process.capability: Process capability analysis
In qcc: Quality Control Charts

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.

process.capability(object,spec.limits, target, std.dev, nsigmas, 
                   confidence.level = 0.95, breaks = "scott", 
                   add.stats = TRUE, print = TRUE, 
                   digits = getOption("digits"), restore.par = TRUE)

`object`	a 'qcc' object of type `"xbar"`
`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 `NA`.
`target`	a value specifying the target of the process. If missing the value from the 'qcc' object is used if not `NULL`, otherwise the target is set at the middle value bewteen specification limits.
`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 `hist` for more details.
`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 `par` settings must be restored. If you need to add points, lines, etc. to a chart set this to `FALSE`.

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 (C_p, C_pl, C_pu, C_pk, C_pm) and the corresponding confidence limits.
`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.

qcc

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%