todays paperistomorrows Fish-wrap

  • P-R CriteriaABCXEffort to ImproveSupport & StimulateP-CriteriaPerformanceControl with Carrot & StickR-Criteria

  • A ProcessA product or service is outcome of a process.

  • Type of ProcessesType of process

  • A ProcessKey Process Output Variable, Y = f(X)

  • Process ManagementProcess management involves planning and administering the activities necessary to: achieve a high level of performance in a processidentify opportunities for improving quality and operational performance.

  • Process Control Model

  • Cost Mathematics Selling Price = Cost price + Profit

    Profit = Selling price - Cost price

  • Value Added & Non Value Added ActivitiesCostPriceCost ofnon value addedactivitiesCost ofvalue addedactivities=+10%90%50%50%

  • Non Value Added ActivitiesWaitingTransportationInventoriesNon conforming productNon involvement of the people

  • Goal Post StrategySuddenLossSuddenLossLSLUSLTarget

  • Interpretation of DataSuddenLossSuddenLossLSLUSLTargetA

  • Taguchis Loss FunctionUSLLSLBestCustomer Dissatisfaction

  • Loss to the Society- increase in deviation from the target- increase in the variation of the processLoss to society increases with

  • What should be Our Prime Goal?ReduceDeviation from target Variation in the process

  • Fords Case of Noisy Automatic TransmissionLSLUSL

  • New Thinking..Our new quality thinking should be to reduce variability around the nominal as operating philosophy for never ending Quality Improvement.

  • Benefits of Six Sigma #1Generates sustained success.- generally business life of a product is 3 years.- To survive we must have double digit growth.- constantly innovates and restructures the organisation.

  • Benefits of Six Sigma #2Sets performance goals for every oneuses common business frame workensures consistency for meeting customer requirements.

  • Benefits of Six Sigma #3aEnhances value to customer

    We want to make our quality so special, so valuable to customer, so important to their success that our products become their only real choice.Jack Welch

  • Benefits of Six Sigma #3bGood and defect free product does not guarantee success. The focus on customers in Six Sigma means what value means to customer and planning how to deliver them profitably.

  • Benefits of Six Sigma #4Accelerates the rate of improvement100 times improvement in four years at Motorola. it helps companies not only to improve performance, but improve the improvement

  • Benefits of Six Sigma #5Promotes Learning and Cross PollinationAccelerates development and sharing of new ideas throughout the organisation. Six Sigma is data based and therefore applicable to any functional area.

  • Benefits of Six Sigma #6Executes Strategic ChangeLaunching new venturesEntering new marketsIntroducing new product Acquiring new organisationare now routine. Six Sigma facilitates change over.

  • Proven Benefits of Six SigmaCost reductionProductivity improvementMarket-share growthCustomer retentionCycle time reductionDefect reductionCultural changeProduct / service change

  • Define Identify Customers and their prioritiesProjects that meets the business objectiveCritical to quality requirements

  • Measure Determine how to measure the process and how it is performing.

    Identify key internal processes that influences CTQs and their impact on nonconformance.

  • Analyse Determine the most likely causes of the defect.Understand impact of key variables on generation of defect.Determine key variables that cause variation

  • Improve Identify the means to remove causes of nonconformance.Confirm the key variable and quantify their effects on the CTQ requirements.Identify the maximum acceptable ranges of key variables.Modify the process to stay in acceptable range.

  • ControlDetermine how to maintain improvements.

    Ensuring key input variable remain within range.

  • What is Statistics?A science that deals with:Collection of dataSummarization of dataAnalysis of dataDrawing information from data

  • Why statistics?More economical to assess a sample and predict the properties of population from which the sample was drawn.

