StatisticalProcessControl(SPC).pptx

Materials QualityPCS Training - Rev 2 Feb 23 20016/25/97Materials QualityPCS Training - Rev 2 Feb 23 2001Create Measurement PlanEstablish Monitor (SPC)Implement Response Flow Checklist (RFC)Element 1Element 2Element 32Materials QualityPCS Training - Rev 2 Feb 23 2001 Introduction What is SPC What is Stability What is a Control Chart How to Set-up a Control Chart Type of Control Charts Available How to Calculate the Control Limits SPC Trend Rules When to Revise Control Limits Process Capability Study Spec limits VS Control Limits Stability VS Capability Control Chart Reduction/Elimination SPC Expectations3Materials QualityPCS Training - Rev 2 Feb 23 2001 Statistical Anything that deals with the collection, analysis, interpretation & presentation of numerical data Gaining information for making informed decisions Process Combination of machines, tools, methods, materials & people employed to attain process specification A similar procedure/event that is happening repetitively Control To keep something within a desired condition Make something behave the way we want it to behaveThe use of statistical techniques such as control charts to analyze a process, take appropriate actions to achieve & maintain a stable process, & improve process capability. 4Materials QualityPCS Training - Rev 2 Feb 23 2001What is Stability? A process is said to be Stable if it has the following properties: Pattern appears random Constant process mean Uniform variability over time No trends, runs, shifts, erratic ups & downs Important for many reasons: Increased productivity of engineering & manufacturing personnel Predictable, repeatable results within a specified range5Materials QualityPCS Training - Rev 2 Feb 23 2001What is a Control Chart? A trend chart with control limits Graphical representation of process performance, where data is collected at regular time sequence of production Valuable tool for differentiating between common cause and special cause variation Evaluating whether a process is or is not in a state of statistical control It lets the data talk by itself & basis for data-driven decisions6Materials QualityPCS Training - Rev 2 Feb 23 2001Control LimitsA typical control chart consists of three lines :-Upper ControlLimit (UCL)Center Line(CL)Lower ControlLimit (LCL)CL: The average (measure of location) process performance when the process is in-controlUCL & LCL: The range of usual process performance when the process is stable. Lines drawn 3 standard deviations (3 sigma) on each side of the center line.7Materials QualityPCS Training - Rev 2 Feb 23 2001Control Chart Assumptions Process Stability The process must be in statistical control Normality The underlying process distribution is normalNote: If the assumptions are not met, the control limits calculated are misleading & do not accurately indicate 3 sigma control limits. See your site statistician for advice on calculation methods when assumptions are violated.8Materials QualityPCS Training - Rev 2 Feb 23 2001Test for Control Chart Assumptions Process Stability (no outliers) Screen out outliers from the database before computing final control limits by using a control chart. Any point beyond either control limit is an outlier. Report number of outliers screened. Normality Plot a normal probability plot of the data or overlay a normal curve over the histogram. Normally distributed data will roughly fall on a straight line. Test for normality by using Shapiro-Wilk W test in JMP 9Materials QualityPCS Training - Rev 2 Feb 23 2001 Select appropriate type of control chart to be used Gather data to establish the control chart. A minimum of 30 subgroups is required over a time frame as determined by the sampling plan. Plot the data in time order on a Trend ChartHow to Set-up a Control Chart?10Materials QualityPCS Training - Rev 2 Feb 23 2001 Compute the control limits & plot them on the trend chart Outliers identification & exclusion Exclude the Out-of Control (OOC) points or outliers for which there are verified/confirmed special causes from the chart Re-compute the control limits, excluding the OOC points If there are fewer than 30 points remaining at any time, collect more data. Its very important that the control limits are calculated using at least 30 subgroups.How to Set-up a Control Chart?Note: Refer to Appendix A for Control Charts for Limited Production, i.e. 30 subgroups.11Materials QualityPCS Training - Rev 2 Feb 23 2001 Validate the computed control limits against data collected by re-plotting the control chart with data & new control limits Do the limits detect known problems? Are the limits too sensitive? Would they flag problems you do not know how to react to? Use the control limits established to monitor the critical parameter identified For each parameter, every machine should have a separate control chart with separately computed control limitsHow to Set-up a Control Chart?12Materials QualityPCS Training - Rev 2 Feb 23 2001Control