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Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,S6-,*,Click to edit Master title style,Operations Management,Statistical Process ControlSupplement 6,1/2549 (IM10),1,Outline,STATISTICAL PROCESS CONTROL (SPC),Control Charts for Variables,The Central Limit Theorem,Setting Mean Chart Limits,Setting Range Chart Limits (,R,-Charts),Using Mean and Range Charts,Control Charts for Attributes,Managerial Issues and Control Charts,PROCESS CAPABILITY,Process Capability Ratio (C,p,),Process Capability Index (C,pk,),ACCEPTANCE SAMPLING,Operating Characteristic (OC) Curves,Average Outgoing Quality,2,When you complete this chapter, you should be able to,Identify or Define,:,Natural and assignable causes of variation,Central limit theorem,Attribute and variable inspection,Process control,LCL and UCL,p-charts and C-charts,Learning Objectives,3,When you complete this chapter, you should be able to,Identify or Define,:,Acceptance sampling,OC curve,AQL and LTPD,AOQ,Producers and consumers risk,Learning Objectives - Continued,When you complete this chapter, you should be able to,Describe or explain,:,The role of statistical quality control,4,Measures performance of a,process,Uses mathematics (i.e., statistics),Involves collecting, organizing, & interpreting data,Objective: provide statistical signal when assignable causes of variation are present,Used to,Control the process as products are produced,Inspect samples of finished products,Statistical Quality Control (SPC),5,Statistical,Quality Control,Process Control,Acceptance Sampling,Variables Charts,Attributes Charts,Types of Statistical Quality Control,6,Natural and Assignable Variation,7,Characteristics for which you focus on defects,Classify products as either good or bad, or count # defects,e.g., radio works or not,Categorical or discrete random variables,Attributes,Variables,Quality Characteristics,Characteristics that you measure, e.g., weight, length,May be in whole or in fractional numbers,Continuous random variables,8,Statistical technique used to ensure process is making product to standard,All process are subject to variability,Natural causes,: Random variations,Assignable causes,: Correctable problems,Machine wear, unskilled workers, poor material,Objective: Identify,assignable,causes,Uses process control charts,Statistical Process Control (SPC),9,Process Control: Three Types of Process Outputs,Frequency,Lower control limit,Size,(Weight, length, speed, etc. ),Upper control limit,(,b),In statistical control,but not capable of producing within control limits.,A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; and,(c),Out of control.,A process out of control having assignable causes of variation.,(a),In statistical control and capable of producing within control limits.,A process with only natural causes of variation and capable of producing within the specified control limits,.,10,The Relationship Between Population and Sampling Distributions,Uniform,Normal,Beta,Distribution of sample means,Standard deviation of the sample means,(mean),Three population distributions,11,Sampling Distribution of Means, and Process Distribution,Sampling distribution of the means,Process distribution of the sample,12,Process Control Charts,13,Show changes in data pattern,e.g., trends,Make corrections,before,process is out of control,Show causes of changes in data,Assignable causes,Data outside control limits or trend in data,Natural causes,Random variations around average,Control Chart Purposes,14,As sample size gets large enough,sampling distribution becomes almost normal regardless of population distribution.,Central Limit Theorem,Theoretical Basis of Control Charts,15,Mean,Central Limit Theorem,Standard deviation,Theoretical Basis of Control Charts,16,Theoretical Basis of Control Charts,Properties of normal distribution,17,Control,Charts,R,Chart,Variables,Charts,Attributes,Charts,X,Chart,P,Chart,C,Chart,Continuous Numerical Data,Categorical or Discrete Numerical Data,Control Chart Types,18,Statistical Process Control Steps,Produce Good,Provide Service,Stop Process,Yes,No,Take Sample,Inspect Sample,Find Out Why,Create,Control Chart,Start,Can we assign causes?,19,Type of variables control chart,Interval or ratio scaled numerical data,Shows sample means over time,Monitors process average,Example: Weigh samples of coffee Plot,X,Chart,20,Control Chart for Samples of 9 Boxes,Variation due to natural causes,17=UCL,16=Mean,15=LCL,Variation due to assignable causes,Variation due to assignable causes,Out of control,1 2 3 4 5 6 7 8 9 10 11 12,Sample Number,21,X,Chart Control Limits,Range for sample i,# Samples,Mean for sample i,From Table S6.1,22,Factors for Computing Control Chart Limits,23,Type of variables control chart,Interval or ratio scaled numerical data,Shows sample ranges over time,Difference between smallest & largest values in inspection sample,Monitors variability in process,Example: Weigh samples of coffee Plot,R,Chart,24,R,Chart Control Limits,Range for Sample,i,# Samples,From Table S6.1,25,Steps to Follow When Using Control Charts,Collect 20 to 25 samples of,n=4,or,n=5,from a stable process and compute the mean.,Compute the overall means, set approximate control limits,and calculate the preliminary upper and lower control limits.,If the process is not currently stable, use the desired mean instead of the overall mean to calculate limits.,Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits.,26,Steps to Follow When Using Control Charts - continued,Investigate points or patterns that indicate the process is out of control. Assign causes for the variations.,Collect additional samples and revalidate the control limits.,27,Mean and Range Charts Complement Each Other,28,Type of attributes control chart,Nominally scaled categorical data,e.g., good-bad,Shows % of nonconforming items,Example: Count # defective chairs Plot,Chair is either defective or not defective,p,Chart,29,p,Chart Control Limits,# Defective Items in Sample i,Size of sample i,z,= 2 for 95.5% limits;,z,= 3 for 99.7% limits,30,P-Chart for Data Entry Example,UCL,p,LCL,p,31,Type of attributes control chart,Discrete quantitative data,Shows number of nonconformities (defects) in a unit,Unit may be chair, steel sheet, car etc.,Size of unit must be constant,Example: Count # defects (scratches, chips etc.) in,each,chair of a sample of 100 chairs; Plot,c,Chart,32,c,Chart Control Limits,# Defects in Unit i,# Units Sampled,Use,3 for 99.7% limits,33,Patterns to Look for in Control Charts,34,Deciding Which Control Chart to Use,Using an X and R chart:,Observations are,variables,Collect 20-25 samples of n=4, or n=5, or more each from a stable process and compute the mean for the X chart and range for the R chart.,Track samples of n observations each.,Using the P-Chart:,We deal with fraction, proportion, or percent defectives,Observations are,attributes,that can be categorized in two states,Have several samples, each with many observations,Assume a binomial distribution unless the number of samples is very large then assume a normal distribution.,35,Deciding Which Control Chart to Use,Using a C-Chart:,Observations are,attributes,whose defects per unit of output can be counted,The number counted is often a small part of the possible occurrences,Assume a Poisson distribution,Defects such as: number of blemishes on a desk, number of typos in a page of text, flaws in a bolt of cloth,36,Process Capability Ratio, C,p,37,Process Capability C,pk,Assumes that the process is,:,under control,normally distributed,38,Meanings of C,pk,Measures,C,pk,= negative number,C,pk,= zero,C,pk,= between 0 and 1,C,pk,= 1,C,pk, 1,39,Form of quality testing used for incoming materials or finished goods,e.g., purchased material & components,Procedure,Take one or more samples at random from a lot (shipment) of items,Inspect each of the items in the sample,Decide whether to reject the whole lot based on the inspection results,What Is Acceptance Sampling?,40,Set of procedures for inspecting incoming materials or finished goods,Identifies,Type of sample,Sample size (,n,),Criteria (,c,) used to reject or accept a lot,Producer (supplier) & consumer (buyer) must negotiate,What Is an Acceptance Plan?,41,Shows how well a sampling plan discriminates between good & bad lots (shipments),Shows the relationship between the probability of accepting a lot & its quality,Operating Characteristics Curve,42,% Defective in Lot,P(Accept Whole Shipment),100%,0%,Cut-Off,1,2,3,4,5,6,7,8,9,10,0,Return whole shipment,Keep whole shipment,OC Curve100% Inspection,43,OC Curve with Less than 100% Sampling,P(Accept Whole Shipment),100%,0%,% Defective in Lot,Cut-Off,1,2,3,4,5,6,7,8,9,10,0,Return whole shipment,Keep whole shipment,Probability is not 100%: Risk of keeping bad shipment or returning good one.,44,Acceptable quality level (AQL),Quality level of a good lot,Producer (supplier) does not want lots with fewer defects than AQL rejected,Lot tolerance percent defective (LTPD),Quality level of a bad lot,Consumer (buyer) does not want lots with more defects than LTPD accepted,AQL & LTPD,45,Producers risk (,),Probability of rejecting a good lot,Probability of rejecting a lot when fraction defective is AQL,Consumers risk (),Probability of accepting a bad lot,Probability of accepting a lot when fraction defective is LTPD,Producers & Consumers Risk,46,An Operating Characteristic (OC) Curve Showing Risks, = 0.05 producers risk for AQL,= 0.10,Consumers risk for LTPD,Probability of Acceptance,Percent Defective,Bad lots,Indifference zone,Good lots,LTPD,AQL,0 1 2 3 4 5 6 7 8,100,95,75,50,25,10,0,47,OC Curves for Different Sampling Plans,1,2,3,4,5,6,7,8,9,10,0,% Defective in Lot,P(Accept Whole Shipment),100%,0%,LTPD,AQL,n = 50, c = 1,n = 100, c = 2,48,Average Outgoing Quality,Where: P,d,= true percent defective of the lot,P,a,= probability of accepting the lot,N = number of items in the lot,n = number of items in the sample,49,Negotiate between producer (supplier) and consumer (buyer),Both parties attempt to minimize risk,Affects sample size & cut-off criterion,Methods,MIL-STD-105D Tables,Dodge-Romig Tables,Statistical Formulas,Developing a Sample Plan,50,Statistical Process Control - Identify and Reduce Process Variability,Lower specification limit,Upper specification limit,(a) Acceptance sampling Some bad units accepted; the “lot” is good or bad,(b) Statistical process control Keep the process in “control”,(c) c,pk,1 Design a process that is in control,51,
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