    Prediction can be with degree of confidence

  • Population Sample ModelBase population

  • Process Redesign DisconnectBottleneckRedundancyRework loopinspection

  • CE-Diagram for Defective Items

  • Pareto Analysis For Prioritization

    Chart2

    6868

    45113

    30143

    10153

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    5173

    3176

    Events

    Frequency

    Sheet1

    SNEventFREQUENCYCUM Freq

    1A6868

    2B45113

    3C30143

    4D10153

    5E8161

    6F7168

    7G5173

    8H3176

    Sheet1

    Events

    Frequency

    Sheet2

    Sheet3

  • Histogram

    Chart2

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    Frequency

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    Frequency

    Sheet1 (3)

    79.176.280.783.883.685.273.479.383.376.7

    77.974.974.577.177.773.678.378.880.478.9

    79.078.984.079.779.478.585.982.687.178.0

    85.075.281.682.785.879.778.482.078.982.3

    75.777.575.478.979.980.179.086.674.877.8

    72.384.376.278.082.381.482.681.875.976.7

    82.181.077.279.380.481.780.477.385.781.5

    80.282.582.678.177.283.376.475.382.181.9

    N80BinBinFrequency

    Minimum72.371.471.40.0

    Maximum87.173.173.11.0

    Range14.974.874.83

    No. of cells8.976.476.40

    Bin width1.778.178.18

    79.779.712

    81.481.46

    83.183.10

    84.784.74

    86.486.40

    88.188.13

    89.70

    91.42

    93.0

    94.71

    Sheet1 (3)

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    Sheet1 (2)

    79.176.280.783.883.685.273.479.383.376.7

    77.974.974.577.177.773.678.378.880.478.9

    79.078.984.079.779.478.585.982.687.178.0

    85.075.281.682.785.879.778.482.078.982.3

    75.777.575.478.979.980.179.086.674.877.8

    72.384.376.278.082.381.482.681.875.976.7

    82.181.077.279.380.481.780.477.385.781.5

    80.282.582.678.177.283.376.475.382.181.9

    final

    79.176.280.783.883.685.273.479.383.376.7

    77.974.974.577.177.773.678.378.880.478.9

    79.078.984.079.779.478.585.982.687.178.0

    85.075.281.682.785.879.778.482.078.982.3

    75.777.575.478.979.980.179.086.674.877.8

    72.384.376.278.082.381.482.681.875.976.7

    82.181.077.279.380.481.780.477.385.781.5

    80.282.582.678.177.283.376.475.382.181.9

    N80BinBinFrequency

    Minimum72.371.470.00

    Maximum87.173.172.00

    Range14.974.874.03

    No. of cells8.976.476.08

    Bin width1.778.178.013

    79.780.020

    81.482.013

    83.184.014

    84.786.07

    86.488.02

    88.188.10

    final

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    Sheet2

    39.136.240.743.843.645.233.439.343.336.7

    37.934.934.537.137.733.638.338.840.438.9

    39.038.944.039.739.438.545.942.647.138.0

    45.035.241.642.745.839.738.442.038.942.3

    35.737.535.438.939.940.139.046.634.837.8

    Sheet3

  • Normal Probability PlotUsed for assessing:Normal distributionDistribution dealing with life of productEquality of variances of different sample

    Chart1

    7.3

    7.9

    8.5

    9.1

    9.7

    10.3

    10.9

    11.5

    12.1

    Z

    X

    Sheet4

    Sheet1

    9.708.7210.2411.2811.2011.737.829.77

    11.108.919.318.318.159.029.237.88

    9.439.6010.139.639.679.6311.349.91

    9.819.4911.9710.8712.389.3511.668.39

    10.5410.9011.929.929.4810.689.6210.76

    8.569.158.489.649.9710.039.6812.19

    8.269.267.4211.458.729.3510.7610.47

    10.8710.608.638.8810.6910.329.069.76

    7.42BinFrequency

    12.3870

    4.957.610.50.50.0078125-2.41754605677.3

    0.61915443448.2322.50.0390625-1.76167304747.9

    78.885.580.125-1.15034936248.5

    7.69.4109170.265625-0.62609842649.1

    8.2101713.530.50.4765625-0.05878291639.7

    8.810.671242.50.66406250.423576693710.3

    9.411.29850.50.78906250.803172497410.9

    1011.85757.50.89843751.272699137211.5

    10.612.444.5620.968751.862727003812.1

    11.264

    11.8

    12.4

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  • Gauge Repeatability & Reproducibility StudiesVariable Scale

  • Run chart

    Chart1

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    44.889267327448.0560551194

    50.977029230948.0560551194

    55.105894160848.0560551194

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    41.265649441648.0560551194

