# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

21 Pages

### Lec 12 - Attributes Control Charts

Course: ENG 300, Fall 2011
School: Rutgers
Rating:

Word Count: 847

#### Document Preview

Control Attributes Charts Variables Control Charts for continuous measurements Attribute Control Charts for discrete measurements P Charts for Fraction Defective Monitors fraction defective Defective is unusable fraction of broken glass plates fraction of defective chips on a wafer fraction of defective truffle shells go-no-go gauge 2 P Chart Based on Binomial Distribution sample size n for sample i Xi...

Register Now

#### Unformatted Document Excerpt

Coursehero >> New Jersey >> Rutgers >> ENG 300

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Control Attributes Charts Variables Control Charts for continuous measurements Attribute Control Charts for discrete measurements P Charts for Fraction Defective Monitors fraction defective Defective is unusable fraction of broken glass plates fraction of defective chips on a wafer fraction of defective truffle shells go-no-go gauge 2 P Chart Based on Binomial Distribution sample size n for sample i Xi = number of defectives in sample of n p = fraction defective in popln = P(unit is defective) r. v. X i Binomial(n, p) n P(X i = x ) = p x ( 1 p ) n x x E(X)=np V(X)=np(1-p) 3 x = 0,1, . . . , n Sample Statistic is Fraction Defective At each sample time plot pi = xi n Note: 1 E( x i ) = p n 1 np ( 1 p ) p ( 1 p ) V (pi ) = 2 V ( xi ) = = n n2 n E( p i ) = Control Limits UCL = p + 3 p(1 p ) n CL = p LCL = p 3 p(1 p ) n 4 Some Notes on P Charts If LCL is negative, make it zero Test statistic is not normal - don't use zone rules If pi = 0, process in-control 5 Estimating p From Initial Data Data: draw m (say 20) subsamples of size n X1, X2, ... , Xm Sample Statistics: p1, p2, ... , pm Estimate for CL = p p= x1 + . . . + x m nm 6 Example for P Charts A process that produces bearing housings is investigated. 10 samples of size 100 are selected. Is process in-control? Sample # # Noncon 1 5 2 2 3 3 4 8 5 4 6 1 7 2 8 6 9 3 10 4 Make initial control chart: m D total # defectives i p= = i =1 = 0.038 total # sampled mn UCL = 0.038 + 3 0.038(1 0.038) = 0.095 100 CL = 0.038 LCL = 0.038 + 3 0.038(1 0.038) = 0.02 0 100 7 P Chart for C1 Proportion 0.10 3.0SL=0.09536 0.05 P=0.03800 0.00 - 3.0SL=0.000 0 1 2 3 4 5 6 7 8 9 10 Sampl e Number No iterations are needed all points in the baseline sample fall within the control limits. Sample # # Nonco n pi 1 2 3 4 5 6 7 8 9 10 5 2 3 8 4 1 2 6 3 4 . . . . . . . . . .04 05 02 03 08 04 01 02 06 03 8 P-Chart and Average Run Length If the fraction defective shifts from its current value 0.038 to 0.060, find the probability of detecting this on the first sample following the shift. r. v. D = number of defectives in sample of 100 r.v. D Binomial(n = 100 , p = 0.06) P ( sample point above UCL) = P ( p > UCL / p = 0.06) D = P( > UCL / p = 0.06) = P ( D > 100 * 0.095) 100 9.5 6 = P(Z > ) = P ( Z > 1.47) = 0.07 100 * .06 * .94 Find the expected number of samples until detection ARL = 1 = 14.3 0.07 9 Selecting a Sample Size for P-charts Criterion: Select a sample size such that the probability of finding at least one defective in a sample exceeds 95% Example: The fraction defective is 1%. Recommend a sample size using the above criterion. r.v.D Binomial (n, p = 0.01) P ( D 1) > 0.95 1 P ( D = 0) > 0.95 n 0 1 p (1 p ) n > 0.95 0.05 > 0.99 n 0 n > 300 10 C for Charts Number of Defects Monitors Number of Defects (not defectives) Examples: # of defects (contaminants) per sample of recycled plastic # of defects (all types) per sample of cars # of defects (scratches, bubbles, etc.) per sample of a painted surface An item may be acceptable with a few defects 11 The Defect Distribution is the Poisson r. v. X = # of defects per sample parameter: c = mean # of defects per sample e ccx P( X = x ) = x! E(X) = c x = 0 , 1, 2, . . . Var(X) = c Control Limits for C Chart # of Defects per Sample UCL = c + 3 c LCL = c - 3 c CL = c Estimating C from Initial Data ci = number of defects per sample initial data ci, i=1...m estimate mean number of defects per sample with c= m 1 m c i i=1 12 Example for C Charts 6.40 The number of nonconformities found on final inspection of a cassette deck is shown below. The initial sample consists of 18cassette decks. Is the process in statistical control? 