1、,SPC Basics,SPC Implementation Model,Cells, process improvement teams, MCABS, etc.,Can I predict where the next measurement will be?,CONTROL:,CAPABILITY:,CENTERING:,Pareto of SRR by P/N,A B C D,Brainstorm Ideas!,Allows the process to talk to you Is the window to making better decisions about the pro
2、cess Allows you to describe the process behavior Gives a picture of the process Provides factual information about the process, operation, product, cause, problem or improvement Eliminates guesswork Changes problem solving from dealing with OPINIONS to dealing with FACTS People can usually agree on
3、facts,Data,SPC Data Collection,Ask the following questions: What is the purpose? Why are we doing it? What is the exact nature of the problem we are trying to solve? Is valid data already available? How will data be gathered? Measuring device Special form Special instructions What is the PLAN? Who,
4、what, when, where and how? How will the data be analyzed and presented? Should we measure the entire POPULATION or a SAMPLE of the population? Should the sample data consist of random measurements or consecutive measurements? How much data is needed?,Planning for Data Collection,SPC Data Collection
5、- continued,1. Small VariationNot “Targeted”,2. Large VariationNot “Targeted”,3. Small VariationProperly ”Targeted”,4. Large VariationProperly ”Targeted”,A small variation not “targeted” can be adjusted to hit the bullseye.A large variation not targeted must be improved before it can hit the bullsey
6、e.,EXERCISE: Which bullseye represents:Accuracy & No Precision _Precision & No Accuracy _Accuracy & Precision _No Accuracy & No Precision _,Examples of Variation - Accuracy vs. Precision,Sigma ( ) The measure a variability (spread and/or precision) within a set of data.Range (R) Another measure of v
7、ariability in a set a data, arrived at by taking the difference of the highest value in the sample and subtracting the lowest value from it. The range is less sensitive at determining process variability than Sigma.X-bar (X) The measure of the average (mean and/or accuracy) of a set of data.,Quick R
8、eview of Some SPC Basics,Assessing Accuracy and Precision,Accuracy Refers to the location of the process Measured by the average (or “mean”)of the data,Measures of Variation,Precision Refers to the variability of the process Measured by either the range or standard deviation (sigma) Range = R = high
9、 value - low value Sigma = S = = more precise measure of variation than the range Sigma is used to make predictions about a process performance Sigma is calculated using all data from a sample, not just the high and low values= S = sample standard deviation,Symbol X,Range,X = Center of Data,n-1,n-1,
10、Standard Deviation,Measures of Variation (cont.),Standard deviation is the square root of the average squared deviation of each measurement from the mean.,Sx =,xxxx x xx x xx x x x xx x x x x x x x x x x x x x,11 12 13 14 16 17 18 19,X = 15,4 3 2 1 0 1 2 3 4,Distance from X,M,Calculating the Standar
11、d Deviation,Measures of Variation (cont.),Data = 12, 14, 13, 15, 18, 16, 18, 16, 14, 14,Xi = 150,n = 10,(Xi - X)2 =,Xi n,150 10,X =,=,Sxi =,(Xi - X)2,n-1,M,M,M,M,WHAT ARE THE THREE “Cs OF SPC?,CONTROL, CAPABILITY and CENTERING,What are the three questions they ask?,CONTROLMeasures: Processbehavior,C
12、APABILITY (Cp, Pp)Measures: PrecisionKey parameter: Range or Sigma,CENTERING (Cpk, Ppk)Measures: AccuracyKey parameter: Xbar, the Mean,asks:,asks:,asks:,Am I able to predict where the,next part will be?,Can I meet the required engineering tolerance from the B/P or operation sheet 100% of the time.,A