    49.063275026948.0560551194

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    42.612356436448.0560551194

    46.089482010648.0560551194

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    41.528275131748.0560551194

    47.728300513748.0560551194

    48.383809725148.0560551194

    50.539412212748.0560551194

    48.538028194248.0560551194

    X

    Median

    Time Sequence

    X

    Sheet1

    SNXMedian

    148.848.1

    244.948.1

    351.048.1

    455.148.1

    554.848.1

    656.948.1

    741.348.1

    849.148.1

    954.448.1

    1045.748.1

    1147.248.1

    1243.248.1

    1342.648.1

    1446.148.1

    1546.948.1

    1641.548.1

    1747.748.1

    1848.448.1

    1950.548.1

    2048.548.1

    Median48.1

    Sheet1

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    00

    00

    00

    00

    X

    Median

    Time Sequence

    X

    Runchart

    Sheet2

    Sheet3

  • Control chart

    Chart1

    49.47553.35536447.06263650.209

    50.153.35536447.06263650.209

    50.753.35536447.06263650.209

    50.02553.35536447.06263650.209

    50.453.35536447.06263650.209

    50.5553.35536447.06263650.209

    51.5553.35536447.06263650.209

    49.5553.35536447.06263650.209

    51.7553.35536447.06263650.209

    50.57553.35536447.06263650.209

    47.92553.35536447.06263650.209

    49.4553.35536447.06263650.209

    50.853.35536447.06263650.209

    50.853.35536447.06263650.209

    49.97553.35536447.06263650.209

    50.67553.35536447.06263650.209

    49.0553.35536447.06263650.209

    50.9553.35536447.06263650.209

    48.6553.35536447.06263650.209

    50.453.35536447.06263650.209

    50.97553.35536447.06263650.209

    49.12553.35536447.06263650.209

    49.653.35536447.06263650.209

    49.853.35536447.06263650.209

    52.37553.35536447.06263650.209

    Subgroup No.

    Mean

    Sheet3

    Sheet1

    SNx1x2x3x4x5

    14.465.084.915.175.04

    25.155.204.745.075.13

    34.824.834.645.005.37

    45.365.114.885.034.85

    55.015.184.835.094.47

    64.765.174.984.995.00

    74.975.204.964.505.05

    85.305.075.015.045.13

    95.274.905.135.145.13

    105.064.894.934.875.01

    114.714.825.185.174.75

    125.245.215.085.204.95

    135.045.175.094.535.01

    145.065.065.295.004.81

    154.835.355.105.224.97

    165.085.124.844.715.13

    174.744.805.205.105.25

    185.135.454.594.985.12

    194.945.055.145.135.04

    205.354.935.064.955.54

    Sheet2

    SNX1X2X3X4MeanRangeUCLmLCLmCLmUCLrLCLrCLr

    144.651.548.253.649.59.053.447.150.29.84911204.3

    250.147.649.753.050.15.453.447.150.29.84911204.3

    352.750.647.152.450.75.653.447.150.29.84911204.3

    450.450.648.350.850.02.553.447.150.29.84911204.3

    547.451.349.453.550.46.153.447.150.29.84911204.3

    650.852.048.351.150.63.753.447.150.29.84911204.3

    751.851.752.050.751.61.353.447.150.29.84911204.3

    849.048.948.252.149.63.953.447.150.29.84911204.3

    951.750.653.551.251.82.953.447.150.29.84911204.3

    1048.054.550.549.350.66.553.447.150.29.84911204.3

    1149.147.446.448.847.92.753.447.150.29.84911204.3

    1248.349.849.650.149.51.853.447.150.29.84911204.3

    1351.349.351.850.850.82.553.447.150.29.84911204.3

    1450.952.951.048.450.84.553.447.150.29.84911204.3

    1552.045.951.450.650.06.153.447.150.29.84911204.3

    1651.750.750.050.350.71.753.447.150.29.84911204.3

    1750.949.945.050.449.15.953.447.150.29.84911204.3

    1851.448.751.752.051.03.353.447.150.29.84911204.3

    1945.350.052.247.148.76.953.447.150.29.84911204.3

    2051.049.851.349.550.41.853.447.150.29.84911204.3

    2150.451.353.748.551.05.253.447.150.29.84911204.3

    2244.750.050.551.349.16.653.447.150.29.84911204.3

    2351.350.147.549.549.63.853.447.150.29.84911204.3

    2450.148.149.751.349.83.253.447.150.29.84911204.3

    2552.551.250.455.452.45.053.447.150.29.84911204.3

    50.24.3

    =$F$27+0.729*$G$27

    =$F$27-0.729*$G$27

    =$F$27

    =2.282*$G$27

    =0*$G$27

    =$G$27

    Sheet2

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    Subgroup No.