Chart ClassificationsClassifications of control charts are depending onthe type of data Variables data A characteristic measured on a continuous scale resulting in a numerical value Examples: Void Size, Bond Pull Strength, Coplanarity, Ball Height, etc. Attributes data A characteristic measured by # of conforming & non-conforming to a specification. Output is classified as pass/fail or accept/reject. E.g. Broken Wire, Lifted Bond, FM, Chipping, Bent Lead, etc. Can be expressed in terms of fraction, percentage, count or DPM13Materials QualityPCS Training - Rev 2 Feb 23 2001 Control Chart When to Use (Guidelines only)? X-R - when subgrouping of samples or (Mean-Range) Chart measurements is applicable - n 1014Materials QualityPCS Training - Rev 2 Feb 23 2001Why MR Method is used to determine Control Limits for Mean & Variability (Range & Standard Deviation) Chart? Most batch production processes have a larger run-to-run variation than within-run variation Traditional control chart formulas developed in the 20s by Walter Shewhart considerably underestimate control limits, i.e. too narrow 15Materials QualityPCS Training - Rev 2 Feb 23 2001Traditional vs. MR Method859095100105110115OrderAvg=99.1LCL=96.5UCL=101.8Mean of Meas.708090100110120130OrderAvg=99.1LCL=76.7UCL=121.5Mean(Meas.)Traditional control chart formulasare used.Moving Range (MR) Method is used.X-bar Control ChartX-bar Control Chart16Materials QualityPCS Training - Rev 2 Feb 23 2001X - S Chart ConceptConsists of Two Portions: X Chart Plots the mean of the X values in the sample Shows the changes of the mean of one sample to another S Chart Plots the standard deviation of a sample Shows the changes in dispersion or process variability of one sample to another17Materials QualityPCS Training - Rev 2 Feb 23 2001Computing Control Limits for X - S Chart Obtain at least k = 30 subgroups Compute the Mean for each subgroup of size n Compute the Standard Deviation for each subgroup Compute the Moving Range for each subgroup mean, MRXi = | Xi - Xi-1 | Compute the Moving Range for each subgroup range, MRSi = | Si - Si-1 |18Materials QualityPCS Training - Rev 2 Feb 23 2001Computing Control limits for X - R Chart Compute the Overall Mean, X = (X1 + X2 + X3 . + Xk) / k Compute the Average of Range, S = (S1 + S2 + S3 . + Sk) / k Compute the Average of Moving Range for the mean, MRX = (MRX2 + MRX3 + MRX4 . + MRXk) / (k - 1) Compute the Average of Moving Range for the range, MRS = (MRS2 + MRS3 + MRS4 . + MRSk) / (k - 1)=19Materials QualityPCS Training - Rev 2 Feb 23 2001 Compute the Control Limits: Draw the control limits on both the X - S chart respectively If LCL (S) 0, put as 0 or N/AX ChartUCL (X) = X + 2.66MRXCL (X) = XLCL (X) = X - 2.66MRX=Computing Control limits for X - R ChartS ChartUCL (S) = S + 2.66MRSCL (S) = SLCL (S) = S - 2.66MRS20Materials QualityPCS Training - Rev 2 Feb 23 2001ObservationsMeanMoving RangeS. D.Moving RangeSubgroup #12345(X - bar)(MRX)(S)(MR S )18.07.78.18.07.87.92-0.16-27.16.97.47.37.27.180.740.190.0338.07.57.67.87.97.760.580.210.02:307.57.87.97.87.67.720.700.160.04Average7.640.680.190.03 X ChartUCL (X) = X + 2.66MRX= 7.64 + 2.66(0.68) = 9.45CL (X) = X = 7.64LCL (X) = X - 2.66MRX= 7.64 - 2.66(0.68) = 5.83Example of Computing Control Limits for X - S Chart S ChartUCL (S) = S + 2.66MRS= 0.19 + 2.66(0.03) = 0.27CL (S) = S = 0.55 LCL (S) = S - 2.66MRS= 0.19 - 2.66(0.03) = 0.1121Materials QualityPCS Training - Rev 2 Feb 23 2001Open the dataset Thickness.jmp. 1. Compute the mean for each lot. Select Summary from the Tables menu. Select Lot as the Group variable. Highlight Thickness & select Mean from the Statistics menu. Then, highlight Thickness & select Std Dev from the Statistics menu. Click OK.2. Create an individuals control chart using the table of lot means & ranges. Select Control Chart from the Graph menu. Select Mean(thickness) & StdDev(Thickness) as the Process variable. Select Lot as the Sample Label variable. Verify option settings. Chart Type is “IR”. Individual Measurement box is selected. Moving Range box is not selected. K-sigma is selected, and K = 3. Range Span = 2. Click on OK.Example of Computing Control Limits for X - S Chart using JMP22Materials QualityPCS Training - Rev 2 Feb 23 2001WARNINGS:Group / Summary will sort the new table in alphabetical order of the grouping variable. Control charts must always be plotted in time order. Therefore, if the summary table is not in time order, you will have to sort the table in correct time order before making the control chart. Example of Computing Control Limits for X - S Chart using JMPLCL (S) = 023Materials QualityPCS Training - Rev 2 Feb 23 2001Exercise 1Open the dataset Exer1.jmp. Compute the X-S control limits using JMP for lead width. - What are the control limits?