Statistical Techniques for Validation Sampling. Copyright GCI, Inc. 2016

Transcription

1 Statistical Techniques for Validation Sampling

2 Tie Risk to Sampling Data Type Confidence Level Reliability and Risk Typical Performance Levels One-sided or two-sided spec Distribution (variables)

3 Risk in Sampling Data Type Confidence Level Risk Defective Rate Reliability Variables 95% Attribute 90% or 95% FDA Mandated 0.% 99.90% High 0.30% 99.70% Low 5% 95% High 1% 99% Low 3% 97% Source: Taylor, W. A., Guide to Acceptance Sampling, Taylor Enterprises, 1992

4 Attribute Single & Double Sampling Plans

5 LTPD.05 = 3% Attribute Plans with 95% Confidence Type Parameters AQL LTPD 0.05 Single n=0, a=0 0.05% 3% Double n1=1, a1=0, r1=2, n2=120, a2=2 0.2% 3% Single n=2, a=2 0.39% 3%

6 Variables Sampling Plans LSL USL

7 P pk P pk is a measure of how close the process is to the nearest spec relative to the variation Variables sampling plans for 1-sided spec limits are based on P pk P pk = Distance from mean to nearest spec 3 s

8 P p Variables sampling plans for 2-sided spec limits are based on Ppk and Pp s is standard deviation (total) Compares width of process (6 s) to width of spec (USL - LSL) P p is similar to C p but uses total rather than within subgroup standard deviation P p = USL - 6 s LSL

9 2-Sided Variables Sampling Plans LTPD 0.05 = 1% 95% confidence Parameters AQL LTPD 0.05 n=15, P pk =1.17, P p = % (P pk =1.55) 1% (P pk =0.7) n=20, P pk =1.11, P p = % (P pk =1.2) 1% (P pk =0.7) n=30, P pk =1.03, P p = % (P pk =1.27) 1% (P pk =0.7) n=0, P pk =0.99, P p = % (P pk =1.19) 1% (P pk =0.7)

10 Interactive Exercise: Process validation, 3 lots, 95% confidence level, 99.7% reliability based on high risk, continuous data, 1-sided spec: tensile force 2.5 lb/in 2

11 Choose a Sampling Plan 1-sided LTPD 0.05 = 0.3% 95% confidence Given: Ppk = 1. (historic data) Parameters AQL LTPD 0.05 n=15, P pk =1.7 = % (P pk =1.0) 0.3% (P pk =0.92) n=20, P pk = % (P pk =1.69) 0.3% (P pk =0.92) n=30, P pk = % (P pk =1.7) 0.3% (P pk =0.92) n=0, P pk = % (P pk =1.3) 0.3% (P pk =0.92) n=15 has a 50% probability of acceptance n=30 has a 95% probability of acceptance

12 Collect the Data Collect data on 30 samples per lot Repeat for all 3 lots

13 Analyze the Data Normality Test Stability Fail (p<.05) Pass (p.05) *Transformation Capability Analysis

14 Lot 1: Normality Test

15 Sample Range Sample Mean Lot 1: Stability Xbar-R Chart of Lot _ UC L=11.56 X=. LC L= Sample UC L=3.70 _ R=1. LC L= Sample 7 9

16 Lot 1: Capability Analysis Process Capability of Lot1 Process Data LSL 2.5 Target * USL * Sample Mean.0952 Sample N 30 StDev (Within) StDev (O v erall) LSL Within Overall Potential (Within) C apability C p * C PL 2.99 C PU * C pk 2.99 O v erall C apability Pp * PPL 2.6 PPU * Ppk 2.6 C pm * O bserv ed Performance PPM < LSL 0.00 PPM > USL * PPM Total 0.00 Exp. Within Performance PPM < LSL 0.00 PPM > USL * PPM Total 0.00 Exp. O v erall Performance PPM < LSL 0.00 PPM > USL * PPM Total 0.00

17 Lot 2: Normality Test Summary for Lot2 A nderson-darling Normality Test A -Squared 2.30 P-V alue < Mean.15 StDev V ariance 1.01 Skew ness Kurtosis N Minimum st Q uartile Median rd Q uartile 9.27 Maximum % C onfidence Interv al for Mean % C onfidence Interv al for Median % Confidence Intervals 95% C onfidence Interv al for StDev Mean Median 6 7 9