    Mean

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    Subgroup No.

    Range

    Chart2

    99.84911204.316

    5.49.84911204.316

    5.69.84911204.316

    2.59.84911204.316

    6.19.84911204.316

    3.79.84911204.316

    1.39.84911204.316

    3.99.84911204.316

    2.99.84911204.316

    6.59.84911204.316

    2.79.84911204.316

    1.89.84911204.316

    2.59.84911204.316

    4.59.84911204.316

    6.19.84911204.316

    1.79.84911204.316

    5.99.84911204.316

    3.39.84911204.316

    6.99.84911204.316

    1.89.84911204.316

    5.29.84911204.316

    6.69.84911204.316

    3.89.84911204.316

    3.29.84911204.316

    59.84911204.316

    Subgroup No.

    Range

    Sheet3

    Sheet1

    SNx1x2x3x4x5

    14.465.084.915.175.04

    25.155.204.745.075.13

    34.824.834.645.005.37

    45.365.114.885.034.85

    55.015.184.835.094.47

    64.765.174.984.995.00

    74.975.204.964.505.05

    85.305.075.015.045.13

    95.274.905.135.145.13

    105.064.894.934.875.01

    114.714.825.185.174.75

    125.245.215.085.204.95

    135.045.175.094.535.01

    145.065.065.295.004.81

    154.835.355.105.224.97

    165.085.124.844.715.13

    174.744.805.205.105.25

    185.135.454.594.985.12

    194.945.055.145.135.04

    205.354.935.064.955.54

    Sheet2

    SNX1X2X3X4MeanRangeUCLmLCLmCLmUCLrLCLrCLr

    144.651.548.253.649.59.053.447.150.29.84911204.3

    250.147.649.753.050.15.453.447.150.29.84911204.3

    352.750.647.152.450.75.653.447.150.29.84911204.3

    450.450.648.350.850.02.553.447.150.29.84911204.3

    547.451.349.453.550.46.153.447.150.29.84911204.3

    650.852.048.351.150.63.753.447.150.29.84911204.3

    751.851.752.050.751.61.353.447.150.29.84911204.3

    849.048.948.252.149.63.953.447.150.29.84911204.3

    951.750.653.551.251.82.953.447.150.29.84911204.3

    1048.054.550.549.350.66.553.447.150.29.84911204.3

    1149.147.446.448.847.92.753.447.150.29.84911204.3

    1248.349.849.650.149.51.853.447.150.29.84911204.3

    1351.349.351.850.850.82.553.447.150.29.84911204.3

    1450.952.951.048.450.84.553.447.150.29.84911204.3

    1552.045.951.450.650.06.153.447.150.29.84911204.3

    1651.750.750.050.350.71.753.447.150.29.84911204.3

    1750.949.945.050.449.15.953.447.150.29.84911204.3

    1851.448.751.752.051.03.353.447.150.29.84911204.3

    1945.350.052.247.148.76.953.447.150.29.84911204.3

    2051.049.851.349.550.41.853.447.150.29.84911204.3

    2150.451.353.748.551.05.253.447.150.29.84911204.3

    2244.750.050.551.349.16.653.447.150.29.84911204.3

    2351.350.147.549.549.63.853.447.150.29.84911204.3

    2450.148.149.751.349.83.253.447.150.29.84911204.3

    2552.551.250.455.452.45.053.447.150.29.84911204.3

    50.24.3

    =$F$27+0.729*$G$27

    =$F$27-0.729*$G$27

    =$F$27

    =2.282*$G$27

    =0*$G$27

    =$G$27

    Sheet2

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    Subgroup No.

    Mean

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    Subgroup No.

