Re: Attribute vs. variable data

["William J. Latzko" <latzko@worldnet.att.net>]

At 11:20 8/9/1999 -0500, Cynthia Nadalini wrote:
>They are using an np control chart to plot that efficiency, 
>but I was wondering if that efficiency satisfied the assumptions of the 
>binomial model, or if an X chart should be made instead.  Why or why not? 
> Thanks a lot.
>

Dear Cynthia

The np chart and the p chart (Binomial model) are both attribute charts. To
use the np chart the denominator must be the same for each measurement. If
the number of hours worked are the same every day and if one assumes that
the machine specification production is the same every day, one would plot
the actual number of bags produced (np) using a center line of npbar and an
upper and lower limit of npbar +/- 3 times square root(npbar*(1- pbar)).

It is also possible to use the p-chart in such a case provided the expected
number of bags is the same each day. The ordinate scale is simply np/n in
that case.

If the number of expected bags varies from day to day, one uses the
p-chart. This is constructed by computing pbar, the sum of all bags
produced divided by the sum of all possible bags that could have been
produced in the measurement period. The center line is pbar with the upper
and lower limit of pbar +/- 3 times square root((pbar * (1 - pbar))/nsubi).
The nsubi is the expected volume of bags on day i. This number can vary.
Note that if all nsubi's are equal, one can use the np chart. One can also
see the equivalency of the np-chart to the p-chart if all the nsubi's are
equal.

The assumption is that we are dealing with attributes. One counts only
whole bags. The count decides that it either is a bag or it is not a bag.
Presumably, there are no partially filled bags or they are counted as whole
bags or not according to a scheme set by operations.

The use of an X chart (chart for individuals?) introduces an extra amount
of variation. The percentage has an internal variation by forming the
average p = x/n *100. Using a chart for individuals generates an additional
variation from the variation between observations. From sample theory we
know that the total variation is Vsubw + Vsubb - rho*covariance. Vsubw is
the variance within the data (from forming p), Vsubb is the variance
between values of p, and rho is the correlation coefficient. In most cases
rho = 0.

What the preceding paragraph is saying is that the control limits are
effected by using a chart for individuals which can lead to an erroneous
conclusion. Therefore, if you are dealing with attribute data, it is best
to use attribute charts like the p-chart.

Bill Latzko 
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