0 1 1 0 2 1 1 3 2 1 0 3 2 5 1 2 1 1 Create a c chart c= 27 = 1.5 defects per sample 18 UCL = c + 3 c = 5.17 LCL = c - 3 c = 2.17 0 CL = c = 1.5 Yes process is in-control. All points within limits. 13 Suppose we implement a c chart to monitor the cassette decks with a sample size of 4 unitsGive control limits this c chart If I use 4 cassettes, the average number of defects per sample will be 4*1.5=6.0 and the c chart is UCL = c + 3 c = 13.35 LCL = c - 3 c = 1.35 0 CL = c = 6.0 14 U Chart for Number of Defects per Unit Convenient Y axis sample size n count # of defects ci sample statistic - plot: ui=ci/n From Baseline data c1cm Estimate m u= c i =1 i n*m Control Limits u UCL = u + 3 n u CL = u LCL = u 3 n 15 Example for U Charts sampl e 1 2 3 4 5 6 7 8 9 10 defect s 10 15 18 20 13 12 15 13 14 16 There are 10 samples in the baseline and each consists of 2 disk drive assemblies. The number of defects in the sample is gi ven above. Show a standard 3sigma u-chart that would be appropriate for monitoring this data. m c i 146 u= = = 7.3 n * m 20 i =1 16 u = 9.86 n CL = u = 7.3 UCL = u + 3 LCL = u 3 u = 4.74 n 17 sampl e 1 2 3 4 5 6 7 8 9 10 Defect s in sampl e 10 15 18 20 13 12 15 13 14 16 Defect s per unit 5 7. 5 9 10 6. 5 6 7. 5 6. 5 7 8 UCL=9.86 CL=7.3 LCL=4.74 Sample 4 is outside UCL iterate and recompute limits with only 9 samples. m u= c i =1 i n*m = 136 = 7.56 18 18 CL=7.56 UCL=10.17 LCL=4.95 19 What would be the control limits for this u-chart with a false alarm rate of 1 percent? UCL = u + 2.54 u = 9.77 n CL = u = 7.56 LCL = u 2.54 u = 5.35 n 20 Summary of Attributes Control Charts Chart Sample Statistic CL p pi fraction defective p c c i # defects per sample ui # defects per unit c u u UCL/LCL p3 p (1 p ) n c3 c u3 21 u n
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Rutgers - ENG - 300
Control Charts for IndividualMeasurementsSometimes repeated measures in asubsample don't make senseoven temperatureinventory levelaccounts payableIf variation in subsample only reflectsmeasurement error, use individualmeasurementsProcess Industr
Rutgers - ENG - 300
Some Useful ApproximationsBinomialPoissonIf np&lt;5 and p&lt;.1 or p&gt;.9Approx withPOISSONIf np&gt;5 or .1&lt;p&lt;.9Approx withNORMAL Approximate Binomial withPoissonNormal Approximate Poisson withNormalApprox withNORMALApproximate Binomial with Poisson
Rutgers - ENG - 300
Accept or reject a lot?Three approaches to lot sentencing :1. Accept with no inspection Cp is 3 or 4; vendor isexcellent; has excellent process control2. 100% inspection critical component, technologyavailable3. Acceptance sampling -Goal is decisio
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS INOPERATIONS RESEARCHLecture 1: Introduction, Administration,Examples of mathematical programsClass Meeting: MTH 2 10:20-11:40am (SEC-209)Recitation W6-7pm (SEC-217)Prof. W. Art Chaovalitwongse(Dr. Chao-va-lit-wongs, Dr
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS INOPERATIONS RESEARCHLecture 2: Chapter 2 3.1Class Meeting: Mon Jan 24th 10:20-11:40amRecitation: Basic linear algebra (matrix operations)Prof. W. Art ChaovalitwongseA Linear Programming Problemis an optimization proble
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS INOPERATIONS RESEARCHLecture 3: Chapter 3.1 - 3.3Class Meeting: Thu Jan 27th 10:20-11:40amRecitation: Introduction to Linear ProgrammingProf. W. Art ChaovalitwongseExample: GTC ProblemWant to determine the number of wre
