quality and statistical quality control

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    ` Conformance to specifications

    ` Fulfilling customer needs

    ` Fitness for use

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    ` According to Feigenbaumthe underlying principle

    of total quality is that ,to provide genuine

    effectiveness, control must start with the design of

    the product and end only when the product hasbeen in the hands of a customer who remains

    satisfied.

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    ` Performance

    ` Features

    ` Reliability

    ` Conformance` Durability

    ` Serviceability

    ` Aesthetics

    ` Safety` Other perceptions

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    ` system for verifying and maintaining a desired

    level of quality in a product or process by careful

    planning, use of proper equipment, continued

    inspection, and corrective action as required

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    ` The production processes are not perfect!

    ` Which means that the output of these processes will not be

    perfect correct and deterministic.

    ` Successive runs of the same production process will produce

    non-identical parts.

    ` Alternately, seemingly similar runs of the production process

    will vary, by some degree, and impart the variation into the

    some product characteristics.

    ` Because of these variations in the products, we needprobabilistic models and robust statistical techniques to

    analyze quality of such products.

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    ` No matter how carefully a production process is controlled,these quality measurements will vary from item to item, andthere will be a probability distribution associated with the

    population of such measurements.

    ` If all important sources of variations are under control in aproduction process, then the slight variations among thequality measurements usually cause no serious problems.

    ` Such a process should produce the same distribution of qualitymeasurements no matter when it is sampled, thus this is a

    stable system.

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    ` Objective ofquality control is to develop a scheme forsampling a process, making a quality measurement of intereston sample items, and then making a decision as to whether ornot the process is in the stable state, or in control.

    ` If the sample data suggests that the process is out of control,a cause is for the abnormality is sought.

    ` A common method for making these decisions involves theuse ofcontrol charts.

    ` These are very important and widely used techniques in

    industry, and everyone in the industry, even if not directlyrelated to quality control, should be aware of these.

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    Statistical process control

    ` Methodology formonitoring a process to identify special

    causes of variation and signaling the need to take corrective

    action.

    ` Whenspecial causes are present, the system said to be

    statistically out of control.

    ` If the variations are due to common causes alone, the process

    is said to be in statistical control.

    ` SPC relies heavily on control charts.

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    Control Chart Selection: Attribute DataControl Chart Selection: Attribute Data

    X, R chart

    Process ControlProduct Control

    Variables Attributes Variables Attributes

    Acceptance Sampling (Single/Double

    Sampling Plan)c, p, np chart

    In Process control Techniques

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    Control Charts: Recognizing Sources ofControl Charts: Recognizing Sources of

    VariationVariation

    Why Use a Control Chart? To monitor, control, and improveprocess performance over time by

    studying variation and its source.

    What Does a Control Chart Do? Focuses attention on detecting and monitoring process variation over

    time;

    Distinguishesspecialfrom common causes of variation, as a guide tolocal or management action;

    Serves as a tool for ongoing control of a process;

    Helps improve a process to perform consistently and predictably forhigher quality, lower cost, and higher effective capacity;

    Provides a common language for discussing process performance.

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    Control Charts:Control Charts:

    Recognizing Sources of VariationRecognizing Sources of Variation

    How Do I Use Control Charts?

    There are many types of control charts. The control

    charts that you or your team decides to use should be

    determined by the type of data that you have.

    Use the following tree diagram to determine whichchart will best fit your situation. Only the most

    common types of charts are addressed.

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    ` Attributes A performance characteristics that is either

    present or absentin the product or service under

    consideration.

    ` Examples: Order is either complete or incomplete; an invoice

    can have one, two, or more errors.

    ` Attributes data are discrete and tell whether the characteristics

    conforms to specifications.

    ` Attributes measurements typically represented as proportions

    or rates. e.g. rate of errors per opportunity.` Typically measured by Go-No Go gauges.

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    ` Variable Continuous data that is concerned with degree ofconformance to specifications.

    ` Generally expressed with statistical measures such as averagesand standard deviations.

    ` Sophisticated instruments (caliper) used.

    ` In statistical sense, attributes inspection less efficient thanvariable inspection.

    ` Attribute data requires larger sample than variable inspectionto obtain same amount of statistical information.

    ` Most quality characteristics in service industry are attributes.

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    Statistical Process ControlStatistical Process Control

    Statistical Process Control (SPC) can be

    thought of as the application of statistical

    methods for the purposes of quality controland improvement.

