An elementary model for statistical lot inspection and its application to sampling by variables.

*(English)*Zbl 0876.62087Summary: Recently some critical papers have initiated a discussion on pros and cons of standard sampling by variables (sampling by measurement). This discussion demonstrates the need for clarification by a sound stochastic model of statistical lot inspection. On the basis of such a model, variables sampling for lot proportion nonconforming and attributes sampling can be compared in terms of the theory of statistical hypothesis testing. This comparison refutes the well-known dogma of “same protection at lower sample size with variables plans”. Sampling by measurement for lot means, however, emerges as a perfectly valid method of statistical lot inspection.

##### MSC:

62P30 | Applications of statistics in engineering and industry; control charts |

62F03 | Parametric hypothesis testing |

**OpenURL**

##### References:

[1] | Burr IW (1976) Statistical quality control methods. Marcel Dekker, New York Basel · Zbl 0357.62086 |

[2] | von Collani E (1990) ANSI/ASQC Z1.4 versus ANSI/ASQC Z1.9. Economic Quality Control 5:60–64 · Zbl 0695.62229 |

[3] | von Collani E (1991) A note on acceptance sampling for variables. Metrika 38:19–36 · Zbl 0714.62094 |

[4] | Dodge HF (1969) Notes on the evolution of acceptance sampling plans. Parts I, II, III. Journal of Quality Technology 1:77–88, 155–162, 225–232 |

[5] | Dodge HF (1970) Notes on the evolution of acceptance sampling plans. Part IV. Journal of Quality Technology 2:1–8 |

[6] | Dodge HF, Romig HG (1959) Sampling inspection tables. 2nd ed. John Wiley New York |

[7] | Duncan AJ (1986) Quality control and industrial statistics. Fifth ed. Richard D Irwin Homewood Illinois |

[8] | Grant EL (1964) Statistical quality control. McGraw-Hill, New York Toronto London |

[9] | Gryna FM (1962) Statistical methods in the quality function. In: Juran JM, Seder LA, Gryna FM (Eds) Qualify Control Handbook. Second Edition, McGraw-Hill New York Toronto London |

[10] | Hryniewicz O (1991) A note on E. von Collanis paper ”ANSI/ASQC Z1.4 versus ANSI/ASQC Z1.9”. Economic Quality Control 6: 16–18 |

[11] | International Organization for Standardization (1989a) ISO 2859: Sampling procedures for inspection by attributes. International Organization for Standardization, Geneva |

[12] | International Organization for Standardization (1989b) ISO 3951: Sampling procedures and charts for inspection by variables for percent nonconforming. International Organization for Standardization, Geneva |

[13] | Ishikawa K (1985) What is total quality control? The Japanese way. Prentice-Hall, Englewood Cliffs New Jersey |

[14] | Jennett WJ, Welch BL (1939) The control of proportion defective as judged by a single quality characteristic varying on a continuous scale. Supplement to the Journal of the Royal Statistical Society 6:80–88 · Zbl 0021.14806 |

[15] | Lehmann EL (1959) Testing statistical hypotheses. John Wiley New York · Zbl 0089.14102 |

[16] | Romig HG (1939) Allowable average in sampling inspection. PhD Thesis, Columbia University New York |

[17] | Schilling EG (1982) Acceptance sampling in quality control. Marcel Dekker, New York Basel · Zbl 0508.62087 |

[18] | Shewhart WA (1931) Economic control of quality of manufactured product. D. van Nostrand Company, Princeton New Jersey |

[19] | Thyregod P (1973) On exchangeable prior information in sampling finite populations. In: Bulletin of the International Institute, Proceedings of the 39th Session 3:530–535 |

[20] | US Department of Defense (1957) Military standard, sampling procedures and tables for inspection by variables for percent defective (MIL-STD-414). US Government Printing Office, Washington DC |

[21] | US Department of Defense (1963) Military standard, sampling procedures and tables for inspection by attributes (MIL-STD-105D). US Government Printing Office, Washington DC |

[22] | Wadsworth HM, Stephens KS, Godfrey AB (1986) Modern methods for quality control and improvement. John Wiley, New York |

[23] | Wolff H (1992) A note on the evaluation of von Collani’s critique about acceptance sampling by variables. In: Proceedings of the Second Würzburg-Umeå Conference in Statistics. Institut für Angewandte Mathematik und Statistik der Universität Würzburg, 305–312 |

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