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© 2008 Prentice Hall, Inc. S6 – 1

Process Control

Process CapabilityMeasurement & Index

Process Control

Process CapabilityMeasurement & Index

BY:- ABHISHEK RAJPUTBY:- ABHISHEK RAJPUT SAKSHI SRIVASTAVSAKSHI SRIVASTAV

SWATI TANDONSWATI TANDON


Process Control Process Control

Process CapabilityProcess Capability Process Capability Ratio Process Capability Ratio (C(Cpp))

Process Capability Index Process Capability Index (C(Cpkpk ))


Variability is inherent in every process

Natural or common causes

Special or assignable causes Provides a statistical signal when

assignable causes are present Detect and eliminate assignable causes of

variation


Also called common causesAlso called common causes

Affect virtually all production processesAffect virtually all production processes

Expected amount of variationExpected amount of variation

Output measures follow a probability Output measures follow a probability distributiondistribution

For any distribution there is a measure For any distribution there is a measure of central tendency and dispersionof central tendency and dispersion

If the distribution of outputs falls within If the distribution of outputs falls within acceptable limits, the process is said to acceptable limits, the process is said to be “in control”be “in control”


Also called special causes of variationAlso called special causes of variation Generally this is some change in the processGenerally this is some change in the process

Variations that can be traced to a specific Variations that can be traced to a specific reasonreason

The objective is to discover when The objective is to discover when assignable causes are presentassignable causes are present Eliminate the bad causesEliminate the bad causes

Incorporate the good causesIncorporate the good causes


To measure the process, we take samples To measure the process, we take samples and analyze the sample statistics following and analyze the sample statistics following these stepsthese steps

(a)(a) Samples of the Samples of the product, say five product, say five boxes of cereal boxes of cereal taken off the filling taken off the filling machine line, vary machine line, vary from each other in from each other in weightweight

Fre

qu

ency

Fre

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WeightWeight

##

#### ##

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## ## #### ## ####

## ## #### ## #### ## ####

Each of these Each of these represents one represents one sample of five sample of five

boxes of cerealboxes of cereal

Figure S6.1Figure S6.1



(b)(b) After enough After enough samples are samples are taken from a taken from a stable process, stable process, they form a they form a pattern called a pattern called a distributiondistribution

The solid line The solid line represents the represents the

distributiondistribution

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ency

Fre

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ency

WeightWeightFigure S6.1Figure S6.1



(c)(c) There are many types of distributions, including There are many types of distributions, including the normal (bell-shaped) distribution, but the normal (bell-shaped) distribution, but distributions do differ in terms of central distributions do differ in terms of central tendency (mean), standard deviation or tendency (mean), standard deviation or variance, and shapevariance, and shape

WeightWeight

Central tendencyCentral tendency

WeightWeight

VariationVariation

WeightWeight

ShapeShape

Fre

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ency

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(d)(d) If only natural If only natural causes of causes of variation are variation are present, the present, the output of a output of a process forms a process forms a distribution that distribution that is stable over is stable over time and is time and is predictablepredictable

WeightWeightTimeTimeF

req

uen

cyF

req

uen

cy PredictionPrediction




(e)(e) If assignable If assignable causes are causes are present, the present, the process output is process output is not stable over not stable over time and is not time and is not predicablepredicable

WeightWeightTimeTimeF

req

uen

cyF

req

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cy PredictionPrediction

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Constructed from historical data, the Constructed from historical data, the purpose of control charts is to help purpose of control charts is to help distinguish between natural variations distinguish between natural variations and variations due to assignable and variations due to assignable causescauses


FrequencyFrequency

(weight, length, speed, etc.)(weight, length, speed, etc.)SizeSize

Lower control limitLower control limit Upper control limitUpper control limit

(a) In statistical (a) In statistical control and capable control and capable of producing within of producing within control limitscontrol limits

(b) In statistical (b) In statistical control but not control but not capable of producing capable of producing within control limitswithin control limits

(c) Out of control(c) Out of control


Characteristics that Characteristics that can take any real can take any real valuevalue

May be in whole or May be in whole or in fractional in fractional numbersnumbers

Continuous random Continuous random variablesvariables

VariablesVariables AttributesAttributes Defect-related Defect-related

characteristics characteristics

Classify products Classify products as either good or as either good or bad or count bad or count defectsdefects

Categorical or Categorical or discrete random discrete random variablesvariables


1.1. Take samples from the population and Take samples from the population and compute the appropriate sample statisticcompute the appropriate sample statistic

2.2. Use the sample statistic to calculate control Use the sample statistic to calculate control limits and draw the control chartlimits and draw the control chart

3.3. Plot sample results on the control chart and Plot sample results on the control chart and determine the state of the process (in or out of determine the state of the process (in or out of control)control)

4.4. Investigate possible assignable causes and Investigate possible assignable causes and take any indicated actionstake any indicated actions

5.5. Continue sampling from the process and reset Continue sampling from the process and reset the control limits when necessarythe control limits when necessary


The natural variation of a process The natural variation of a process should be small enough to produce should be small enough to produce products that meet the standards products that meet the standards requiredrequired

A process in statistical control does not A process in statistical control does not necessarily meet the design necessarily meet the design specificationsspecifications

Process capability is a measure of the Process capability is a measure of the relationship between the natural relationship between the natural variation of the process and the design variation of the process and the design specificationsspecifications


CCpp = = Upper Specification - Lower SpecificationUpper Specification - Lower Specification

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A capable process must have a A capable process must have a CCpp of at of at least least 1.01.0

Does not look at how well the process Does not look at how well the process is centered in the specification range is centered in the specification range

Often a target value of Often a target value of CCpp = 1.33 = 1.33 is used is used to allow for off-center processesto allow for off-center processes

Six Sigma quality requires aSix Sigma quality requires a C Cpp = 2.0 = 2.0



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Insurance claims processInsurance claims process

Process mean x Process mean x = 210.0= 210.0 minutes minutesProcess standard deviation Process standard deviation = .516 = .516 minutes minutesDesign specification Design specification = 210 ± 3= 210 ± 3 minutes minutes



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= = 1.938= = 1.938213 - 207213 - 207

6(.516)6(.516)



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= = 1.938= = 1.938213 - 207213 - 207

6(.516)6(.516)Process is

capable


A capable process must have a A capable process must have a CCpkpk of at of at least least 1.01.0

A capable process is not necessarily in the A capable process is not necessarily in the center of the specification, but it falls within center of the specification, but it falls within the specification limit at both extremesthe specification limit at both extremes

CCpkpk = minimum of , = minimum of ,

UpperUpperSpecification - xSpecification - xLimitLimit

LowerLowerx -x - SpecificationSpecification

LimitLimit


New Cutting MachineNew Cutting Machine

New process mean x New process mean x = .250 inches= .250 inchesProcess standard deviation Process standard deviation = .0005 inches = .0005 inchesUpper Specification Limit Upper Specification Limit = .251 inches= .251 inchesLower Specification LimitLower Specification Limit = .249 inches = .249 inches




CCpkpk = minimum of , = minimum of ,(.251) - .250(.251) - .250

(3).0005(3).0005




CCpkpk = = 0.67 = = 0.67.001.001

.0015.0015

New machine is NOT capable

CCpkpk = minimum of , = minimum of ,(.251) - .250(.251) - .250

(3).0005(3).0005.250 - (.249).250 - (.249)

(3).0005(3).0005

Both calculations result inBoth calculations result in


THANK YOUTHANK YOU

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process forms aprocess

sample statistics followingand

assignable causes of