    Range

  • Process capability studies

    Chart1

    40

    41

    0.001014524

    0.0045467813

    0.0158698259

    0.0431386594

    0.0913245427

    0.1505687161

    0.1933340584

    0.1933340584

    0.1505687161

    0.0913245427

    0.0431386594

    0.0158698259

    0.0045467813

    0.001014524

    0.0001762978

    57

    58

    59

    60

    LSL

    USL

    Mean

    T

    Sheet2

    40

    41

    420.001014524

    430.0045467813

    440.0158698259

    450.0431386594

    460.0913245427

    470.1505687161

    480.1933340584

    490.1933340584

    500.1505687161

    510.0913245427

    520.0431386594

    530.0158698259

    540.0045467813

    550.001014524

    560.0001762978

    57

    58

    59

    60

    Sheet2

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    LSL

    USL

    Mean

    T

    original

    SNX1X2X3X4X5MeanUCLmLCLmCLmRangeUCLrCLr

    123.421.424.526.626.4

    227.519.623.526.221.8

    322.620.620.322.022.5

    419.822.923.224.323.3

    523.323.326.723.823.6

    623.027.925.728.822.7

    727.320.825.125.827.8

    823.823.025.423.225.5

    921.122.321.023.323.9

    1024.123.428.420.522.5

    1118.826.921.422.725.5

    1224.925.725.221.321.8

    1325.424.622.123.524.3

    1425.124.322.227.825.0

    1524.125.725.722.722.2

    1626.221.620.925.425.3

    1728.426.926.624.224.0

    1824.923.921.920.525.7

    1924.925.224.421.926.5

    2023.422.322.423.123.1

    Grand meanMean Range

    normal probability plot

    SNXPiZ

    118.80.005-2.5758345146

    219.60.015-2.1700907382

    319.80.025-1.9599610823

    420.30.035-1.8119135348

    520.50.045-1.6953981685

    620.50.055-1.5981913748

    720.60.065-1.5141040421

    820.80.075-1.4395300241

    920.90.085-1.3722046788

    1021.00.095-1.3105795915

    1121.10.105-1.2535656424

    1221.30.115-1.2003602023

    1321.40.125-1.1503493624

    1421.40.135-1.1030624592

    1521.60.145-1.0581220522

    1621.80.155-1.0152211871

    1721.80.165-0.9741143003

    1821.90.175-0.9345899343

    1921.90.185-0.8964730114

    2022.00.195-0.8596180123

    2122.10.205-0.8238930604

    2222.20.215-0.7891912901

    2322.20.225-0.7554149306

    2422.30.235-0.7224787169

    2522.30.245-0.6903087524

    2622.40.255-0.658837962

    2722.50.265-0.6280060916

    2822.50.275-0.5977608453

    2922.60.285-0.5680522008

    3022.70.295-0.5388358204

    3122.70.305-0.5100741873

    3222.70.315-0.4817275112

    3322.90.325-0.4537628229

    3423.00.335-0.42614829

    3523.00.345-0.3988554909

    3623.10.355-0.3718560038

    3723.10.365-0.3451259545

    3823.20.375-0.318639195

    3923.20.385-0.2923752618

    4023.30.395-0.2663114174

    4123.30.405-0.2404260613

    4223.30.415-0.2147021405

    4323.30.425-0.1891180545

    4423.40.435-0.1636590241

    4523.40.445-0.1383045856

    4623.40.455-0.1130388227

    4723.50.465-0.0878446826

    4823.50.475-0.0627062491

    4923.60.485-0.0376076059

    5023.80.495-0.012532837

    5123.80.5050.012532837

    5223.90.5150.0376076059

    5323.90.5250.0627062491

    5424.00.5350.0878446826

    5524.10.5450.1130388227

    5624.10.5550.1383045856

    5724.20.5650.1636590241

    5824.30.5750.1891180545

    5924.30.5850.2147021405

    6024.30.5950.2404260613

    6124.40.6050.2663114174

    6224.50.6150.2923752618

    6324.60.6250.318639195

    6424.90.6350.3451259545

    6524.90.6450.3718560038

    6624.90.6550.3988554909

