Description Usage Arguments Details Value Author(s) References See Also Examples

Computes process capability indices for a 'qcc' object of type `"xbar"`

and plot the histogram.

1 2 3 4 |

`object` |
a 'qcc' object of type |

`spec.limits` |
a two-values vector specifying the lower and upper specification limits. For one-sided specification limits, the value of the missing limit must be set to |

`target` |
a value specifying the target of the process. If missing the value from the 'qcc' object is used if not |

`std.dev` |
a value specifying the within-group standard deviation. If not provided is taken from the 'qcc' object. |

`nsigmas` |
a numeric value specifying the number of sigmas to use. If not provided is taken from the 'qcc' object. |

`confidence.level` |
a numeric value between 0 and 1 specifying the level to use for computing confidence intervals. |

`breaks` |
a value or string used to draw the histogram. See the help for |

`add.stats` |
a logical value indicating whether statistics and capability indices should be added at the bottom of the chart. |

`print` |
a logical value indicating whether statistics and capability indices should be printed. |

`digits` |
the number of significant digits to use. |

`restore.par` |
a logical value indicating whether the previous |

This function calculates confidence limits for *C_p* using the method described by Chou et al. (1990).
Approximate confidence limits for *C_pl*, *C_pu* and *C_pk* are computed using the method in Bissell (1990).
Confidence limits for *C_pm* are based on the method of Boyles (1991); this method is approximate and it assumes that the target is midway between the specification limits.

Invisibly returns a list with components:

`nobs` |
number of observations |

`center` |
center |

`std.dev` |
standard deviation |

`target` |
target |

`spec.limits` |
a vector of values giving the lower specification limit (LSL) and the upper specification limit (USL) |

`indices` |
a matrix of capability indices ( |

`exp` |
a vector of values giving the expected fraction, based on a normal approximation, of the observations less than LSL and greater than USL. |

`obs` |
a vector of values giving the fraction of observations less than LSL and greater than USL. |

Luca Scrucca

Bissell, A.F. (1990) *How reliable is your capability index?*, Applied Statistics, 39, 331-340.

Boyles, R.A. (1991) *The Taguchi capability index*, Journal of Quality Technology, 23, 107-126.

Chou, Y., Owen D.B. and Borrego S.A. (1990) *Lower Confidence Limits on Process Capability Indices*, Journal of Quality Technology, 22, 223-229.

Montgomery, D.C. (2005) *Introduction to Statistical Quality Control*, 5th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) *Statistical Process Control*. New York: Chapman & Hall.

1 2 3 4 5 6 7 8 | ```
data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)
q <- qcc(diameter[1:25,], type="xbar", nsigmas=3, plot=FALSE)
process.capability(q, spec.limits=c(73.95,74.05))
process.capability(q, spec.limits=c(73.95,74.05), target=74.02)
process.capability(q, spec.limits=c(73.99,74.01))
process.capability(q, spec.limits = c(73.99, 74.1))
``` |

```
Package 'qcc' version 2.7
Type 'citation("qcc")' for citing this R package in publications.
Process Capability Analysis
Call:
process.capability(object = q, spec.limits = c(73.95, 74.05))
Number of obs = 125 Target = 74
Center = 74 LSL = 73.95
StdDev = 0.009785 USL = 74.05
Capability indices:
Value 2.5% 97.5%
Cp 1.703 1.491 1.915
Cp_l 1.743 1.555 1.932
Cp_u 1.663 1.483 1.844
Cp_k 1.663 1.448 1.878
Cpm 1.691 1.480 1.902
Exp<LSL 0% Obs<LSL 0%
Exp>USL 0% Obs>USL 0%
Process Capability Analysis
Call:
process.capability(object = q, spec.limits = c(73.95, 74.05), target = 74.02)
Number of obs = 125 Target = 74.02
Center = 74 LSL = 73.95
StdDev = 0.009785 USL = 74.05
Capability indices:
Value 2.5% 97.5%
Cp 1.7033 1.4914 1.9148
Cp_l 1.7433 1.5548 1.9319
Cp_u 1.6632 1.4827 1.8437
Cp_k 1.6632 1.4481 1.8783
Cpm 0.7856 0.6556 0.9154
Exp<LSL 0% Obs<LSL 0%
Exp>USL 0% Obs>USL 0%
Process Capability Analysis
Call:
process.capability(object = q, spec.limits = c(73.99, 74.01))
Number of obs = 125 Target = 74
Center = 74 LSL = 73.99
StdDev = 0.009785 USL = 74.01
Capability indices:
Value 2.5% 97.5%
Cp 0.3407 0.2983 0.3830
Cp_l 0.3807 0.3176 0.4439
Cp_u 0.3006 0.2424 0.3588
Cp_k 0.3006 0.2312 0.3700
Cpm 0.3382 0.2960 0.3804
Exp<LSL 13% Obs<LSL 12%
Exp>USL 18% Obs>USL 16%
Process Capability Analysis
Call:
process.capability(object = q, spec.limits = c(73.99, 74.1))
Number of obs = 125 Target = 74.05
Center = 74 LSL = 73.99
StdDev = 0.009785 USL = 74.1
Capability indices:
Value 2.5% 97.5%
Cp 1.8736 1.6406 2.1063
Cp_l 0.3807 0.3176 0.4439
Cp_u 3.3665 3.0115 3.7215
Cp_k 0.3807 0.3055 0.4559
Cpm 0.4083 0.3377 0.4788
Exp<LSL 13% Obs<LSL 12%
Exp>USL 0% Obs>USL 0%
```

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