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• Points which might be emphasized include: - Statistical process control measures the performance of a process, it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance. - Statistical process control requires the collection and analysis of data - therefore it is not helpful when total production consists of a small number of units - While statistical process control can not help identify a “good” or “bad” unit, it can enable one to decide whether or not to accept an entire production lot. If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot. The issue of rejecting a lot which was actually good can be raised here, but is probably better left to later.
• Students should understand both the concepts of natural and assignable variation, and the nature of the efforts required to deal with them.
• This slide helps introduce different process outputs. It can also be used to illustrate natural and assignable variation.
• Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process.
• ### Qm

1. 1. © 2008 Prentice Hall, Inc. S6 – 1 Process Control Process Capability Measurement & Index BY:- ABHISHEK RAJPUTBY:- ABHISHEK RAJPUT SAKSHI SRIVASTAVSAKSHI SRIVASTAV SWATI TANDONSWATI TANDON
2. 2. © 2008 Prentice Hall, Inc. S6 – 2  Process ControlProcess Control  Process CapabilityProcess Capability  Process Capability RatioProcess Capability Ratio (C(Cpp))  Process Capability IndexProcess Capability Index (C(Cpkpk ))
3. 3. © 2008 Prentice Hall, Inc. S6 – 3  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
4. 4. © 2008 Prentice Hall, Inc. S6 – 4  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 probabilityOutput measures follow a probability distributiondistribution  For any distribution there is a measureFor any distribution there is a measure of central tendency and dispersionof central tendency and dispersion  If the distribution of outputs falls withinIf the distribution of outputs falls within acceptable limits, the process is said toacceptable limits, the process is said to be “in control”be “in control”
5. 5. © 2008 Prentice Hall, Inc. S6 – 5  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 specificVariations that can be traced to a specific reasonreason  The objective is to discover whenThe 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
6. 6. © 2008 Prentice Hall, Inc. S6 – 6 To measure the process, we take samplesTo measure the process, we take samples and analyze the sample statistics followingand analyze the sample statistics following these stepsthese steps (a)(a) Samples of theSamples of the product, say fiveproduct, say five boxes of cerealboxes of cereal taken off the fillingtaken off the filling machine line, varymachine line, vary from each other infrom each other in weightweight FrequencyFrequency WeightWeight ## #### ## #### #### ## ## ## #### ## #### ## ## #### ## #### ## #### Each of theseEach of these represents onerepresents one sample of fivesample of five boxes of cerealboxes of cereal Figure S6.1Figure S6.1
7. 7. © 2008 Prentice Hall, Inc. S6 – 7 To measure the process, we take samplesTo measure the process, we take samples and analyze the sample statistics followingand analyze the sample statistics following these stepsthese steps (b)(b) After enoughAfter enough samples aresamples are taken from ataken from a stable process,stable process, they form athey form a pattern called apattern called a distributiondistribution The solid lineThe solid line represents therepresents the distributiondistribution FrequencyFrequency WeightWeightFigure S6.1Figure S6.1
8. 8. © 2008 Prentice Hall, Inc. S6 – 8 To measure the process, we take samplesTo measure the process, we take samples and analyze the sample statistics followingand analyze the sample statistics following these stepsthese steps (c)(c) There are many types of distributions, includingThere are many types of distributions, including the normal (bell-shaped) distribution, butthe normal (bell-shaped) distribution, but distributions do differ in terms of centraldistributions do differ in terms of central tendency (mean), standard deviation ortendency (mean), standard deviation or variance, and shapevariance, and shape WeightWeight Central tendencyCentral tendency WeightWeight VariationVariation WeightWeight ShapeShape FrequencyFrequency Figure S6.1Figure S6.1
9. 9. © 2008 Prentice Hall, Inc. S6 – 9 To measure the process, we take samplesTo measure the process, we take samples and analyze the sample statistics followingand analyze the sample statistics following these stepsthese steps (d)(d) If only naturalIf only natural causes ofcauses of variation arevariation are present, thepresent, the output of aoutput of a process forms aprocess forms a distribution thatdistribution that is stable overis stable over time and istime and is predictablepredictable WeightWeight Time Time FrequencyFrequency PredictionPrediction Figure S6.1Figure S6.1
10. 10. © 2008 Prentice Hall, Inc. S6 – 10 To measure the process, we take samplesTo measure the process, we take samples and analyze the sample statistics followingand analyze the sample statistics following these stepsthese steps (e)(e) If assignableIf assignable causes arecauses are present, thepresent, the process output isprocess output is not stable overnot stable over time and is nottime and is not predicablepredicable WeightWeight Time Time FrequencyFrequency PredictionPrediction ???? ?? ?? ?? ?? ?? ?????? ?? ?? ?? ?? ?? ?? ?????? Figure S6.1Figure S6.1
11. 11. © 2008 Prentice Hall, Inc. S6 – 11 Constructed from historical data, theConstructed from historical data, the purpose of control charts is to helppurpose of control charts is to help distinguish between natural variationsdistinguish between natural variations and variations due to assignableand variations due to assignable causescauses
