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Booklet No. 9 Machine and Process Capability Quality Management in the Bosch Group | Technical Statistics 9. Machine and Process Capability Booklet No. 9 ― Machine and Process Capability Quality Management in the Bosch Group Technical Statistics Booklet No. 9 Machine and Process Capability Edition 11.2019 © Robert Bosch GmbH 2019 | 11.2019 Booklet No. 9 ― Machine and Process Capability 5. Edition 05.11.2019 4. Edition 01.06.2016 3. Edition 01.07.2004 2. Edition 29.07.1991 1. Edition 11.04.1990 All minimum requirements specified in this booklet for capability and performance criteria correspond to the status at the time of printing (issue date). CDQ 0301 is relevant for the current definition. © Robert Bosch GmbH 2019 | 11.2019 Booklet No. 9 ― Machine and Process Capability Table of contents 1 Introduction ..................................................................................................................................... 5 2 Area of application ........................................................................................................................... 6 3 Flowchart ......................................................................................................................................... 7 4 Machine capability ........................................................................................................................... 8 4.1 Data collection ....................................................................................................................... 9 4.2 Investigation of the temporal stability ................................................................................ 10 4.3 Investigation of the statistic distribution ............................................................................. 10 4.4 Calculation of capability indices ........................................................................................... 11 4.5 Criteria for machine capability ............................................................................................. 11 4.6 Machine capability with reduced effort .............................................................................. 12 5 Process capability (short-term) ...................................................................................................... 13 6 Process capability (long-term) ....................................................................................................... 14 6.1 Data collection ..................................................................................................................... 15 6.2 Outliers................................................................................................................................. 16 6.3 Classification and rounding .................................................................................................. 17 6.4 Investigation of the process stability ................................................................................... 18 6.5 Investigation of the distribution .......................................................................................... 19 6.6 Calculation of capability and performance indices .............................................................. 20 6.7 Criteria for process capability and performance .................................................................. 20 7 Distribution models ........................................................................................................................ 21 7.1 Normal distribution.............................................................................................................. 21 7.2 Logarithmic normal distribution .......................................................................................... 22 7.3 Folded normal distribution .................................................................................................. 22 7.4 Rayleigh distribution ............................................................................................................ 23 7.5 Weibull distribution ............................................................................................................. 23 7.6 Distributions for characteristics limited at the upper end .................................................. 24 7.7 Mixture distribution ............................................................................................................. 24 7.8 Extended normal distribution .............................................................................................. 25 7.9 Distributions with offset ...................................................................................................... 26 7.10 Distributions with convolution ............................................................................................ 26 8 Calculation of capability and performance indices ........................................................................ 27 8.1 Basic principles ..................................................................................................................... 27 Potential and critical capability and performance indices................................................... 28 Unilaterally restricted characteristics .................................................................................. 28 Estimate values .................................................................................................................... 29 Capability and performance ................................................................................................ 29 8.2 Quantile method M2,1 according to ISO 22514-2 ................................................................. 30 8.3 Further methods according to ISO 22514-2 ........................................................................ 31 8.4 Extended normal distribution .............................................................................................. 33 9 Additional notes to capability indices ............................................................................................ 34 9.1 Capability indices and fractions nonconforming ................................................................. 34 © Robert Bosch GmbH 2019 | 11.2019 3 Booklet No. 9 ― Machine and Process Capability 9.2 Influence of the sample size ................................................................................................ 35 9.3 Influence of the measurement system ................................................................................ 35 10 Report: Calculated capability and performance indices ................................................................ 35 11 Revalidation ................................................................................................................................... 36 12 Examples ........................................................................................................................................ 38 13 Forms ............................................................................................................................................. 42 14 Capability indices for two-dimensional characteristics ................................................................. 44 A Time series analysis ........................................................................................................................ 46 A.1 Tests for constancy of process variation ............................................................................. 46 A.2 Tests for constancy of process location ............................................................................... 47 A.3 Test for trend ....................................................................................................................... 47 A.4 Test for randomness ............................................................................................................ 48 B Simple statistical stability tests ...................................................................................................... 49 B.1 Location of the individual samples ...................................................................................... 49 B.2 Variation range of the individual samples ........................................................................... 50 B.3 Standard deviation of the sample means ............................................................................ 50 C Measurement results and distribution models ............................................................................. 51 C.1 Assignment of distribution models ...................................................................................... 51 C.2 Selection of distribution models .......................................................................................... 53 C.3 Parameter stimation and confidence interval ..................................................................... 54 C.4 Notes for selection of distribution models .......................................................................... 56 C.5 Options for very large data sets ........................................................................................... 57 D Statistical distribution tests............................................................................................................ 59 D.1 Tests for normal distribution ............................................................................................... 59 D.2 Tests on arbitrary distributions (except ND) ......................................................................
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