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SNSchart Package

Luis Benavides

2021-04-05

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.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.