ENGM 621: SPC Process Capability

Outline Process Capability Process Capability Indices 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

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

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:

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

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:

Process Capability Ratio Note There are many ways we can estimate the capability of our process If σ is unknown, we can replace it with one of the following estimates: The sample standard deviation S R-bar / d2

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

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

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

PCR and an Off-Center Process CPK = min (CPU, CPL) Generally, if CP = CPK, then the process is centered at the midpoint of the specifications If CP ≠ CPK, then the process is off-center PCR=potential capability PCR(k) = actual capability

Quality Design & Process Variation Lower Spec Limit Upper Spec Limit Acceptance Sampling 60 80 100 120 140 Statistical Process Control 60 140 Experimental Design 140 60