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  • Grado en Ingeniera

    Asignatura: Estadstica

    Tema 3: Control Estadstico de Procesos (SPC)- IN ENGLISH

    Grado en IngenierGrado en Ingeniera a

    Asignatura: EstadAsignatura: Estadsticastica

    Tema 3: Control EstadTema 3: Control Estadstico de Procesos (SPC)stico de Procesos (SPC)-- IN ENGLISHIN ENGLISH

    Grado en Ingeniera. Estadstica. Tema 3

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 2

    Statistical Process Control (SPC)StatisticalStatistical ProcessProcess Control (SPC)Control (SPC)

    IntroductionThe variability of a production process

    Assignable causesNon-assignable causes

    Control by variablesThe capability of a process. Capability indexControl by variables graphsInitial study of a process. Determining the capacityMonitorization process

    Control by attributes

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 3

    SPC. IntroductionSPC. SPC. IntroductionIntroduction

    ProductionprocessRaw material

    Finished product

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 4

    Does it have sufficient quality? Is it adequate?Does it have sufficientquality in order to be

    competitive in the market?

    SPC. IntroductionSPC. SPC. IntroductionIntroduction

    ProductionprocessRaw material

    Finished product

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 5

    OBJECTIVE

    To test that the process is operating under optimum conditions

    To obtain information that allows the process to be improved

    HOW?

    Measurement during the production process

    Specified measurement intervals

    Graphical representation of the evolution of a quality characteristic

    SPC. IntroductionSPC. SPC. IntroductionIntroduction

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 6

    SPC. IntroductionSPC. SPC. IntroductionIntroduction

    Suppose X is the variable of interest (for example: length).Periodic samples of X are takenIn the control graphs the evolution of a statistic of X is plotted. (For example, the sample mean)

    1x 2x 3x

    Upper control limit

    Lower control limit

    If any point is outside the control limits, or if non-random behaviour is observed, this isevidence that the process is not operating under optimum conditions.

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 7

    Statistical Process control. TYPES:

    By variables (ranges): we analyze a measureable characteristic

    of the production (for example, the diameter of an axis)

    By attributes (defective / non-comforming fraction): we analyze

    a qualitative characteristic of the production (for example: accept /

    defect)

    SPC. IntroductionSPC. SPC. IntroductionIntroduction

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 8

    Statistical Process Control (SPC)StatisticalStatistical ProcessProcess Control (SPC)Control (SPC)

    IntroductionThe variability of a production process

    Assignable causesNon-assignable causes

    Control by variablesThe capacity of a process. Capability indexControl by variables graphsInitial study of a process. Determining the capacityMonitorization process

    Control by attributes

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 9

    SPC. Variability of a processSPC. SPC. VariabilityVariability ofof a a processprocess

    PROCESS CHARACTERISTICS:

    VARIABILITY: two outputs never the same.

    REPEATABILITY: the capability of production with a stable level ofquality

    processinputs outputs

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 10

    SPC. Variability of a processSPC. SPC. VariabilityVariability ofof a a processprocess

    VARIABILITY: Even though an exhaustive relationship of the causes of the

    variablity cannot be given, it is interesting to classify as either causes assignable

    to specific factors (and therefore controllable) and unassignable causes.

    ASSIGNABLE CAUSES

    Produced by important factors that can be controlled in order to maintain

    them at acceptable levels. The appear sporadically.

    They produce unstable, significant and UNPREDICTABLE variability

    NON-ASSIGNABLES CAUSES

    Produced by secondary factors whose effect is not considered significant.

    They are a permanent and inherent part of the production process.

    They produce stable, non-significant, accepted and PREDICTABLE

    variablity

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 11

    PROCESS IN CONTROL:PROCESS IN CONTROL:PROCESS IN CONTROL:PROCESS IN CONTROL:We say a process is IN CONTROL when only

    non-assignable causes are present

    NON- ASIGNABLES CAUSES stable, non-significant, PREDICTABLE variability

    SPC. Variability of a processSPC. SPC. VariabilityVariability ofof a a processprocess

    The control graphs allow thepresence of assignable

    causes in the process to be detected

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 12

    Statistical Process Control (SPC)StatisticalStatistical ProcessProcess Control (SPC)Control (SPC)

    IntroductionThe variability of a production process

    Assignable causesNon-assignable causes

    Control by variablesThe capability of a process. Capability indexControl by variables graphsInitial study of a process. Determining the capacityMonitorization process

    Control by attributes

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 13

    SPC. Capacity of a processSPC. SPC. CapacityCapacity ofof a a processprocess

    PREMISE:

    The characteristic of production that we control (for example: thediameter of an axis, the packaged weight ) follows a normal distribution WHEN the process is under control.

