Basic Training for Statistical Process Control 12/5/2018 Basic Training for Statistical Process Control Process Capability & Measurement System Capability Analysis Process Capability Analysis

Process Capability Analysis Outline Process Capability Natural Tolerance Limits Histogram and Normal Probability Plot Process Capability Indices Cp Cpk Cpm & Cpkm Measurement System Capability Using Control Charts Using Factorial Experiment Design (ANOVA) Hands On Measurement System Capability Study 12/5/2018 Process Capability Analysis

Process Capability Analysis Process Capability Analysis (PCA) Is only done when the process is in a state of Statistical Control Meaning: NO SPECIAL CAUSES are present Process does not have to be centered to do PCA Yield will improve if process is centered, but the value is in knowing what / where to improve the process PCA is done periodically when the process has been operating in a state of statistical control Allows for measuring improvement over time Allows for marketing your competitive edge 12/5/2018 Process Capability Analysis

Process Capability - Timing Reduce Variability Identify Special Causes - Good (Incorporate) Improving Process Capability and Performance Characterize Stable Process Capability Head Off Shifts in Location, Spread Identify Special Causes - Bad (Remove) Continually Improve the System Process Capability Analysis is performed when there are NO special causes of variability present – ie. when the process is in a state of statistical control, as illustrated at this point. Time Center the Process LSL 0 USL 12/5/2018 Process Capability Analysis

Process Capability Analysis Process Capability is INDEPENDENT of product specifications Most specifications are set without regard for process capability However, understanding process capability helps the engineer to set more reasonable specifications PCA reflects only the Natural Tolerance Limits of the process PCA is done by examining the process Histogram Normal Probability Plot 12/5/2018 Process Capability Analysis

Natural Tolerance Limits The natural tolerance limits assume: The process is well-modeled by the Normal Distribution Three sigma is an acceptable proportion of the process to yield The Upper and Lower Natural Tolerance Limits are derived from: The process mean () and The process standard deviation () Equations: 12/5/2018 Process Capability Analysis

Natural Tolerance Limits  +2 -2 +3 or UNTL -3 or LNTL + - The Natural Tolerance Limits cover 99.73% of the process output   1 :68.26% of the total area   2 :95.46% of the total area   3 :99.73% of the total area 12/5/2018 Process Capability Analysis

PCA: Histogram Construction Verify rough shape and location of histogram Symmetric (roughly bell-shaped) Mean = median = mode Quickly confirm applicability prior to statistical analysis Can be very hard to distinguish a Normal Distribution from a t-Distribution Sometimes even a Normal distribution doesn’t look normal More data and columns (bins) can make a difference Verify location of process with respect to Specifications Quick inspection will show what to do to improve the process 12/5/2018 Process Capability Analysis

PCA: Normal Probability Plot A Normal Plot better clarifies whether the distribution is Normal by a visual inspection for: Non-random patterns (non-Normal) Fat Pencil Test (Normal if passes) C u m F r e q X 12/5/2018 Process Capability Analysis

PCA: Parameter Estimation The Normal Plot mid-point estimates the process mean The slope of the “best fit” line for the Normal Plot estimates the standard deviation Choose the 25th and 75th percentile points to calculate the slope The Histogram mode should be close to the mean The range/d2 (from Histogram) should be close to the standard deviation Can also estimate standard deviation by subtracting 50th percentile from the 84th percentile of the Histogram 12/5/2018 Process Capability Analysis

Process Capability Indices Cp: Measures the potential capability of the current process - if the process were centered within the product specifications Two-sided Limits: One-sided Limit: 12/5/2018 Process Capability Analysis

Cp Relation to Process Fallout Recommended Minimum Ratios: (D. C. Montgomery, 2001) Existing Process 1.25 (1-sided) 1.33 (2-sided) Existing, Safety / Critical Parameter 1.45 1.50 New Process 1.45 1.50 New, Safety / Critical Parameter 1.60 1.67 12/5/2018 Process Capability Analysis

