# Capability Analysis

### Description

Calculates the process capability indices cp, cpk, cpL cpU, cpm, cpmk for a qcs object and normal distribution.
Also, 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
the target is midway between the specification limits.
Moreover, calculates the process capability indices cnp, cnpk, cnpm, cnpmk for a qcs object.
A histogramm with a density curve is displayed along with the specification limits, a
Quantile-Quantile Plot for the specified distribution and contour graph is plotted for estimate the indice cpm.

### Usage

1 2 3 |

### Arguments

`object` |
qcs object of type |

`limits` |
A vector specifying the lower and upper specification limits. |

`target` |
A value specifying the target of the process.
If is |

`std.dev` |
A value specifying the within-group standard deviation. |

`nsigmas` |
A numeric value specifying the number of sigmas to use. |

`confidence` |
A numeric value between 0 and 1 specifying the probabilities for computing the quantiles. This values is used only when object values is provided. The default value is 0.9973. |

`plot` |
Logical value indicating whether graph should be plotted. |

`main` |
Title of the plot. |

`...` |
Arguments to be passed to or from methods. |

### References

Montgomery, D.C. (1991) *Introduction to Statistical Quality Control*, 2nd
ed, New York, John Wiley & Sons.

Tong, L.I. and Chen, J.P. (1998), *Lower con???dence limits of process capability
indices for nonnormal process distributions.* International Journal of Quality & Reliability Management,
Vol. 15 No. 8/9, pp. 907-19.

Vannman, K (1995) *A Unified Approach to Capability Indices*. Statitica Sinica,5,805-820.

Vannman, K. (2001). *A Graphical Method to Control Process Capability*. Frontiers in Statistical Quality Control,
No 6, Editors: H-J Lenz and P-TH Wilrich. Physica-Verlag, Heidelberg, 290-311.

Hubele and Vannman (2004). *The E???ect of Pooled and Un-pooled Variance Estimators on Cpm When Using Subsamples*.
Journal Quality Technology, 36, 207-222.

### Examples

1 2 3 4 5 6 | ```
library(qcr)
data(pistonrings)
xbar <- qcs.xbar(pistonrings[1:125,],plot = TRUE)
LSL=73.99; USL=74.01
limits = c(lsl = 73.99, usl = 74.01)
qcs.ca(xbar, limits = limits)
``` |