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS INOPERATIONS RESEARCHLecture 4: Chapter 3.5 3.12Class Meeting: Thu Feb 2nd 10:20-11:40amProf. W. Art ChaovalitwongseExample 1ABC, Inc., manufactures wooden soldiers and trains.Each soldier built: Sell for \$27 and uses
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture6:Chapter4.14.4TheSimplexAlgorithmClassMeeCng:MonFeb7th10:2011:40amProf.W.ArtChaovalitwongse4.1HowtoConvertanLPtoStandardFormBefore the simplex algorithm can be used to solve an LP, theLP must b
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture6:Chapter4.64.12ClassMeeDng:ThuFeb10th10:2011:40amProf.W.ArtChaovalitwongseSimplexandItsGeometrymax z = 3x1 + 2x2s.t.-x1 + 3x2 12x1 + x2 82x1 - x2 10x1, x2 0max z = + 3x1+ 2x2s.t.-x1 + 3x2
Rutgers - ENG - 300
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 8: Chapters 34 Class MeeBng: Thu Feb 24th 10:2011:40am Prof. W. Art Chaovalitwongse Key to Success From the problem statement, IDENTIFY Decision variabl
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 09: Chapter 5 Class MeeAng: Mon Mar 7th 10:2011:40am Prof. W. Art Chaovalitwongse 5.1 A Graphical Approach to SensiDvity Analysis max z = 3X + 10Y Y = -
Rutgers - ENG - 300
540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 10: Chapter 5 Class Mee@ng: Thu Mar 24th 10:2011:40am Prof. W. Art Chaovalitwongse 5.4 What happens to the Op@mal zValue if the Current Basis Is No
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture11:Chapter5ClassMee@ng:MonMar27th10:2011:40amProf.W.ArtChaovalitwongseRecallfromChapter5&gt;6.1If we change the value of b1, then as long as the point where thefinishing and carpentry constraints in
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture12:Midterm2ReviewClassMeeDng:ThuApr7th10:2011:40amProf.W.ArtChaovalitwongseTopicsBigMTwoPhaseGraphicalSensiEvityAnalysisComputerSensiEvityAnalysisMatrixNotaEonMatrixSensiEvityAnalysis100%Rul
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture13:Chapter6.56.10ClassMeeCng:ThuApril14th10:2011:40amProf.W.ArtChaovalitwongse6.5FindingtheDualofanLPAssociated with any LP is another LP called the dual.Knowledge of the dual provides interestin
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture14:Chapter8.18.3ClassMeeCng:MonApril18th10:2011:40amProf.W.ArtChaovalitwongseDescripConManyimportantop@miza@onproblemscanbeanalyzedbymeansofgraphicalornetworkrepresenta@on.Thefollowingnetworkmo
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture15:Chapter9.19.4ClassMeeCng:ThuApril21st10:2011:40amProf.W.ArtChaovalitwongseIntegerProgrammingDeniBon AnIntegerProgrammingproblem(IP)isaLinearProgramming(LP)inwhichsomeorallthevariablesarerequi
Rutgers - ENG - 300
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture17:FinalReview1Prof.W.ArtChaovalitwongseTopics Ch.4:SimplexMethod Ch.5:Sensi@vityAnalysis GraphicalSensi@vityAnalysis LINDOSensi@vityAnalysis(including100%rule) Ch.6:MatrixNota@on SimplexM
Rutgers - ENG - 300
540:311DETERMINISTICMODELSINOPERATIONSRESEARCHLecture18:FinalReview2Prof.W.ArtChaovalitwongseTopics Ch.4:SimplexMethod Ch.5:Sensi@vityAnalysis GraphicalSensi@vityAnalysis LINDOSensi@vityAnalysis(including100%rule) Ch.6:MatrixNota@on SimplexM
Rutgers - ENG - 303
General Course InformationRutgers University, Department of Industrial Engineering540:303 Manufacturing Processes, Spring 2010,Time: MW 1:40-3:00 p.m.Place: HILL -009Course Coordinator and InstructorProfessor Tugrul Ozel, CoRE-208Office Hours: M W
Rutgers - ENG - 303
Engineering Materials andTheirTheir PropertiesManufacturing Processes Spring 2011Prof. T. zelManufacturing ProcessesNet shape processes Bulk Deformation(Forging, Rolling, Extrusion, Drawing) Sheet Metal Forming (Shearing, Bending) Metal Casting
Rutgers - ENG - 303
Chapter 3Structure and Manufacturing Properties ofMetalsMetalsManufacturing Processes Spring 2011Prof. Tugrul OzelTurbine Blades for Jet EnginesFIGURE 3.1 Turbine blades for jet engines, manufactured by three differentmethods: (a) conventionally c
Rutgers - ENG - 303