18 Sample Range Sample Mean Lot 2: Stability Xbar-R Chart of Lot2 16 UC L= _ X= Sample 7 9 LC L= UC L= _ R= LC L= Sample 7 9

19 StDev Lot 2: Data Transformation Box-Cox Plot of Lot Lower CL Upper CL Lambda (using 95.0% confidence) Estimate -1. Lower CL Upper CL Rounded Value Don t forget to transform the specification! 15 5 Limit Lambda

20 Transformed Normality Test

21 Lot 2: Capability Analysis Process Capability of Lot2 Using Box-Cox Transformation With Lambda = -1 Process Data LSL 2.5 Target * USL * Sample Mean.15 Sample N 30 StDev (Within) StDev (O v erall) A fter Transformation LSL* 0. Target* * USL* * Sample Mean* StDev (Within)* StDev (O v erall)* transformed data LSL* Within O v erall Potential (Within) C apability C p * C PL 1.90 C PU * C pk 1.90 O v erall C apability Pp * PPL 1.6 PPU * Ppk 1.6 C pm * O bserv ed Performance PPM < LSL 0.00 PPM > USL * PPM Total 0.00 Exp. Within Performance PPM > LSL* 0.01 PPM < USL* * PPM Total 0.01 Exp. O v erall Performance PPM > LSL* 0.3 PPM < USL* * PPM Total 0.3

22 Lot 3: Normality Test Summary for Lot3 A nderson-darling Normality Test A -Squared 0.99 P-V alue Mean StDev V ariance Skew ness Kurtosis N Minimum st Q uartile.73 Median rd Q uartile.322 Maximum % C onfidence Interv al for Mean % C onfidence Interv al for Median % Confidence Intervals 95% C onfidence Interv al for StDev Mean Median

23 Sample Range Sample Mean Lot 3: Stability Xbar-R Chart of Lot UC L=12.20 _ X=9.26 LC L= Sample UC L=7.3 _ R=2.7 0 LC L= Sample 7 9

24 Percent Percent Percent Percent Lot 3: Data Transformation Probability Plot for Lot3 2-Parameter Exponential - 95% C I Weibull - 95% C I Goodness of F it Test 2-Parameter Exponential A D = P-V alue < 0.0 Weibull A D = 0.69 P-V alue = Lot3 - T hreshold 3-Parameter Weibull - 95% C I Lot3 Smallest Extreme V alue - 95% C I 3-Parameter Weibull A D = 0.2 P-V alue > Smallest Extreme V alue A D = 0.2 P-V alue > Lot3 - T hreshold Lot3 9 12

25 Lot 3: Capability Analysis Process Capability of Lot3 Calculations Based on Weibull Distribution Model Process Data LSL 2.5 Target * USL * Sample Mean Sample N 30 Shape Scale O bserv ed Performance PPM < LSL 0.00 PPM > USL * PPM Total 0.00 LSL O v erall C apability Pp * PPL 1.31 PPU * Ppk 1.31 Exp. O v erall Performance PPM < LSL PPM > USL * PPM Total

26 Conclusion All three lots met criteria to conclude that the validation passes. With 95% confidence, the process average across each lot produces at least 99% reliability, or With 95% confidence, the process average across each lot produces less than 1% defective. Note: all 3 lots combined are at a 99.99% confidence level.

27 Distribution Analysis Attribute sampling plans Normality established Data transformation (special cases) Distribution-free methods such as VP: Require unimodality Requires sufficient distance between mean and specification limit Can be used with very skewed distributions

28 References EN ISO 135: Medical Devices Quality Management Systems. 21 CFR 20, Quality System Regulation, Subparts C, G & O (design control, production and process controls, statistical techniques). Taylor, W., Guide to Acceptance Sampling, Taylor Enterprises, Inc., D. F. Vysochanskij, Y. I. Petunin (190). "Justification of the 3σ rule for unimodal distributions." Theory of Probability and Mathematical Statistics 21: