# Sample NP Control Chart

NP CONTROL CHART Graphics Commands

2-150 March 10, 1997 DATAPLOT Reference Manual

NP CONTROL CHART

PURPOSE

Generates a (binomial) counts control chart.

DESCRIPTION

An NP chart is a data analysis technique for determining if a measurement process has gone out of statistical control. It is sensitive to

changes in the number of defective items in the measurement process. The “NP” in NP charts stands for the np (the mean number of

successes) of a binomial distribution. The NP control chart consists of:

Vertical axis = the number of defectives for each sub-group;

Horizontal axis = the sub-group designation.

A sub-group is frequently a time sequence (e.g., the number of defecti ves in a daily production run where each day is considered a sub-

group). If the times are equally spaced, the horizontal axis variable can be generated as a sequence (e.g., LET X = SEQUENCE 1 1 N

where N is the number of sub-groups).

In addition, horizontal lines are drawn at the mean number of defectives and at the upper and lower control limits. The distribution of

the number of defective items is assumed to be binomial. This assumption is the basis for the calculating the upper and lower control

limits. The control limits are calculated as:

(EQ 2-14)

(EQ 2-15)

where n is the number of items and p is the proportion of defective items. Also, zero serves as a lower bound on the LCL value.

SYNTAX

NP CHART <y> <size> <x> <SUBSET/EXCEPT/FOR qualiﬁcation>

where <y> is a variable containing the number of defective items in each sub-group;

<size> is a variable containing the sample size for each sub-group;

<x> is a variable containing the sub-group identiﬁer (usually 1, 2, 3, ...);

and where the <SUBSET/EXCEPT/FOR qualiﬁcation> is optional.

EXAMPLES

NP CHART Y SIZE X

NP CHART NUMDEF NUMTOT X

NOTE 1

The P CONTROL CHART is similar to the NP CONTROL CHART. The distinction is that the P CONTROL CHART plots the

percentage of defectives while the NP CONTROL CHART plots the number of defectives. The NP CONTROL CHART is typically

used for equal sample sizes and P CONTROL CHART is typically used for unequal sample sizes.

NOTE 2

The attributes of the 4 traces that make up the P control chart are controlled by the standard LINES, CHARACTERS, SPIKES, and

BAR commands. Trace 1 is the response variable, trace 2 is the mean line, and traces 3 and 4 are the upper and lower control limits.

Some analysts prefer to draw the response variable as a character or a spike rather than a connected line. The example program

demonstrates setting the line attributes (the control lines are drawn as dotted lines).

DEFAULT

None

SYNONYMS

NP CHART for NP CONTROL CHART

RELATED COMMANDS

U CHART = Generates a U control chart.

C CHART = Generates a C control chart.

P CHART = Generates a P control chart.

XBAR CHART = Generates a xbar control chart.

L

CL np 3– np 1 p–

( )=

UCL np 3 np 1 p–(

)+=

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