Chapter 4Surfaces, Tribology, DimensionalCharacteristics, Inspection andProduct Quality AssuranceManufacturing ProcessesProf. Tugrul OzelSurface Characteristics and TribologySurface conditions of a manufacturing part directlyinfluence the processi
Rutgers - ENG - 303
CHAPTER 8MaterialRemovalProcesses:CuttingPart-1Manufacturing ProcessesProf. Tugrul OzelManufacturing Processes: MachiningChapter 8Chapter 9Chapter 9Schematic illustrations of various machining and finishingillfiprocesses.Manufacturing Proce
Rutgers - ENG - 303
CHAPTER 8MaterialRemovalProcesses:CuttingPart-2Manufacturing ProcessesProf. Tugrul OzelLatheOperationsFIGURE 8.40Various cuttingoperations that cantithbe performed on alathe.Manufacturing ProcessesProf. Tugrul OzelDesignations for aRigh
Rutgers - ENG - 303
Chapter 6Bulk DeformationProcessesProcessesManufacturing ProcessesProf. T. zelManufacturing Processes: Forming and ShapingExtrusion/DrawingSchematic illustration of various bulk deformation processesManufacturing ProcessesProf. T. zelBULK DEFOR
Rutgers - ENG - 303
CHAPTER 7Sheet-Metal Forming ProcessesManufacturing ProcessesProf. Tugrul OzelManufacturing Processes: Forming and ShapingSchematic illustration of various sheet metal formingillustration of various sheet metal formingprocessesManufacturing Proces
Rutgers - ENG - 303
CHAPTER 9Abrasive andNon-TraditionalMaterialRemovalProcessesProcessesManufacturing ProcessesProf. Tugrul OzelRelative Knoop Hardness9.2 AbrasivesPCDCBN1. Conventional abrasives: Aluminum oxide (Al2O3) Silicon carbide (SiC)SiliconCarbideAlu
Rutgers - ENG - 303
CHAPTER 10Processing ofPolymers andReinforced Plastics;Rapid Prototyping andRapidRapid ToolingManufacturing ProcessesProf. Tugrul OzelPolymersThe characteristics of polymersinclude: Corrosion resistance and resistance tochemicals Low electri
Rutgers - ENG - 303
CHAPTERCHAPTER 13:MicrofabricationProcesses &amp;NanomanufacturingManufacturing ProcessesProf. T. zelFabrication Sequence forIntegratedIntegrated Circuits Microfabrication processes are utilized in fabrication ofcomponents and systems for microelec
Rutgers - ENG - 303
Large Projects 1.Fully Automated Elevator Maintenance System 2. Injury Proof Office Environment 3. Automated Quality Control for Seal Inspection System 4. Waste Minimization and Revenue MaximizationCutting System5. Shop Mate for Picking up Objects6
Rutgers - ENG - 303
SensorA sensor is an element in a measurement system thatdetects the magnitude of a physical parameter andchanges it into a signal that can be processed by thesystem.Input SignalOutput SignalSensor A sensor is a device that receives a stimulus and
Rutgers - ENG - 303
Arduino Board SelectionArduino Board= Controller + digital and analog I/O + a serial or USB interface to the hostTestLEDDigital I/OPowerLEDResetButtonTX/RXLEDsAnalog InputDESIGN OF ENGINEERING SYSTEMS IMarch 28, 2011Arduino Board SelectionA
Rutgers - ENG - 303
Filters and AmplifiersLow-pass filterDESIGN OF ENGINEERING SYSTEMS IMarch 30, 2011Filters and AmplifiersHigh-pass filterBand-pass filterDESIGN OF ENGINEERING SYSTEMS IMarch 30, 2011Filters and Amplifiers No current flows into the inputs of the o
Rutgers - ENG - 303
Group Meeting Current Status Milestones Key issues or problems Decisions Next Step Timeline Project scope Meeting time Send me an emailDESIGN OF ENGINEERING SYSTEMS IIMarch 21, 2011Electronic Motors Electric motors areby far the mostubiquit
Rutgers - ENG - 303
Stepper Motors Brushed permanent magnet DC motors providecontinuous motion at some controllable speed What if we like to control the position?Brushed or brushless DC motor will work but you may needother components such as encoders to work in closed-
Rutgers - ENG - 303
Belts and Chains FunctionsAmplify torque and reduce speed max speed ratio: 3.5:1Transfer torque from driver to drivenGear: ratio, Belt: high speed/low torque Chain: Low speed/high torqueBelt: high speed/low torque Chain: Low speed/high torqueSpan la
Rutgers - ENG - 303