12. 12. © 2008 Prentice Hall, Inc. S6 – 12 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 capablecontrol and capable of producing withinof producing within control limitscontrol limits (b) In statistical(b) In statistical control but notcontrol but not capable of producingcapable of producing within control limitswithin control limits (c) Out of control(c) Out of control
13. 13. © 2008 Prentice Hall, Inc. S6 – 13  Characteristics thatCharacteristics that can take any realcan take any real valuevalue  May be in whole orMay be in whole or in fractionalin fractional numbersnumbers  Continuous randomContinuous random variablesvariables VariablesVariables AttributesAttributes  Defect-relatedDefect-related characteristicscharacteristics  Classify productsClassify products as either good oras either good or bad or countbad or count defectsdefects  Categorical orCategorical or discrete randomdiscrete random variablesvariables
14. 14. © 2008 Prentice Hall, Inc. S6 – 14 1.1. Take samples from the population andTake samples from the population and compute the appropriate sample statisticcompute the appropriate sample statistic 2.2. Use the sample statistic to calculate controlUse 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 andPlot sample results on the control chart and determine the state of the process (in or out ofdetermine the state of the process (in or out of control)control) 4.4. Investigate possible assignable causes andInvestigate possible assignable causes and take any indicated actionstake any indicated actions 5.5. Continue sampling from the process and resetContinue sampling from the process and reset the control limits when necessarythe control limits when necessary
15. 15. © 2008 Prentice Hall, Inc. S6 – 15
16. 16. © 2008 Prentice Hall, Inc. S6 – 16  The natural variation of a processThe natural variation of a process should be small enough to produceshould be small enough to produce products that meet the standardsproducts that meet the standards requiredrequired  A process in statistical control does notA process in statistical control does not necessarily meet the designnecessarily meet the design specificationsspecifications  Process capability is a measure of theProcess capability is a measure of the relationship between the naturalrelationship between the natural variation of the process and the designvariation of the process and the design specificationsspecifications
17. 17. © 2008 Prentice Hall, Inc. S6 – 17 CCpp == Upper Specification - Lower SpecificationUpper Specification - Lower Specification 66σσ  A capable process must have aA capable process must have a CCpp of atof at leastleast 1.01.0  Does not look at how well the processDoes not look at how well the process is centered in the specification rangeis centered in the specification range  Often a target value ofOften a target value of CCpp = 1.33= 1.33 is usedis used to allow for off-center processesto allow for off-center processes  Six Sigma quality requires aSix Sigma quality requires a CCpp = 2.0= 2.0
18. 18. © 2008 Prentice Hall, Inc. S6 – 18 CCpp == Upper Specification - Lower SpecificationUpper Specification - Lower Specification 66σσ Insurance claims processInsurance claims process Process mean xProcess mean x = 210.0= 210.0 minutesminutes Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes Design specificationDesign specification = 210 ± 3= 210 ± 3 minutesminutes
19. 19. © 2008 Prentice Hall, Inc. S6 – 19 CCpp == Upper Specification - Lower SpecificationUpper Specification - Lower Specification 66σσ Insurance claims processInsurance claims process Process mean xProcess mean x = 210.0= 210.0 minutesminutes Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes Design specificationDesign specification = 210 ± 3= 210 ± 3 minutesminutes = = 1.938= = 1.938 213 - 207213 - 207 6(.516)6(.516)
20. 20. © 2008 Prentice Hall, Inc. S6 – 20 CCpp == Upper Specification - Lower SpecificationUpper Specification - Lower Specification 66σσ Insurance claims processInsurance claims process Process mean xProcess mean x = 210.0= 210.0 minutesminutes Process standard deviationProcess standard deviation σσ = .516= .516 minutesminutes Design specificationDesign specification = 210 ± 3= 210 ± 3 minutesminutes = = 1.938= = 1.938 213 - 207213 - 207 6(.516)6(.516) Process is capable
21. 21. © 2008 Prentice Hall, Inc. S6 – 21  A capable process must have aA capable process must have a CCpkpk of atof at leastleast 1.01.0  A capable process is not necessarily in theA capable process is not necessarily in the center of the specification, but it falls withincenter of the specification, but it falls within the specification limit at both extremesthe specification limit at both extremes CCpkpk = minimum of ,= minimum of , UpperUpper Specification - xSpecification - x LimitLimit 3σ3σ LowerLower x -x - SpecificationSpecification LimitLimit 3σ3σ
22. 22. © 2008 Prentice Hall, Inc. S6 – 22 New Cutting MachineNew Cutting Machine New process mean xNew process mean x = .250 inches= .250 inches Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches Lower Specification LimitLower Specification Limit = .249 inches= .249 inches
23. 23. © 2008 Prentice Hall, Inc. S6 – 23 New Cutting MachineNew Cutting Machine New process mean xNew process mean x = .250 inches= .250 inches Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches Lower Specification LimitLower Specification Limit = .249 inches= .249 inches CCpkpk = minimum of ,= minimum of , (.251) - .250(.251) - .250 (3).0005(3).0005
24. 24. © 2008 Prentice Hall, Inc. S6 – 24 New Cutting MachineNew Cutting Machine New process mean xNew process mean x = .250 inches= .250 inches Process standard deviationProcess standard deviation σσ = .0005 inches= .0005 inches Upper Specification LimitUpper Specification Limit = .251 inches= .251 inches Lower Specification LimitLower Specification Limit = .249 inches= .249 inches 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
25. 25. © 2008 Prentice Hall, Inc. S6 – 25 THANK YOUTHANK YOU