    Quality Improvement is perhaps foremost

    among all areas in business for applicationof statistical methods.

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    Control Chart ConstructionControl Chart Construction

    Initiate data collection:

    Run the process untouched, and gather sampled data. Record data on an appropriate Control Chart sheet or

    other graph paper. Include any unusual events that occur.

    Calculate the appropriate statistics and control limits:

    Use the appropriate formulas.

    Construct the control chart(s) and plot the data.

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    CL

    U1SL

    U2SWL

    UCL

    L1SL

    L2SWL

    LCL

    A

    B

    C

    C

    B

    A

    Control Charts: Colors UsedControl Charts: Colors Used

    *

    ** *

    *

    * *

    **

    **

    *

    *

    *

    *

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    Control Chart InterpretationControl Chart Interpretation

    Center line (CL) positioned at the estimated mean

    Upper and lower one standard deviation lines (U1SL and

    L1SL) positioned one standard deviation above andbelow the mean.

    Upper and lower two standard deviation warning lines(U2SWL and L2SWL) positioned at two standard

    deviations above and below the mean.

    Upper and lower control lines (UCL and LCL) positionedat three standard deviations above and below the mean.

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    Control Charts for theControl Charts for the

    Process Mean and DispersionProcess Mean and Dispersion

    X bar ChartTypically used to monitor process centrality (or location)

    Limits depend on the measure is used to monitor process dispersion(R or S may be used).

    S orStandard Deviation Chart:Used to monitor process dispersion

    R orRange Chart:

    Also used to monitor process dispersion

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    m = 20 to 40 initial samples of n observations each.

    Xi = mean of ith sample

    Si = standard deviation of ith sample

    Ri = range of ith sample

    Sample Summary InformationSample Summary Information

    X = (X1 + X2 +... + Xm) / mR = (R1 + R2 + ... +Rm)/m

    S = (S1 + S2 + ... + Sm)/m

    W = R/d2 where d2 depends only on n

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    Coordinates for the XCoordinates for the X--bar Control Chart: Rbar Control Chart: R

    CL= X,

    UCL= X+ A2R,

    UCL= X- A2R

    U2SWL= X+ 2A2R/3

    L2SWL= X- 2A2R/3

    U1SL= X+ A2

    R/3

    L1SL= X- A2R/3

    A2 is a constant that depends only on n.

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    Coordinates for an R Control ChartCoordinates for an R Control Chart

    CL= R

    UCL= D4R

    LCL= D3R U2SWL= R+ 2(D4-1)R/3

    L2SWL= R- 2(D4-1)R/3

    U1SL= R+ (D4

    -1)R/3

    L1SL= R- (D4-1)R/3

    where D3 and D4 depend only on n

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    Championship

    Championship Card CompanyChampionship Card Company

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    Championship Card CompanyChampionship Card Company

    Championship Card Company (CCC) produces collectiblesports cards of college and professional athletes.

    CCCs card-front design uses a picture of the athlete, bordered

    all-the-way-around with one-eighth inch gold foil. However,

    the process used to center an athletes picture does not functionperfectly.

    Five cards are randomly selected from each 1000 cards produced

    and measured to determine the degree of off-centeredness of each

    cards picture. The measurement taken represents percentageof total margin (.25) that is on the left edge of a card. Data

    from 30 consecutive samples is included with your materials,

    and summarized on the following slides.

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    Championship Card CompanyChampionship Card Company

    Sample X-bar R Sample X-bar R Sample X-bar R

    1 55.6 22 11 51.2 15 21 50.0 11

    2 61.0 23 12 49.4 14 22 47.0 14

    3 45.2 20 13 44.0 32 23 50.6 15

    4 46.2 11 14 51.6 14 24 48.8 165 46.8 18 15 53.2 12 25 44.6 22

    6 49.8 23 16 52.4 23 26 46.8 16

    7 46.8 18 17 50.6 8 27 49.2 88 44.2 20 18 56.0 18 28 45.6 19

    9 50.8 32 19 50.2 19 29 57.6 40

    10 48.4 16 20 44.0 23 30 51.4 17

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    Championship Card CompanyChampionship Card Company