- Is the process stable?24Materials QualityPCS Training - Rev 2 Feb 23 2001Interpretation of X - S ChartSome special causes of out-of-control for X Chart Changes in machine setting or adjustment MS-to-MS technique inconsistent Changes in material S Chart Machine in need of repair or adjustment New MSes Materials are not uniform25Materials QualityPCS Training - Rev 2 Feb 23 2001Attributes Control Charts Attribute control charts are useful when it is difficult or impractical to monitor a process numerically (on a continuous scale) A defect is an individual failure to meet a single requirement A defective unit is a unit that contains one or more defects26Materials QualityPCS Training - Rev 2 Feb 23 2001Control Charts For AttributesControl Chart Symbol Descriptionp Chartp% Defectivenp chartnp# defective27Materials QualityPCS Training - Rev 2 Feb 23 2001p Chart Concept It plots proportion of defective units in a sample The proportion of defective units in a sample can be in terms of fraction, percent or dpm It allows us to chart production processes where sample size cannot be equal28Materials QualityPCS Training - Rev 2 Feb 23 2001Computing Control Limits for p Chart with MR-Method Obtain at least k = 30 subgroups or lots. Data collected in # of units inspected & # of units rejected. Compute the defective rate from the ith lot (i =1,2,.,k),pi = # of units rejected / # of units inspected Compute the control limits using:UCL (p) = p + 2.66MRpCL (p) = pLCL (p) = p- 2.66MRp When LCL UCL or Point LCL For an automated SPC system with automated application of SPC trend rules, its highly recommended to add 5th rule to detect large shifts in mean, (i.e. 2 out of 3 rule) Add other rules depending upon process knowledge ability to respond criticality of the monitor sensitivity requirements for the monitor47Materials QualityPCS Training - Rev 2 Feb 23 2001Trend Rule Recommendations Only use the trend rules that signal process instabilities for which you are capable of responding Justification needed for not using other SPC trend rules Std dev & range charts may choose not to react to Point 1.0 Definitely a problem : |Change Ratio| 1.553Materials QualityPCS Training - Rev 2 Feb 23 2001Given Thickness.jmp example:UCLcurrent = 130.0LCLcurrent = 70.0Newly collected data resulted the following:UCLcalc = 119.41LCLcalc = 78.72 run-run(calc) = 2.66 MR / 3 = 20.35 / 3 = 6.78UCL Change Ratio= (UCLcalc - UCLcurrent) / run-run(calc) = -1.56LCL Change Ratio = (LCLcurrent - LCLcalc) / run-run(calc) = -1.28= Indicates a need to change the current control limits!Change Ratio ExampleMaterials QualityPCS Training - Rev 2 Feb 23 2001Process Capability20040060080010001300103050LSLUSL25507550150250350LSLUSL Process capability is the ability of a process to meet specifications. A process must be stable before its capability can be computed. Not Capable Capable A capability index is a statistic that quantifies & describes the capability of a process55Materials QualityPCS Training - Rev 2 Feb 23 2001Specification Limits The region where product is known to function well in terms of performance, yield, reliability, or other desired outcome Acceptable range of values for a product parameter Define what is acceptable/unacceptable product Determined by Design requirements & simulation models Engineering judgement (typically product eng. & integration) Customer agreement/requirements Data driven validation: Process window characterization Historical data identifying in-line or EOL problems Used to determine process capability56Materials QualityPCS Training - Rev 2 Feb 23 2001Control Limits Calculated from data, based on actual process performance Describe the natural range of performance of a stable process Describe the amount of natural process variation Used to determine process stability57Materials QualityPCS Training - Rev 2 Feb 23 2001Spec Limits vs. Control LimitsSpec Limits Based on performance required of the product What the customer wants - “what we want” Tells us when to disposition the product/material Apply only to individual (raw) data valuesControl Limits Based on actual historical process performance What the process delivers - “what we get” Tells us when to take action on the process/equipment Apply to summary statistics (e.g. : X-bar, std dev, range, etc. charts)Never use spec limits on a control chart!58Materials QualityPCS Training - Rev 2 Feb 23 2001Stability vs. Capability A process is said to be in statistical control when the only source of variation is of natural causes, (i.e. no special causes variation present) A process is said to be capable when variation from natural causes is reduced such that it can meet product specification tolerance when the control limits are well within the specification limits A process is said to be not capable if the control limits are outside the specification limits59Materials QualityPCS Training - Rev 2 Feb 23 2001Exercise 302040608010012014016018020002468specspeccontrolcontrol02468020406080100120140160180200specspeccontrolcontrolInterpretation : Y/N_Stable_CapableInterpretation : Y/N_Stable_Capable60Materials QualityPCS Training - Rev 2 Feb 23 200102468020406080100120140160180200specspeccontrolcontrolInterpretation : Y/N_Sta