quality management

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  • Step 1:Calculate the Mean of Each Sample

    Time 1Time 2Time 3Observation 115.816.116.0Observation 315.815.815.9Observation 415.915.915.8Sample means (X-bar)15.87515.97515.9

  • Step 2: Calculate the Standard Deviation of the Sample Mean

  • Step 3: Calculate CL, UCL, LCL

    Center line (x-double bar):

    Control limits for 3 limits (z = 3):

    Step 4: Draw the Chart

  • An Alternative Method for the X-bar Chart Using R-bar and the A2 FactorUse this method when sigma for the process distribution is not known. Use factor A2 from Table

  • Step 1: Calculate the Range of Each Sample and Average Range

    Time 1Time 2Time 3Observation 115.816.116.0Observation 315.815.815.9Observation 415.915.915.8Sample ranges (R)

  • Step 2: Calculate CL, UCL, LCL

    Center line:

    Control limits for 3 limits:

    Control Chart for Range (R-Chart)Center Line and Control Limit calculations:

    R-Bar Control Chart

    Control Charts for Attributes: P-Charts & C-ChartsUse P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisionsPercent of leaking caulking tubes in a box of 48Percent of broken eggs in a carton

    Use C-Charts for discrete defects when there can be more than one defect per unitNumber of flaws or stains in a carpet sample cut from a production runNumber of complaints per customer at a hotel

  • Constructing a P-Chart:A Production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table below shows the number of defective tires in each sample of 20 tires.

    SampleSample Size (n)Number Defective12032202320142025201

  • Step 1:Calculate the Percent defective of Each Sample and the Overall Percent Defective (P-Bar)

    SampleNumber DefectiveSample SizePercent Defective1320.152220.103120.054220.105120.05Total9100.09

  • Step 2: Calculate the Standard Deviation of P.

  • Step 3: Calculate CL, UCL, LCL

    Center line (p bar):

    Control limits for 3 limits:

    Step 4: Draw the Chart

  • Constructing a C-Chart:The number of weekly customer complaints are monitored in a large hotel. Develop a three sigma control limits For a C-Chart using the data table On the right.

    WeekNumber of Complaints132233415363728193101Total22

  • Calculate CL, UCL, LCL

    Center line (c bar):

    Control limits for 3 limits:

    Six Sigma QualityA philosophy and set of methods companies use to eliminate defects in their products and processesSeeks to reduce variation in the processes that lead to product defectsThe name six sigma refers to the variation that exists within plus or minus six standard deviations of the process outputsA statistical concept that measures a process in terms of defects at the six sigma level, there 3.4 defects per million opportunities.


    Sigma Level ( Process Capability) Defects per Million Opportunities 2308,537366,80746,210523363.4

    Six Sigma Quality

    Six Sigma Roadmap (DMAIC)Next ProjectCelebrate Project $

    Tools used for continuous improvement1. Process flowchart

    Tools used for continuous improvement2. Run Chart

    Tools used for continuous improvement3. Control Charts Performance MetricTime

    Tools used for continuous improvement4. Cause and effect diagram (fishbone)

    Tools used for continuous improvement5. Check sheet


    Tools used for continuous improvement6. Histogram

    Tools used for continuous improvement7. Pareto AnalysisABCDEFFrequencyPercentage50%100%0%75%25%102030405060

    Summary of ToolsProcess flow chartRun diagramControl chartsFishboneCheck sheetHistogramPareto analysis

    Case: shortening telephone waiting timeA bank is employing a call answering service

    The main goal in terms of quality is zero waiting time - customers get a bad impression - company vision to be friendly and easy access

    The question is how to analyze the situation and improve quality

    The current processOperatorCustomer AReceivingPartyHow can we reduce waiting time?

    Fishbone diagram analysis

    Reasons why customers have to wait(12-day analysis with check sheet)

    Daily averageTotal numberAOne operator (partner out of office)14.3172BReceiving party not present6.173CNo one present in the section receiving call5.161DSection and name of the party not given1.619EInquiry about branch office locations1.316FOther reasons0.81029.2351

    Pareto Analysis: reasons why customers have to wait

    Ideas for improvementTaking lunches on three different shiftsAsk all employees to leave messages when leaving desksCompiling a directory where next to personnels name appears her/his title

    Results of implementing the recommendations BeforeAfter

    In general, how can we monitor quality?Assignable variation: we can assess the causeCommon variation: variation that may not be possible to correct (random variation, random noise)By observingvariation inoutput measures!