13、m I targeted to my NOMINAL,dimension?,X,LSL,USL,NOMINAL,X,LSL,USL,NOMINAL,Quick Review of Some SPC Basics,Sampling,SAMPLE,POPULATION,POPULATION,SAMPLE,Refers to all persons, objects, items, dimensions, etc., under consideration.,Refers to a portion of the population.,Samples are taken to represent t
14、he population.,Samples save time, money, or product when seeking information about the population.,SPC Data Collection - continued,SPC Data Collection - continued,Advantages of Sampling,Sample Size,How large a sample is necessary?,Too small a sample size increases the risk of not getting a true pict
15、ure of the population.,Too small a subgroup may not detect a change in the process.,Sampling tables based on the laws of probability are used for evaluation of lots.,If the proper sampling method is used, 20 subgroups of data provides a representative picture of most populations (20 subgroups of dat
16、a should be the minimum collected).,SPC Data Collection - continued,Importance of Valid Data,SPC Data Collection - continued,Types of Variation,SPC Data Collection - continued,Process Stability,STABLE,A STABLE process contains only COMMON CAUSE variations and remains centered on the targeted value o
17、ver time:,SMALL VARIATION,TIME,LARGE VARIATION,TIME,SPC Data Collection - continued,Process Stability (cont.),UNSTABLE,An UNSTABLE process is affected by SPECIAL CAUSE variations which cause the process to move away from the targeted value, or change in the amount of variation.,CONSTANT VARIATION, C
18、HANGING LOCATION (SHIFTING),TIME,CHANGING VARIATION, CONSTANT LOCATION,TIME,SPC Data Collection - continued,Variation is the Enemy of Quality,EXCESSIVE VARIATION IS NON-COMPETITIVE,LARGE VARIATION IS EXPENSIVE,SMALL VARIATION IS THE GOAL,NO VARIATION IS IMPOSSIBLE,BENEFITS OF REDUCING VARIATION,1. M
19、ore uniform product,2. Reduce cost by economic targeting of process average,3. Design optimization,4. Less costly to control,5. Process can tolerate minor disturbances,6. Avoid scrap, rework and repair (SRR),7. Reduce internal & external costs of quality,8. Improved reliability,9. Reduce appraisal c
20、osts of quality,10. Customer satisfaction,SPC Data Collection - continued,Process Capability - Cp,Cp = Process Potential Index Formula: Cp = Engineering Tolerance (ET)/Natural Tolerance (NT) Where: ET = Upper Specification Level - Lower Specification LevelNT = Natural Tolerance = 6 X SigmaSigma = Av
21、erage Range/d2Whats it used for: Measures the short-term process precision for a given Key Characteristic - essentially it measures Machine Capability Short-term process capability is computed using the short-term process variation (Rbar/d2). This is the machine and gage variation at a certain momen
22、t in time (last 20-30 pieces made) If the gauge variation, as measured by a gauge capability study, is less than 20%. .we can conclude the key process input driving the variation in the short-term is the machine.What question does Cp ask? Does the process have the precision to potentially make every
23、 part 100% to blueprint specification at this moment in time?,GOAL: Cp greater than or equal to 1.33 (equates to a 63 DPM rate or better).,Cpk = Process Potential Index that Accounts for Centering Formula: Whats it used for: Measures the short-term process accuracy for a given Key Characteristic - e
24、ssentially it measures how close to the targeted value the process is running at. Cpk is the smaller of Cpl or Cpu, depending which side of the tolerance the process is shifted towards. Cpk should be compared to Cp. The closer Cpk is to Cp, the more centered the process is running. Cpk is affected b
25、y different operators, shifts, raw materials, tool adjustments as well as machine and gage error.What questions does Cpk ask? Is the process targeted to the NOMINAL dimension, i.e, is the process centered? If a shift is present within the process, should I be concerned?,GOAL: Cpk greater than or equ