Process Capability Indices Cpk: Measures actual capability of current process - at its’ current location with respect to product specifications Formula: Where: 12/5/2018 Process Capability Analysis

Process Capability Indices Regarding Cp and Cpk: Both assume that the process is Normally distributed Both assume that the process is in Statistical Control When they are equal to each other, the process is perfectly centered Both are pretty common reporting ratios among vendors and purchasers 12/5/2018 Process Capability Analysis

Process Capability Indices Two very different processes can have identical Cpk values, though: because spread and location interact! USL LSL 12/5/2018 Process Capability Analysis

Process Capability Indices Cpm: Measures the current capability of the process - using the process target center point within the product specifications in the calculation Formula: Where target T is: 12/5/2018 Process Capability Analysis

Process Capability Indices Cpkm: Similar to Cpm - just more sensitive to departures from the process target center point Not really in very common use Formula: 12/5/2018 Process Capability Analysis

Measurement System Capability Examines the relative variability in the product and measurement systems, together Total variation is the result of Product variation Gage variation Operator variation gaging system variation Random variation 12/5/2018 Process Capability Analysis

Measurement System Analysis Measurement system can be assessed by X-bar and R-Charts Using a single part as the rational subgroup Is easy to visualize Requires alternate interpretation of the control charts Designed Experiments Using Analysis of Variance Allows assessment of part x operator interactions Is statistically complex to compute & analyze 12/5/2018 Process Capability Analysis

Process Capability Analysis X-Bar & R-Chart Method Have each operator measure the same part twice - so the part becomes the rational sample unit Parts should be representative of those to be measured Use a sample of 20 - 25 parts Use a representative set of operators Either collect data from every operator, or Randomly select from the set of operators Collect data under representative conditions Carefully specify and control the conditions for measurement Randomly sequence the combination of parts and operators Preserve the time-order of the collected data & note observations 12/5/2018 Process Capability Analysis

Process Capability Analysis X-Bar & R-Chart Method If each operator measures the same part twice: Variation between samples is plotted on the X-Chart Out of control points indicate success in identifying differences between parts Variation within samples is plotted on the R-Chart Centerline of R-Chart is the magnitude of the gage variation Out of control points indicate excessive operator to operator variation (fix with training?) 12/5/2018 Process Capability Analysis

Process Capability Analysis X-Bar & R-Chart Method R - Control Chart LCL UCL Sample Number R X-Bar Control Chart x Out of control points indicate ability to distinguish between product samples (Good) Out of control points indicate inability of operators to use gaging system (Bad) 12/5/2018 Process Capability Analysis

Process Capability Analysis X-Bar & R-Chart Method Precision to Tolerance Ratio (P/T): “Rule of Ten”: The measurement device should be at least ten times more accurate than the smallest measurement Calculations: and Interpretation: Resulting ratio should be 0.10 or smaller if the gage is truly capable 12/5/2018 Process Capability Analysis

X-Bar & R-Chart Method: R & R Repeatability: Inherent precision of the gage Reproducibility: Variability of the gage under differing conditions Environment Operator Time … 12/5/2018 Process Capability Analysis

X-Bar & R-Chart Method: R & R Process is the same as before (20 - 25 parts, …): But we estimate the Repeatability from the Range Mean computed across all the operators and all parts: And we estimate the Reproducibility from the Range of variability across all operators for each individual part: 12/5/2018 Process Capability Analysis

X-Bar & R-Chart Method: R & R What to do with the information? More variation is bad, so… If the reproducibility variation is larger, improve the operators If the repeatability variation is larger, improve the gaging instrument Hands-On Experiment Micrometer Study 12/5/2018 Process Capability Analysis

Gage Capability Analysis: ANOVA A form of Designed Experiment: Two-Treatment Full Factorial with Replications Analysis is done using ANOVA software Comparisons of variance components is through a series of F-tests (either exceed critical region or look for small p-value) Can distinguish part X operator interaction Want to find non-significant operator, interaction terms, and a significant part term - capable system! 12/5/2018 Process Capability Analysis