    Summary InformationSummary Information

    n = 5

    X = 49.63S = 7.42

    R = 18.63

    d2 = 2.326

    A2 = 0.577

    A3 = 1.427

    B3 = NAB4 = 2.089

    D3 = NA

    D4 = 2.115

    W = R/d2 = 8.01

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    3020100

    60

    50

    40

    Sample Number

    SampleMean

    X Bar Chart for Sports Cards Centering Values

    Samples of 5 from each 1000 Cards Printed

    1

    =49.63

    1.0S L=53 .22

    2.0S L=56 .80

    3.0S L=60 .38

    -1.0SL=46.05

    - 2.0S L=42.47

    - 3.0S L=38.89

    Championship Card CompanyChampionship Card Company

    Limits Based on R

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    3020100

    40

    30

    20

    10

    0

    Sample Number

    SampleRang

    e

    R Chart for Sports Card Centering

    Samples of 5 Cards from each 1000 Produced

    R=18.63

    1.0SL=25.55

    2.0S L=32.48

    3.0S L=39.40

    - 1.0S L=11.71

    - 2.0SL =4.791

    - 3.0SL =0.000

    Championship Card CompanyChampionship Card Company

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    Championship Card Company XChampionship Card Company X--bar & Rbar & R

    Chart InterpretationChart Interpretation

    Application of all eight PATs to the X-bar chart indicated aviolation of PAT 1 (one point plotting above the UCL) at sample2. Apparently, a successful process adjustment was made, as

    suggested by examination of the remainder of the chart.

    Application of PATs one through four to the R chart indicated aviolation of PAT 1 at sample 29. Measures would be investigatedto reduce process variation at that point. The violation was a

    close call and was out of character with the remainder of thedata.

    We are close to being able to apply PDCA to the process for thepurpose of achieving lasting process improvements.

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    Coordinates for the X bar Control Chart: SCoordinates for the X bar Control Chart: S

    CL= X

    UCL=X=A3S

    LCL=X- A3S

    U2SWL= X+ 2A3S/3

    L2SWL= X- 2A3S/3

    U1SL= X+ A3S/3

    L1SL= X- A3S/3

    where A3 depends only on n

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    Coordinates on an S Control ChartCoordinates on an S Control Chart

    CL= S

    UCL= B4S

    LCL= B3S

    U2SWL= S+ 2(B4-1)S/3

    L2SWL= S- 2(B4-1)S/3

    U1SL= S+ (B4-1)S/3 L1SL= S- (B4-1)S/3

    where B3 and B4 depend only on n

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    Championship Card CompanyChampionship Card CompanyChampionship Card CompanyChampionship Card Company

    Sample X-bar S Sample X-bar S Sample X-bar S

    1 55.6 9.63 11 51.2 6.83 21 50.0 5.15

    2 61.0 8.63 12 49.4 5.46 22 47.0 5.15

    3 45.2 7.40 13 44.0 14.35 23 50.6 5.55

    4 46.2 4.09 14 51.6 5.18 24 48.8 6.505 46.8 7.22 15 53.2 5.36 25 44.6 8.96

    6 49.8 8.76 16 52.4 9.48 26 46.8 6.50

    7 46.8 6.72 17 50.6 3.44 27 49.2 3.19

    8 44.2 8.53 18 56.0 7.00 28 45.6 7.96

    9 50.8 11.95 19 50.2 7.60 29 57.6 14.38

    10 48.4 6.19 20 44.0 8.46 30 51.4 6.80

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    UCL

    U2SWLU1SL

    CL

    L1SLL2SWL

    LCL

    X based on S S

    60.22

    56.6953.16

    49.63

    46.1142.58

    39.05

    15.49

    12.8010.11

    7.42

    4.722.03

    ------

    Championship Card CompanyChampionship Card Company

    XX--bar and S Chart imitsbar and S Chart imits

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    3020100

    60

    50

    40

    Samp l mber

    SampleMean

    X Bar Chart for Sports Cards Centering Values

    Samples of 5 from each 1000 Cards Printed

    1

    X=49.63

    1.0S L=53 .16

    2.0S L=56.69

    3.0S L=60.22

    - 1.0S L=46 .11

    - 2.0S L=42.58

    - 3.0S L=39.05

    Championship Card CompanyChampionship Card Company

    Limits Based on S

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    3020100

    15

    10

    5

    0

    Sample Number

    SampleStdev

    S Chart for Sports Card Centering Values

    5 Cards Sampled from each 1000 Cards Produced

    S =7.416

    1.0S L=10.11

    2.0S L=12.80

    3.0S L=15.49

    - 1.0S L=4.724

    - 2.0SL =2.032

    - 3.0SL =0.000

    Championship Card CompanyChampionship Card Company