    X N (, )

    Almost all of the production (99.7%) will be in the interval:

    ( 3 ; + 3)

    We call CAPACITY over the previous interval

    CAPACITY = 6

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 14

    SPC. Capacity of a processSPC. SPC. CapacityCapacity ofof a a processprocess

    PROBLEMNot all of the products that we produce can be valid.

    We only accept those that satisfy given specifications.

    ToleranceToleranceToleranceTolerance intervalintervalintervalinterval:::: set of values of X that are considered to be

    admissable or acceptable.

    PRODUCT TOLERANCE INTERVAL (LT2 LT1)

    LT1 LT2

    This is defined by the client, or on occasions by the designer of the product or the personresponsable for the process (it often represents an objective value, , and an acceptable error, L):

    L

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 15

    The relation between the CAPACITY of a process and theTOLERANCE INTERVAL of a product gives us information aboutthe defects produced in our process.

    Mean,Std. dev.1,5

    Normal Distribution

    x

    density

    -24 -14 -4 6 16 26

    0

    0,02

    0,04

    0,06

    0,08

    3 + 3

    SPC. Capacity - Capability indexSPC. SPC. CapacityCapacity -- CapabilityCapability indexindex

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 16

    Mean,Std. dev.1,5

    Normal Distribution

    x

    density

    -24 -14 -4 6 16 26

    0

    0,02

    0,04

    0,06

    0,08

    3 + 3

    LT1 LT2

    SPC. Capacity - Capability indexSPC. SPC. CapacityCapacity -- CapabilityCapability indexindex

    The relation between the CAPACITY of a process and theTOLERANCE INTERVAL of a product gives us information aboutthe defects produced in our process.

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 17

    Mean,Std. dev.1,5

    Normal Distribution

    x

    density

    -24 -14 -4 6 16 26

    0

    0,02

    0,04

    0,06

    0,08

    3 + 3

    LT1 LT2 DEFECTS!!

    SPC. Capacity - Capability indexSPC. SPC. CapacityCapacity -- CapabilityCapability indexindex

    The relation between the CAPACITY of a process and theTOLERANCE INTERVAL of a product gives us information aboutthe defects produced in our process.

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 18

    Mean,Std. dev.1,5

    Normal Distribution

    x

    density

    -24 -14 -4 6 16 26

    0

    0,02

    0,04

    0,06

    0,08

    3 + 3

    LT2LT1

    SPC. Capacity - Capability indexSPC. SPC. CapacityCapacity -- CapabilityCapability indexindex

    The relation between the CAPACITY of a process and theTOLERANCE INTERVAL of a product gives us information aboutthe defects produced in our process.

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 19

    Mean,Std. dev.1,5

    Normal Distribution

    x

    density

    -24 -14 -4 6 16 26

    0

    0,02

    0,04

    0,06

    0,08

    3 + 3

    LT2LT1 NO DEFECTS!!

    SPC. Capacity - Capability indexSPC. SPC. CapacityCapacity -- CapabilityCapability indexindex

    The relation between the CAPACITY of a process and theTOLERANCE INTERVAL of a product gives us information aboutthe defects produced in our process.

  • Grado en Ingeniera. Estadstica. Tema 3Nmero de transparencia: 20

    Mean,Std. dev.1,5

    Normal Distribution

    x

    density

    -24 -14 -4 6 16 26

    0

    0,02

    0,04

    0,06

    0,08

    3 + 3LT1 LT2

    SPC. Capacity - Capability indexSPC. SPC. CapacityCapacity -- CapabilityCapability indexindex

    The relation between the CAPACITY of a process and theTOLERANCE INTERVAL of a product gives us information aboutthe defects produced