HomeworkDESIGN OF ENGINEERING SYSTEMS IApril 14, 2011Threaded Fasteners and Power Screws FunctionsFasteners: mechanically joins or affixes two or more objectsFigures from http:/www.nutsandbolts.com/Power Screw: convert rotation to linear motionhtt
Rutgers - ENG - 303
Power Screw and CNCDESIGN OF ENGINEERING SYSTEMS IApril 18, 2011Power Screw and CNCDESIGN OF ENGINEERING SYSTEMS IApril 18, 2011Spring Design Functionsexert forces, or torques and absorb energyHelical or coil springsA spiral torsion springFigur
Rutgers - ENG - 303
Communications Serial CommunicationRS232, USB (universal serial bus),PCIe, Ethernet Parallel Communication Printer, IEEE1284, SCSI, PCI, ATA Wireless Communication Wi-Fi Cellular communicationDESIGN OF ENGINEERING SYSTEMS IIMarch 21, 2011Serial
Rutgers - ENG - 303
Safety Factor and ReliabilityLet S denote the strength random variable and s the stress random variable. The random variabley = (S s) is then related to the reliability of the component by= P( y 0)R(1)When strength and stress random variables have n
University of Texas - CALCULUS - 7234832
tran (pt4954) 4.9 campisi (54970)This print-out should have 10 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.001Find the value of f (1) whenf ( t) = 9 t 2andf (1) = 5,10.0 pointsFind t
University of Texas - CALCULUS - 7234832
tran (pt4954) 5.3 campisi (54970)This print-out should have 6 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.00143.32010.0 pointsA function h has graph242424242-3-40422
University of Texas - CALCULUS - 7234832
tran (pt4954) 5.5 campisi (54970)This print-out should have 7 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.00110.0 pointsFind the value ofThe graph of f has slopedf= 3xdx2 x2 + 1and
University of Texas - CALCULUS - 7234832
tran (pt4954) 6.1 campisi (54970)This print-out should have 6 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.00110.0 pointsExpress the area, A, between the graph off and the x-axis on the
University of Texas - CALCULUS - 7234832
tran (pt4954) 6.2 campisi (54970)This print-out should have 5 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.00110.0 pointsFind the volume, V , of the solid obtainedby rotating the region
University of Texas - CALCULUS - 7234832
tran (pt4954) 6.2 campisi (54970)This print-out should have 5 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.00110.0 points0023, x = 2, x = 3, y = 0x10.0 pointsFind the volume, V , of
University of Texas - CALCULUS - 7234832
CH 302 SUTCLIFFE EXAM 1 SPRING 2011 EQUATIONS760 mm Hg = 760 torr = 1 atmJL . atmR = 8.314R = 0.08206mol.Kmol.Kq = nCm Tq = mCs TCsqunits(J / g K )fus / vap= nHCmunits( J / mol K )fus / vap , molar0H rxn = nH 0 , products nH 0 , react
University of Texas - CALCULUS - 7234832
tran (pt4954) Homework 1 sutclie (51045)This print-out should have 20 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.001 10.0 pointsIf G is positive, then the forward reactionrxnis (sponta
University of Texas - CALCULUS - 7234832
tran (pt4954) Homework 1 sutclie (51045)This print-out should have 20 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.001 10.0 pointsIf G is positive, then the forward reactionrxnis (sponta
University of Texas - CALCULUS - 7234832
tran (pt4954) Homework 2 sutclie (51045)This print-out should have 21 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.NOTE: AFTER QUESTION 15 READCAREFULLY! Some questions will requireyou to
University of Texas - CALCULUS - 7234832
tran (pt4954) Homework 2 sutclie (51045)This print-out should have 21 questions.Multiple-choice questions may continue onthe next column or page nd all choicesbefore answering.NOTE: AFTER QUESTION 15 READCAREFULLY! Some questions will requireyou to
Universidade Federal de Minas Gerais - ENG - 101
MANUAL DE ANLISE TCNICACAPTULO 1INTRODUOCAPTULO 2PREMISSAS BSICAS E BASE CONCEITUAL DA ANLISE TCNICA2.1 - CONSTRUO DE GRFICOS2.2 - TEORIA DO DOW E CONCEITO BSICO DE TENDNCIA2.3 - CONCEITOS DE SUPORTE E RESISTNCIA2.4 - GAPS: TIPOS E SIGNIFICADOS2.
Universidade Federal de Minas Gerais - ENG - 101