`processCapability.Rd`

Computes process capability indices for a `'qcc'`

object of type `"xbar"`

and plot the histogram.

```
processCapability(object, spec.limits, target,
std.dev, nsigmas,
confidence.level = 0.95, ...)
# S3 method for processCapability
print(x, digits = getOption("digits"), ...)
# S3 method for processCapability
plot(x,
add.stats = qcc.options("add.stats"),
breaks = nclass.scott,
fill = adjustcolor(qcc.options("zones")$fill, alpha.f = 0.5),
color = "white", title, xlab,
digits = getOption("digits"), ...)
```

- 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 between 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.

- x
an object of class 'processCapability'.

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

- breaks
a value or a function used to select the number of bins in a histogram. See the help for

`nclass.scott`

for more details.- fill, color
values specifying the colour of the filled area and the border used for drawing the histogram.

- title
a character string specifying the plot title. Set

`title = NULL`

to remove the title.- xlab
a character string specifying the label for the x-axis.

- digits
the number of significant digits to use.

- ...
catches further ignored arguments.

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.

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. (2013) *Introduction to Statistical Quality Control*, 7th ed. New York: John Wiley & Sons.

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

```
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)
q <- qcc(diameter[1:25,], type="xbar", nsigmas=3)
pc <- processCapability(q, spec.limits=c(73.95,74.05))
pc
#> ── Process Capability Analysis ───────────────────
#>
#> Number of obs = 125 Target = 74
#> Center = 74.00118 LSL = 73.95
#> StdDev = 0.009785039 USL = 74.05
#>
#> Capability indices Value 2.5% 97.5%
#> Cp 1.70 1.49 1.91
#> Cp_l 1.74 1.55 1.93
#> Cp_u 1.66 1.48 1.84
#> Cp_k 1.66 1.45 1.88
#> Cpm 1.69 1.48 1.90
#>
#> Exp<LSL 0% Obs<LSL 0%
#> Exp>USL 0% Obs>USL 0%
plot(pc)
plot(processCapability(q, spec.limits=c(73.95,74.05), target=74.02))
plot(processCapability(q, spec.limits=c(73.99,74.01)))
plot(processCapability(q, spec.limits = c(73.99, 74.1)))
```