    6725.00.6650.42614829

    6825.10.6750.4537628229

    6925.10.6850.4817275112

    7025.20.6950.5100741873

    7125.20.7050.5388358204

    7225.30.7150.5680522008

    7325.40.7250.5977608453

    7425.40.7350.6280060916

    7525.40.7450.658837962

    7625.50.7550.6903087524

    7725.50.7650.7224787169

    7825.70.7750.7554149306

    7925.70.7850.7891912901

    8025.70.7950.8238930604

    8125.70.8050.8596180123

    8225.70.8150.8964730114

    8325.80.8250.9345899343

    8426.20.8350.9741143003

    8526.20.8451.0152211871

    8626.40.8551.0581220522

    8726.50.8651.1030624592

    8826.60.8751.1503493624

    8926.60.8851.2003602023

    9026.70.8951.2535656424

    9126.90.9051.3105795915

    9226.90.9151.3722046788

    9327.30.9251.4395300241

    9427.50.9351.5141040421

    9527.80.9451.5981913748

    9627.80.9551.6953981685

    9727.90.9651.8119135348

    9828.40.9751.9599610823

    9928.40.9852.1700907382

    10028.80.9952.5758345146

    EXERCISE

    SNX1X2X3X4X-barRangeUCLmLCLmCLmUCLrCLr

    147.045.247.949.8

    249.750.643.647.1

    349.545.546.344.5

    444.245.746.143.7

    546.546.847.746.8

    646.946.849.947.3

    747.246.651.049.1

    851.846.350.544.6

    948.549.151.047.3

    1046.648.746.848.9

    1144.946.044.846.8

    1247.447.646.951.5

    1344.446.242.950.1

    1445.246.348.948.3

    1549.148.645.045.5

    1648.748.145.847.1

    1747.748.547.745.9

    1850.948.447.649.0

    1949.146.445.849.5

    2045.344.748.848.6

    2151.550.149.847.7

    2247.548.347.545.6

    2344.349.048.348.6

    2447.945.749.746.9

    2546.046.046.746.7

    Sheet1

    SNX1X2X3X4

    12.872.952.902.98

    22.972.912.942.92

    32.902.972.993.01

    43.012.982.962.99

    52.952.942.972.91

    62.932.972.952.97

    72.953.022.912.97

    82.912.942.883.01

    92.962.962.972.88

    102.982.952.953.00

    112.932.982.872.92

    122.942.892.922.95

    132.932.932.982.94

    142.982.962.912.97

    152.922.932.893.00

    162.922.942.942.95

    172.932.932.942.93

    182.932.953.002.94

    192.942.972.952.93

    202.942.923.062.99

    212.942.992.972.97

    222.972.932.942.91

    232.973.072.952.96

    242.962.992.922.95

    252.972.932.962.97

    Sheet3

    SNx1x2x3x4x5AvgRangeUCLaLCLaClaUCLrLCLrCLr

    119.90019.97519.96219.97519.94819.9520.07620.013810449919.936822673719.9750.141033066800.067

    219.96919.99020.00020.02119.95919.9880.06220.013810449919.936822673719.9750.141033066800.067

    319.93520.01720.02319.99019.98419.9900.08920.013810449919.936822673719.9750.141033066800.067

    419.99719.99920.01219.97919.97219.9920.04020.013810449919.936822673719.9750.141033066800.067

    519.96820.00419.94419.94819.99619.9720.05920.013810449919.936822673719.9750.141033066800.067

    619.97819.94719.99120.02219.98319.9840.07520.013810449919.936822673719.9750.141033066800.067

    719.97019.94819.99219.95419.92819.9580.06320.013810449919.936822673719.9750.141033066800.067

    819.99119.96320.00820.01420.02119.9990.05820.013810449919.936822673719.9750.141033066800.067

    919.96119.94619.95719.92819.96819.9520.04020.013810449919.936822673719.9750.141033066800.067

    1019.97919.98819.94119.90219.99919.9620.09820.013810449919.936822673719.9750.141033066800.067

    1120.01919.98420.02319.94219.97419.9880.08220.013810449919.936822673719.9750.141033066800.067

    1219.96219.99019.95219.96419.97919.9690.03720.013810449919.936822673719.9750.141033066800.067

