six sigma basics
DESCRIPTION
Six Sigma BasicsTRANSCRIPT
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Greek letter, used for denoting process variationWhat is sigma
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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
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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
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Any unit which has one or more defects is defectiveDefective
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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
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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
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Sheet2
Sheet3
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Pattern of population
Chart1
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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
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2.3342.3301
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Curve spreads from - to +
100% population lies between - to +Characteristics of normal pattern
Chart1
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Measurement of locationMean ()
Measurement of spreadStandard deviation ()Measurements of location and variation
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Point to noteSince curve extends to - and + some of the units will have dimensions outside the specification limits
Chart1
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Measuring quality characteristics in terms of distance from target? = 3
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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
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Target LSLUSLkkA k process
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USLkTarget A k process for one side specification limit
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% with in specification = 68.27
DPMO without shift = 3,17,310One Sigma process ( = 2)
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% with in specification = 95.45
DPMO without shift = 45,500A two Sigma process ( = 1)
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16171819202128232425262722% with in specification = 99.73
DPMO without shift = 2,700Three Sigma process (s = 0.667)
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16171819202128232425262722LSLUSL% with in specification = 99.9937
DPMO without shift = 634s4sFour Sigma process ( = 0.5)
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% with in specification = 99.999943
DPMO without shift = 0.5216171819202128232425262722Five Sigma process (s = 0.4)
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% with in specification = 99.9999998
DPMO without shift = 0.00216171819202128232425262722LSLUSLSix Sigma process ( = 0.333)
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Sigma processes at A glance
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DPMO - Best
Sigma levelDPMOOne 3,17,310Two 45,500Three 2,700Four 63Five 0.52Six 0.002
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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
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LSLUSL1.516171819202128232425262722Allowable shift of 1.5
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DPMO With shift
Sigma levelDPMO (with shift)1 697700 2 3087003 668104 62105 2336 3.4
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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
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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.
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Basic Philosophy of Quality Whatever measured must be recorded Records must be analyzed using statistical techniques. Information obtained must be acted upon.
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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
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Defects per Unit, DPU
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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
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Example - YieldAt station No.1, 5 defects were observed in 487 units produced. What is the yield of the process?
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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
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Calculation - Rolled throughput yieldY1Y2Y3Yn-1Yn
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Most products and services have multiple customer requirements and therefore there can be several chances or opportunities for a defect to appear.Defect opportunity
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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
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Defects per Opportunity
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Example - # of units = 330 - # of opportunities(type of defects)= 7 - # total number of defects= 59 Defects per Opportunity
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Defects per Million OpportunitiesDPMO = DPO 106
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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
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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)
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SL= 1.5 + normsinv(success rate) = 1.5 + normsinv(1-failure rate)Formulae for Sigma level performance
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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
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Solution
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SolutionSigma level = 1.5 + normsinv(1-0.002) = 4.378
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Level of Competition
Sigma
DPMO
Cost of poor quality
(% of sales)
Competitive level
6
3.4
40
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Times improvement
From sigma levelTo sigma level3456255514851,02,46531129720,4934271863569
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Improvement times
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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
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Bill SmithSix Sigma Born 0n 15 January 1987Father of Six Sigma sigma
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Number of repairs in factoryField FailuresDiscovery of bill smith
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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
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100 times4 yearsDesire of Bob Galvin
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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
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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.
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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
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Five fold growth in salesAnnual increase of profit 20%Cumulative saving $14 BillionAnnual stock price gain 21.3 %Results of Six Sigma at Motorola
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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
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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
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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
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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
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Redefine Six Sigma
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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
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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.
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Another Way of Defining Six SigmaSix Sigma is a sweeping Cultural Change effort to position a company for greater customer satisfaction, profitability, and competitiveness.
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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
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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
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Six Sigma is a business initiative, rather than quality initiativeHow Six Sigma is Different?
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With traditional approachQuite often Quality ImprovedyetBottom line did not
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Provide quality in such a way that creates economic worth for: customer employees share holders corporationall at the same timeWith Six Sigma Approach
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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?
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What Mr Welch of GE Says?Todays paperistomorrows Fish-wrap
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P-R CriteriaABCXEffort to ImproveSupport & StimulateP-CriteriaPerformanceControl with Carrot & StickR-Criteria
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A ProcessA product or service is outcome of a process.
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Type of ProcessesType of process
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A ProcessKey Process Output Variable, Y = f(X)
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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.
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Process Control Model
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Cost Mathematics Selling Price = Cost price + Profit
Profit = Selling price - Cost price
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Value Added & Non Value Added ActivitiesCostPriceCost ofnon value addedactivitiesCost ofvalue addedactivities=+10%90%50%50%
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Non Value Added ActivitiesWaitingTransportationInventoriesNon conforming productNon involvement of the people
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Goal Post StrategySuddenLossSuddenLossLSLUSLTarget
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Interpretation of DataSuddenLossSuddenLossLSLUSLTargetA
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Taguchis Loss FunctionUSLLSLBestCustomer Dissatisfaction
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Loss to the Society- increase in deviation from the target- increase in the variation of the processLoss to society increases with
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What should be Our Prime Goal?ReduceDeviation from target Variation in the process
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Fords Case of Noisy Automatic TransmissionLSLUSL
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New Thinking..Our new quality thinking should be to reduce variability around the nominal as operating philosophy for never ending Quality Improvement.
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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.
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Benefits of Six Sigma #2Sets performance goals for every oneuses common business frame workensures consistency for meeting customer requirements.
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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
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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.
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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
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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.
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Benefits of Six Sigma #6Executes Strategic ChangeLaunching new venturesEntering new marketsIntroducing new product Acquiring new organisationare now routine. Six Sigma facilitates change over.
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Proven Benefits of Six SigmaCost reductionProductivity improvementMarket-share growthCustomer retentionCycle time reductionDefect reductionCultural changeProduct / service change
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Define Identify Customers and their prioritiesProjects that meets the business objectiveCritical to quality requirements
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Measure Determine how to measure the process and how it is performing.
Identify key internal processes that influences CTQs and their impact on nonconformance.
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Analyse Determine the most likely causes of the defect.Understand impact of key variables on generation of defect.Determine key variables that cause variation
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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.
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ControlDetermine how to maintain improvements.
Ensuring key input variable remain within range.
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What is Statistics?A science that deals with:Collection of dataSummarization of dataAnalysis of dataDrawing information from data
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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
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Population Sample ModelBase population
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Process Redesign DisconnectBottleneckRedundancyRework loopinspection
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CE-Diagram for Defective Items
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Pareto Analysis For Prioritization
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Events
Frequency
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final
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Normal Probability PlotUsed for assessing:Normal distributionDistribution dealing with life of productEquality of variances of different sample
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7.9
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Gauge Repeatability & Reproducibility StudiesVariable Scale
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Run chart
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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
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Sample No.
CUSUM
Sheet2
Sheet3