Description Usage Arguments Value References See Also Examples

Provides 1-sided or 2-sided tolerance intervals for binomial random variables. From a statistical quality control perspective, these limits use the proportion of defective (or acceptable) items in a sample to bound the number of defective (or acceptable) items in future productions of a specified quantity.

1 2 3 4 | ```
bintol.int(x, n, m = NULL, alpha = 0.05, P = 0.99, side = 1,
method = c("LS", "WS", "AC", "JF", "CP", "AS",
"LO", "PR", "PO", "CL", "CC", "CWS"),
a1 = 0.5, a2 = 0.5)
``` |

`x` |
The number of defective (or acceptable) units in the sample. Can be a vector of length |

`n` |
The size of the random sample of units selected for inspection. |

`m` |
The quantity produced in future groups. If |

`alpha` |
The level chosen such that |

`P` |
The proportion of the defective (or acceptable) units in future samples of size |

`side` |
Whether a 1-sided or 2-sided tolerance interval is required (determined by |

`method` |
The method for calculating the lower and upper confidence bounds, which are used in the calculation
of the tolerance bounds. The default method is |

`a1` |
This specifies the first shape hyperparameter when using Jeffreys' method. |

`a2` |
This specifies the second shape hyperparameter when using Jeffreys' method. |

`bintol.int`

returns a data frame with items:

`alpha` |
The specified significance level. |

`P` |
The proportion of defective (or acceptable) units in future samples of size |

`p.hat` |
The proportion of defective (or acceptable) units in the sample, calculated by |

`1-sided.lower` |
The 1-sided lower tolerance bound. This is given only if |

`1-sided.upper` |
The 1-sided upper tolerance bound. This is given only if |

`2-sided.lower` |
The 2-sided lower tolerance bound. This is given only if |

`2-sided.upper` |
The 2-sided upper tolerance bound. This is given only if |

Brown, L. D., Cai, T. T., and DasGupta, A. (2001), Interval Estimation for a Binomial Proportion,
*Statistical Science*, **16**, 101–133.

Hahn, G. J. and Chandra, R. (1981), Tolerance Intervals for Poisson and Binomial Variables,
*Journal of Quality Technology*, **13**, 100–110.

Newcombe, R. G. (1998), Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods, *Statistics in Medicine*, **17**, 857–872.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
## 85%/90% 2-sided binomial tolerance intervals for a future
## lot of 2500 when a sample of 230 were drawn from a lot of
## 1000. All methods but Jeffreys' method are compared
## below.
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "LS")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "WS")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "AC")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "CP")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "AS")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "LO")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "PR")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "PO")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "CL")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "CC")
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 2, method = "CWS")
## Using Jeffreys' method to construct the 85%/90% 1-sided
## binomial tolerance limits. The first calculation assumes
## a prior on the proportion of defects which places greater
## density on values near 0. The second calculation assumes
## a prior on the proportion of defects which places greater
## density on values near 1.
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 1, method = "JF", a1 = 2, a2 = 10)
bintol.int(x = 230, n = 1000, m = 2500, alpha = 0.15, P = 0.90,
side = 1, method = "JF", a1 = 5, a2 = 1)
``` |

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