    1319.95520.03319.95519.98719.96919.9800.07920.013810449919.936822673719.9750.141033066800.067

    1420.00719.93619.97419.98719.94719.9700.07120.013810449919.936822673719.9750.141033066800.067

    1519.98919.97919.99520.01819.97419.9910.04520.013810449919.936822673719.9750.141033066800.067

    1619.92619.97519.99419.97719.98219.9710.06820.013810449919.936822673719.9750.141033066800.067

    1720.00219.96619.99719.90919.94719.9640.09320.013810449919.936822673719.9750.141033066800.067

    1820.03519.99919.97519.97319.98019.9930.06220.013810449919.936822673719.9750.141033066800.067

    1920.01619.93819.93219.95019.95419.9580.08420.013810449919.936822673719.9750.141033066800.067

    2019.95520.01019.97319.96419.95719.9720.05420.013810449919.936822673719.9750.141033066800.067

    GMR-bar

    19.9750.067

    est sig0.0286325512

    zl-2.6304523589

    ZU4.3546045682

    6.6704918906

    Sheet3

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    Sample average

    Average Control Chart

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    0000

    Range

    Range control chart

  • Scatter Diagram

  • Realistic Tolerance and Realistic SpecificationRealistic Tolerance

    Chart8

    6767.798513665.1797638

    6465.718513663.0997638

    62.163.638513661.0197638

    60.161.558513658.9397638

    58.559.478513656.8597638

    56.257.398513654.7797638

    6666.758513664.1397638

    64.265.198513662.5797638

    60.863.118513660.4997638

    59.561.038513658.4197638

    56.958.958513656.3397638

    56.556.878513654.2597638

    Air Pressure

    Wall Thickness

    Example

    Air PressureWall ThicknessUCLLCL

    10567.067.8065.18

    10964.065.7263.10

    11362.163.6461.02

    11760.161.5658.94

    12158.559.4856.86

    12556.257.4054.78

    10766.066.7664.14

    11064.265.2062.58

    11460.863.1260.50

    11859.561.0458.42

    12256.958.9656.34

    12656.556.8854.26

    Example

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    000

    Air Pressure

    Wall Thickness

    Sheet2

    Sheet3

  • Analysis of VarianceIdentifying which of the factors are responsible for variation in output Quality characteristics.One way ANOVATwo way ANOVAGRRS, DOE, Process Capability, Relationship

  • Correlation & Regression AnalysisX2X4YX3X1Y = f(X)

  • DOE

  • Cumulative Sum Graph

    Chart2

    2.575

    2.4627985995

    5.8395643943

    7.0682219377

    9.3885220974

    14.3766123704

    18.3111985505

    17.6379814773

    18.7302209495

    16.7585455755

    16.8337767035

    17.043494813

    14.2041176053

    10.2083679064

    6.858341256

    4.771751676

    3.0244513683

    2.6126246589

    3.7247380708

    4.3446488663

    6.0688408438

    7.6026653484

    Sample No.

    CUSUM

    Sheet1

    52.57522129282.57522129282.575

    49.8877985995-0.11220140052.4627985995

    53.37676579473.37676579475.8395643943

    51.22865754341.22865754347.0682219377

    52.32030015972.32030015979.3885220974

    54.9880902734.98809027314.3766123704

    53.93458618013.934586180118.3111985505

    49.3267829268-0.673217073217.6379814773

    51.09223947221.092239472218.7302209495

    48.0283246259-1.971675374116.7585455755

    50.0752311280.07523112816.8337767035

    50.20971810950.209718109517.043494813

    47.1606227923-2.839377207714.2041176053

    46.0042503012-3.995749698810.2083679064

    46.6499733495-3.35002665056.858341256

    47.91341042-2.086589584.771751676

    48.2526996923-1.74730030773.0244513683

    49.5881732907-0.41182670932.6126246589

    51.11211341191.11211341193.7247380708

    50.61991079540.61991079544.3446488663

    51.72419197751.72419197756.0688408438

    51.53382450461.53382450467.6026653484

    51.83926806841.83926806849.4419334167

    52.63323420572.633234205712.0751676224

    Sheet1

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    0

    Sample No.

    CUSUM

    Sheet2

    Sheet3