Statistical Process Control Gage Capability

Gage Capability Studies TM 720: Statistical Process Control Gage Capability Studies Ensuring an adequate gage and inspection system capability is an important consideration! In any problem involving measurement the observed variability in product due to two sources: Product variability - σ2product Gage variability - σ2gage i.e., measurement error Total observed variance in product: σ2total = σ2product + σ2gage (system) (c) 2002-2006 D.H. Jensen & R.C. Wurl

e.g. Assessing Gage Capability TM 720: Statistical Process Control e.g. Assessing Gage Capability Following data were taken by one operator during gage capability study. (c) 2002-2006 D.H. Jensen & R.C. Wurl

e.g. Assessing Gage Capability Cont'd TM 720: Statistical Process Control e.g. Assessing Gage Capability Cont'd Estimate standard deviation of measurement error: Dist. of measurement error is usually well approximated by the Normal, therefore Estimate gage capability: That is, individual measurements expected to vary as much as owing to gage error. (c) 2002-2006 D.H. Jensen & R.C. Wurl

Precision-to-Tolerance (P/T) Ratio TM 720: Statistical Process Control Precision-to-Tolerance (P/T) Ratio Common practice to compare gage capability with the width of the specifications In gage capability, the specification width is called the tolerance band (not to be confused with natural tolerance limits, NTLs) Suppose specs are given as : m ± 27.5 Rule of Thumb: P/T  0.1  Adequate gage capability (c) 2002-2006 D.H. Jensen & R.C. Wurl

Estimating Variance Components of Total Observed Variability TM 720: Statistical Process Control Estimating Variance Components of Total Observed Variability Estimate total variance: Compute an estimate of product variance Since : (c) 2002-2006 D.H. Jensen & R.C. Wurl

Gage Std Dev Can Be Expressed as % of Product Standard Deviation TM 720: Statistical Process Control Gage Std Dev Can Be Expressed as % of Product Standard Deviation Gage standard deviation as percentage of product standard deviation : This is often a more meaningful expression, because it does not depend on the width of the specification limits (c) 2002-2006 D.H. Jensen & R.C. Wurl

e.g. Assessing Gage Capability TM 720: Statistical Process Control e.g. Assessing Gage Capability Following data were taken by one operator during gage capability study. (c) 2002-2006 D.H. Jensen & R.C. Wurl

Using x and R-Charts for a Gage Capability Study TM 720: Statistical Process Control Using x and R-Charts for a Gage Capability Study (c) 2002-2006 D.H. Jensen & R.C. Wurl

Using x and R-Charts for a Gage Capability Study TM 720: Statistical Process Control Using x and R-Charts for a Gage Capability Study On x chart for measurements: Expect to see many out-of-control points x chart has different meaning than for process control shows the ability of the gage to discriminate between units (discriminating power of instrument) Why? Because estimate of σx used for control limits is based only on measurement error, i.e.: (c) 2002-2006 D.H. Jensen & R.C. Wurl

Using x and R-Charts for a Gage Capability Study TM 720: Statistical Process Control Using x and R-Charts for a Gage Capability Study On R-chart for measurements: R-chart directly shows magnitude of measurement error Values represent differences between measurements made by same operator on same unit using the same instrument Interpretation of chart: In-control: operator has no difficulty making consistent measurements Out-of-control: operator has difficulty making consistent measurements (c) 2002-2006 D.H. Jensen & R.C. Wurl

Repeatability & Reproducibility: Gage R & R Study TM 720: Statistical Process Control Repeatability & Reproducibility: Gage R & R Study If more than one operator used in study then measurement (gage) error has two components of variance: σ2total = σ2product + σ2gage σ2reproducibility + σ2repeatability Repeatability: σ2repeatability - Variance due to measuring instrument Reproducibility: σ2reproducibility - Variance due to different operators (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Ex. Gage R & R Study 20 parts, 3 operators, each operator measures each part twice Estimate repeatability (measurement error): Use d2 for n = 2 since each range uses 2 repeat measures Operator i xi Ri 1 22.30 1.00 2 22.28 1.25 3 22.10 1.20 (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Ex. Gage R & R Study Cont'd Estimate reproducibility: Differences in xi  operator bias since all operators measured same parts Use d2 for n = 3 since Rx is from sample of size 3 (c) 2002-2006 D.H. Jensen & R.C. Wurl

TM 720: Statistical Process Control Ex. Gage R & R Study Cont'd Total Gage variability: Gage standard deviation (measurement error): P/T Ratio: Specs: USL = 60, LSL = 5 Note: Would like P/T < 0.1! (c) 2002-2006 D.H. Jensen & R.C. Wurl

Comparison of Gage Capability Examples TM 720: Statistical Process Control Comparison of Gage Capability Examples Gage capability is not as good when we account for both reproducibility and repeatability Train operators to reduce σ2reproducability from 0.1181 Since σ2repeatability = 1.0195 (largest component), direct effort toward finding another inspection device. σ2 repeatability σ2 reproducibility σ2 product P/T Single operator 0.8865 0.0967 Three operators 1.0195 0.1181 1.0263 0.1120 (c) 2002-2006 D.H. Jensen & R.C. Wurl