Author: Luis Benavides
Date: 2021-04-05

# SNSchart Package

#### Luis Benavides

#### 2021-04-05

Install the package `SNSchart` hosted in github.

    install_github("LuisBenavides/SNSchart")

Load the package

    library("SNSchart")

## Using Sequential Normal Scores to Detect a Change in Location (Shewhart Scheme)

### Example 3.1.1.

Get dataset from Example 8.2 by Qiu (2013) (see Example 3.1.1 from Conover, Tercero, and Cordero-Franco (2019))

    X = SNSchart::example82$X
    X.id = SNSchart::example82$X.id

Table with the dataset using dataframe of (first 10 rows).

X | X.id
--- | ---
-0.623 | 1
-1.068 | 1
0.605 | 1
-0.002 | 1
-0.807 | 1
-0.105 | 2
-0.037 | 2
-0.595 | 2
1.222 | 2
-0.545 | 2

Get the sns of the dataset

    s = SNSchart::SNS(X=X,X.id=X.id)

to plot it

    plot(s)

## CUSUM Variation to Detect a Change in Location

### Example 3.2.1.

Get dataset from Example 8.4 by Qiu (2013) (see Example 3.2.1 from Conover, Tercero, and Cordero-Franco (2019))

    X = SNSchart::example84$X
    X.id = SNSchart::example84$X.id

Table with the dataset using dataframe of (first 10 rows).

X | X.id
--- | ---
-0.393 | 1
-0.685 | 1
0.360 | 1
0.148 | 1
0.867 | 1
-0.552 | 2
-0.462 | 2
-0.979 | 2
-0.580 | 2
-0.008 | 2

Get the sns of the dataset using a CUSUM scheme

    s = SNSchart::SNS(X=X,X.id=X.id, chart="CUSUM", chart.par=c(0.5, 4.389, 3))

to plot it

    plot(s)

## EWMA Variation to Detect a Change in Location

### Example 3.3.1.

Load package and get dataset from Example 8.4 by Qiu (2013) (Example 3.2.1 from Conover, Tercero, and Cordero-Franco (2019))

    X = SNSchart::example84$X
    X.id = SNSchart::example84$X.id

Table with the dataset using dataframe of (first 10 rows).

X | X.id
--- | ---
-0.393 | 1
-0.685 | 1
0.360 | 1
0.148 | 1
0.867 | 1
-0.552 | 2
-0.462 | 2
-0.979 | 2
-0.580 | 2
-0.008 | 2

Get the sns of the dataset using a EWMA scheme

    s = SNSchart::SNS(X=X,X.id=X.id, chart="EWMA", chart.par=c(0.01, 2.0171))

to plot it

    plot(s)

## Sequential Normal Scores with a Reference Data Set (Phase 1)

### Example 3.5.1.

Load package and get dataset from Example 8.7 by Qiu (2013) (Example 3.5.1 from Conover, Tercero, and Cordero-Franco (2019))

    X = SNSchart::example87$X
    X.id = SNSchart::example87$X.id
    Y = SNSchart::example87$Y

Table with the dataset using dataframe of (first 10 rows).

X | X.id | Y
--- | --- | ---
-0.034 | 1 | -0.333
-0.103 | 2 | -0.039
0.463 | 3 | 0.071
0.193 | 4 | -0.303
0.723 | 5 | -0.712
1.362 | 6 | 0.294
-0.366 | 7 | -0.421
-0.610 | 8 | -0.241
0.012 | 9 | 0.740
0.269 | 10 | 0.534

Get the sns of the dataset using a EWMA scheme

    s = SNSchart::SNS(X=X,X.id=X.id, Y=Y, chart="EWMA", chart.par=c(0.01, 2.0171))

to plot it

    plot(s)

## Detecting a Change in Both Location and Scale (SNS Method)

### Example 4.3.1

Load package and get dataset from Example 4.9 by Qiu (2013) (Example 4.3.1 from Conover, Tercero, and Cordero-Franco (2019))

    X = example49$X2
    X.id = example49$X.id
    Y = example49$Y2

Table with the dataset using dataframe of (first 10 rows).

X1 | X2 | Y1 | Y2 | X.id
--- | --- | --- | --- | ---
0.5993625 | -0.7822084 | 0.0187462 | -0.7618043 | 1
0.6654434 | -0.4997350 | -0.1842525 | 0.4193754 | 1
2.3679540 | 2.3102095 | -1.3713305 | -1.0399434 | 1
3.1377671 | -1.7294545 | -0.5991677 | 0.7115740 | 1
1.5058193 | -1.7333567 | 0.2945451 | -0.6332130 | 1
1.7863424 | -4.6420341 | 0.3897943 | 0.5631747 | 2
0.0977881 | 1.2176603 | -1.2080762 | 0.6609867 | 2
1.5328970 | 2.3000121 | -0.3636760 | -1.6580509 | 2
0.3541057 | -2.3991953 | -1.6266727 | 1.0281680 | 2
1.2909875 | -3.1600015 | -0.2564784 | 1.1279536 | 2

Get the SNS^2 of the dataset using a Shewhart scheme. In the example the reference sample is fixed therefore .

    s = SNSchart::SNS(X=X,X.id=X.id, Y=Y, chart="Shewhart", scoring="Z-SQ",isFixed = TRUE)

to plot it. Only the plot of the monitoring sample is presented.

    plot(s)

## Multivariate Sequential Normal Scores to Detect a Change in Location

### Example 6.1.1.

Get dataset from Example 9.1 by Qiu (2013) (see Example 6.1.1 from Conover, Tercero, and Cordero-Franco (2019)).

    X = SNSchart::example91[,1:2]
    X.id = SNSchart::example91$X.id

Table with the dataset using dataframe of (first 10 rows).

X1 | X2 | X.id
--- | --- | ---
-0.692 | -1.230 | 1
0.165 | 0.267 | 1
-0.153 | -0.325 | 1
0.289 | -1.325 | 1
0.140 | 0.211 | 1
0.188 | -0.236 | 1
0.072 | 2.337 | 1
0.685 | 0.614 | 1
-1.245 | -1.013 | 1
-0.153 | 0.189 | 1

Get the multivariate sequential normal scores

    msns = SNSchart::MSNS(X, X.id)

and plot it

    plot(msns)

## Multivariate Sequential Normal Scores to Detect a Change in Location

### Example 6.2.1.

Get dataset from Example 9.3 by Qiu (2013) (see Example 6.2.1 from Conover, Tercero, and Cordero-Franco (2019)).

    X = SNSchart::example93[,1:2]
    X.id = SNSchart::example93$X.id

Table with the dataset using dataframe of (first 10 rows).

X1 | X2 | X.id
--- | --- | ---
-1.197 | -1.060 | 1
-0.536 | -0.447 | 1
1.302 | 1.826 | 1
-0.449 | 0.933 | 1
-2.569 | -2.584 | 1
-0.805 | -0.594 | 1
-0.584 | -0.069 | 1
-1.635 | -2.966 | 1
1.679 | -1.278 | 1
-0.122 | 0.274 | 1

Get the multivariate sequential normal scores. Null distribution considered is the statistic.

    msns = SNSchart::MSNS(X, X.id, null.dist = "F")

and plot it

    plot(msns)

# References

Conover, W. J., Victor G. Tercero, and Alvaro E. Cordero-Franco. 2019. “An Approach to Statistical Process Control That Is New, Nonparametric, Simple, and Powerful.” arXiv Preprint arXiv:1901.04443.
Qiu, Peihua. 2013. Introduction to Statistical Process Control. Chapman; Hall/CRC.