Statistical Software for Process Validation. Featuring Minitab

Transcription

1 Statistical Software for Process Validation Featuring Minitab

2 Regulatory Requirements 21 CFR 820 Subpart O--Statistical Techniques Sec Statistical techniques. (a) Where appropriate, each manufacturer shall establish and maintain procedures for identifying valid statistical techniques required for establishing, controlling, and verifying the acceptability of process capability and product characteristics. (b) Sampling plans, when used, shall be written and based on a valid statistical rationale. Each manufacturer shall establish and maintain procedures to ensure that sampling methods are adequate for their intended use and to ensure that when changes occur the sampling plans are reviewed. These activities shall be documented. -Code of Federal Regulations, Title 21, Volume 8, Subchapter H Medical Devices, Part 820 Quality System Regulation

3 Statistical Requirements 1. Stability 2. Capability 3. Normality

4 1. Stability Total Variation Target

5 First the process must be stable Xbar and r charts IMR charts theory

6 X bar-r charts Variables data Subgroups 8 Monitors the mean and variation of a process. Control limits on the Xbar chart are estimates only. Confirm process variation is stable using R chart first.

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8 I-MR charts Variables data No subgroups Monitors the mean and variation of a process Control limits on the I chart are estimates only. Confirm process variation is stable using MR chart first.

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10 2. Capability Cpk: capability of the process at a point in time (present) Ppk: capability of the process over time (future) Copyright GCI, Inc. 2006

11 P pk versus C pk P pk C pk Uses total standard deviation Measures performance of the process (what the process is actually doing) Uses within subgroup standard deviation Measures what the process is capable of doing if it were stable

12 P pk P pk is a measure of how close the process is to the nearest spec relative to the variation P pk = Distance from mean to nearest spec 3 s Copyright GCI, Inc. 2006

13 P pk LSL Numerator Denominator USL Target

14 Pp P p = USL - LSL 6 s 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 Copyright GCI, Inc. 2006

15 P pk when P p =2 USL P pk = 2 P pk = 1.5 P pk = 1.5 P pk = 1 P pk = 1 P pk = 0.5 P pk = 0.5 LSL

16 3. Normality Variables sampling plans use the normal distribution to predict the percentage of units outside of spec LSL USL 2.3% Out of Spec

17 Normality Assumption Requires a separate normality test Requires a stable process It is possible to transform non-normal data to normal data, but it is not always appropriate to do so.

18 Normality Testing Required For: Design Verification and Process Validation Receiving and In-Process Inspections When Using: Variables Sampling Plans Capability Studies Hypothesis Testing

19 Example LTPD = 0.3% Variables 2-sided 95% Confidence Parameters AQL LTPD 0.05 n=15, P pk =1.37, P p = % (P pk =1.82) 0.3% (P pk =0.92) n=20, P pk =1.29, P p = % (P pk =1.69) 0.3% (P pk =0.92) n=30, P pk =1.21, P p = % (P pk =1.48) 0.3% (P pk =0.92) n=40, P pk =1.16, P p = % (P pk =1.39) 0.3% (P pk =0.92) n=50, P pk =1.13, P p = % (P pk =1.33) 0.3% (P pk =0.92) n=60, P pk =1.11, P p = % (P pk =1.29) 0.3% (P pk =0.92) n=80, P pk =1.08, P p = % (P pk =1.23) 0.3% (P pk =0.92) n=100, P pk =1.06, P p = % (P pk =1.19) 0.3% (P pk =0.92)

20 Minitab

21 Graphical Summary

22 Normality Established

23 Capability Analysis

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26 Conclusion P pk = 1.35 which is above the required value of P pk = 1.29 PASS P p = 1.38 which is above the required value of P p = PASS

27 Skewness and Kurtosis

28 Transformations Lognormal Weibull Box-Cox transformations Procedure in Minitab for identifying which of a family of transformations might work Johnson family of distributions Transformation can be selected for any skewnesskurtosis combination

29 Non-normal Example LTPD = 0.3% Variables 2-sided 95% Confidence Parameters AQL LTPD 0.05 n=15, P pk =1.37, P p = % (P pk =1.82) 0.3% (P pk =0.92) n=20, P pk =1.29, P p = % (P pk =1.69) 0.3% (P pk =0.92) n=30, P pk =1.21, P p = % (P pk =1.48) 0.3% (P pk =0.92) n=40, P pk =1.16, P p = % (P pk =1.39) 0.3% (P pk =0.92) n=50, P pk =1.13, P p = % (P pk =1.33) 0.3% (P pk =0.92) n=60, P pk =1.11, P p = % (P pk =1.29) 0.3% (P pk =0.92) n=80, P pk =1.08, P p = % (P pk =1.23) 0.3% (P pk =0.92) n=100, P pk =1.06, P p = % (P pk =1.19) 0.3% (P pk =0.92)

30 Minitab

31 Test Normality

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33 Normality Test Fails

34 Identify the Distribution

35 Choose Distributions to Test

36 Probability Plots

37 Check p Values

38 Non-normal Capability Analysis

39 Select Lognormal

40 Data and Specs Transformed

41 Conclusion P pk = 1.06 which is at the required value of P pk = 1.06 PASS P p = 1.20 which is above the required value of P p = PASS

42 Contact me with Questions Roberta Goode, MSBE, CQE x310