26、al to 1.33 (equates to a 63 DPM rate or better).,Cpk = Minimum,Process Average (Xbar) - Lower Spec. Limit (LSL)Three Sigma (3 ),Upper Spec. Limit (USL) - Process Average (Xbar)Three Sigma (3 ),or,Cpl,Cpu,What is Process Capability?,Cp & Cpk,LSL,USL,NT = 6o,ET = USL - LSL,Cp 1.0,X,X,3o,USL - X,Cp 1.0
27、,Cpk 1.0,PRECISION,Cp MEASURES,ACCURACY,Cpk MEASURES,OF,A PROCESS,OF,A PROCESS,Cpk RATIO ANSWERS THE QUESTION:,“AM I TARGETED TO THE NOMINAL DIMENSION?“,Cp RATIO ANSWERS THE QUESTION:,“CAN I MEET THE ENGINEERING TOLERANCE,100% OF THE TIME?“,Cpk measures the distance between Xbar and the nearest spec
28、,and compares that to 3-sigma (one-half of the bell curve).,Cp & Cpk (cont.),Lets say that:,Natural Tolerance = NT = 6,Engineering Tolerance = ET = USL - LSL,Cp = ET/NT,then:,Cp = USL - LSL,6,If Cp = 1.0 then the process is capable (but barely!).,If Cp 1.0, then the process is not capable.,If Cp 1.0
29、, then the process is more than capable.,GOAL: Cp greater than or equal to 1.33.,Cp tells us if the process is capable of meeting specs. However it does not,tell us if the process is centered in the middle of the specs.,Cp NOTES:,Cp & Cpk (cont.),Therefore, another index was designed to help us dete
30、rmine if the process is centered. We call this index Cpk.,Cpk = MINIMUM (Cpl, Cpu) = MINIMUM,Cpl = X - LSL,3,Cpu = USL - X,Use the smaller,of these two,formulas .,Cpk NOTES:,Cpk can never be greater than Cp (mathematically impossible).,If Cpk = Cp, then the process is centered in the middle of the s
31、pecs.,If Cpk Cp, then the process is not centered.,If Cpk 1.0, then even if the process is not centered properly nothing will be out-of-spec.,GOAL: Cpk greater than or equal to 1.33.,3,Process Capability (cont.),Unilateral vs. Bilateral Tolerances,How do we handle capability analysis for two-sided t
32、olerances?BILATERAL dimensions (i.e., diameters, linear dimensions, etc.)How do we handle capability analysis for one-sided tolerances?UNILATERAL MAXIMUM dimensions (i.e., runout, flatness, etc.)UNILATERAL MINIMUM dimensions (i.e., wall, thickness, etc.),Process Capability (cont.),Bilateral Toleranc
33、es,BILATERAL Dimensions (i.e., Diameters, Linear Dimensions, etc.),LSL,USL,X,NOMINAL,Cp,=,USL - LSL,6,(Where ),d,2,R,=,CONVENTIONAL CONTROL CHART CAPABILITY ANALYSIS:,GOAL: Cp & Cpk 1.33,Cpk = MINIMUM Cpl, Cpu , where:,Cpl = X - LSL,Cpu = USL - X,3,and,Process Capability (cont.),Unilateral Maximum T
34、olerances,ZERO,USL = MAX,X,Cpu = USL - X,GOAL: Cpu 1.33,CAPABILITY ANALYSIS:,Now it is time to change the rules for Cpk analysis as illustrated for Bilateral,tolerances. Since it is assumed smaller values are always superior to larger,values, the most meaningful capability index for MAXIMUM toleranc
35、es will be:,Cpu ANSWERS:,Is there a probability of making product beyond,the Maximum tolerance allowed?,EXAMPLES:,Process Capability (cont.),Unilateral Minimum Tolerances,Cpl = X - LSL,GOAL: Cpl 1.33,CAPABILITY ANALYSIS:,Since it is assumed larger values are always superior to smaller,values, the mo
36、st meaningful capability index for MINIMUM tolerances will be:,Cpl ANSWERS:,Is there a probability of making product below,the Minimum tolerance allowed?,LSL = MIN.,X,EXAMPLES:,Control Charts.,are a graphic representation of a process.show plotted values of some statistic gathered from thatprocess.h
37、ave one or two control limits. Control limits define the maximum and minimum values expected to be produced by the process.have two basic uses: Determines if a process is in control, I.e., is the process predictable. Used as a level two mistake-proofing device in order to maintain control.,Control C
