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Gage repeatability and reproducibility study

`gagerr(y,{part,operator})gagerr(y,GROUP)gagerr(y,part)gagerr(...,`

`gagerr(y,{part,operator})` performs a gage
repeatability and reproducibility study on measurements in `y` collected
by `operator` on `part`. `y` is
a column vector containing the measurements on different parts. `part` and `operator` are
categorical variables, numeric vectors, character matrices, or cell
arrays of strings. The number of elements in `part` and `operator` should
be the same as in `y`.

`gagerr` prints a table in the command window
in which the decomposition of variance, standard deviation, study
var (5.15 `x` standard deviation) are listed with
respective percentages for different sources. Summary statistics are
printed below the table giving the number of distinct categories (NDC)
and the percentage of Gage R&R of total variations (PRR).

`gagerr` also plots a bar graph showing the
percentage of different components of variations. Gage R&R, repeatability,
reproducibility, and part-to-part variations are plotted as four vertical
bars. Variance and study var are plotted as two groups.

To determine the capability of a measurement system using NDC, use the following guidelines:

If NDC > 5, the measurement system is capable.

If NDC < 2, the measurement system is not capable.

Otherwise, the measurement system may be acceptable.

To determine the capability of a measurement system using PRR, use the following guidelines:

If PRR < 10%, the measurement system is capable.

If PRR > 30%, the measurement system is not capable.

Otherwise, the measurement system may be acceptable.

`gagerr(y,GROUP)` performs a gage R&R
study on measurements in `y` with `part` and `operator` represented
in `GROUP`. `GROUP` is a numeric
matrix whose first and second columns specify different parts and
operators, respectively. The number of rows in `GROUP` should
be the same as the number of elements in `y`.

`gagerr(y,part)` performs a gage R&R
study on measurements in `y` without operator information.
The assumption is that all variability is contributed by `part`.

`gagerr(...,param1,val1,param2,val2,...)` performs
a gage R&R study using one or more of the following parameter
name/value pairs:

`'spec'`— A two-element vector that defines the lower and upper limit of the process, respectively. In this case, summary statistics printed in the command window include Precision-to-Tolerance Ratio (PTR). Also, the bar graph includes an additional group, the percentage of tolerance.To determine the capability of a measurement system using PTR, use the following guidelines:

If PTR < 0.1, the measurement system is capable.

If PTR > 0.3, the measurement system is not capable.

Otherwise, the measurement system may be acceptable.

`'printtable'`— A string with a value`'on'`or`'off'`that indicates whether the tabular output should be printed in the command window or not. The default value is`'on'`.`'printgraph'`— A string with a value`'on'`or`'off'`that indicates whether the bar graph should be plotted or not. The default value is`'on'`.`'randomoperator'`— A logical value,`true`or`false`, that indicates whether the effect of`operator`is random or not. The default value is`true`.`'model'`— The model to use, specified by one of:`'linear'`— Main effects only (default)`'interaction'`— Main effects plus two-factor interactions`'nested'`— Nest`operator`in`part`

The default value is

`'linear'`.

`[TABLE, stats] = gagerr(...)` returns a
6-by-5 matrix `TABLE` and a structure `stats`.
The columns of `TABLE`, from left to right, represent
variance, percentage of variance, standard deviations, study var,
and percentage of study var. The rows of `TABLE`,
from top to bottom, represent different sources of variations: gage
R&R, repeatability, reproducibility, operator, operator and part
interactions, and part. `stats` is a structure containing
summary statistics for the performance of the measurement system.
The fields of `stats` are:

`ndc`— Number of distinct categories`prr`— Percentage of gage R&R of total variations`ptr`— Precision-to-tolerance ratio. The value is`NaN`if the parameter`'spec'`is not given.

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