38、harts (cont.),UPPER CONTROL,LIMIT (UCL),LOWER CONTROL,LIMIT (LCL),CENTRAL LINE (X),TIME,Plotted points from an in-control process will behave in a,statistically predictable manner.,Control limits define the amount of variation to be expected,in plotted points if the process is consistent over time.,
39、The maximum value expected to be seen.,The minimum value expected to be seen.,The average value expected to be seen.,Questions In Control Charting,What sources of variation are to be detected by the Control Chart?,How valid is the measurement process used to collect the data?,How does an Operator re
40、act to an out-of-control point/situation?,How does management react to processes that are out-of-control or not capable?,Will the data collected on the Control Chart answer the questions people have aboutthe process?,What other groups will utilize this Control Chart data for constructive purposes?,W
41、here To Apply Control Charts,As required by the Customer based on form, fit, function and or complaints.Problem areas (initiated from QCPC turnbacks, high scrap & rework).Critical locating dimensions.,Ones goal in life is not to wallpaper the walls of our companys manufacturing and office areas with
42、 charts.,Cautions in Over-Adjusting a Process,Control chart also tells the Operator when to leave the process alone or there will be a risk of incurring the following losses due to over-correcting:1. The labor required to make the adjustments and the downtime of the assembly area.2. Unnecessary adju
43、stments will increase the variability of a stable process. An excessive number of adjustments(over-correcting or knob twiddling) can increase the 6-sigma (natural) tolerance by up to 41%.,LSL,USL,NOMINAL,X,Original 6-Sigma Spread,Spread Resulting From Unnecessary Adjustments,Shift Distribution from
44、Unnecessary AdjustmentsOriginal Distribution,Control Chart Interpretation,Below summarizes the patterns on a control chart that might indicate a Special Cause of variation may be present in the process. Investigate for a special cause if one of these patterns should develop on a control chart you ar
45、e using to monitor a process.,UCLx,LCLx,X,A,B,C,C,B,A,Fixture Moved,POSSIBLE CAUSES Sticky Gauge Worn Die Drift in Controls Etc.,POINT OUTSIDE CONTROL LIMIT,RUN OF EIGHT POINTS ON THE SAME SIDE OF THE CENTER LINE,SEVEN POINTS IN A ROW STEADILY INCREASING (OR DECREASING),FOURTEEN POINTS IN A ROW ALTE
46、RNATING UP & DOWN,STRATIFICATION - POINTS HUGGING THE CENTERLINE,POSSIBLE CAUSES Inadequate Gauge Resolution Improvement toProcess Gauge Sticking Etc.,Quick Review of Some SPC Basics,WHAT ARE THE THREE “Cs OF SPC?,CONTROL, CAPABILITY and CENTERING,What are the three questions they ask?,CONTROLMeasur
47、es: Processbehavior,CAPABILITY (Cp, Pp)Measures: PrecisionKey parameter: Range or Sigma,CENTERING (Cpk, Ppk)Measures: AccuracyKey parameter: Xbar, the Mean,asks:,asks:,asks:,Am I able to predict where the,next part will be?,Can I meet the required engineering tolerance from the B/P or operation shee
48、t 100% of the time?,Am I targeted to my NOMINAL,dimension?,X,LSL,USL,NOMINAL,X,LSL,USL,NOMINAL,Xbar-R Control Charts,Works with small subgroups of data plotted over time. Subgroup sizes are typically 3, 4 & 5. Subgroups composed of similar pieces (homogeneous). Time between plotted subgroups may var
49、y based on experience. More time between plotted subgroups for consistent and capable processes . Less time for processes more susceptible to inconsistencies.Collect at least 20 subgroups of data prior to calculating control limits.Plotted points are the average values from each subgroup measured.The Range Chart is independent of the Averages Chart. Range = High value - low value (for each subgroup).,
