Introduction
Control charts for variables are built using measured values. However, measuring a variable is not always possible or acceptable. Noncompliance is not always quantifiable. Surface flaws, such as scratches or dents, cannot be quantified, for example. The amount of times this sort of default occurs, on the other hand, can be tallied, and this is essentially what an attribute chart accomplishes.
P Chart
A P chart tracks the percentage of defectives in a lot or batch. As a result, it determines the number of non-conforming units in a lot or batch. The lower and upper control limits are established so that the likelihood of a percentage slipping outside these limits is very minimal (i.e. 1%). The lower control limit frequently falls below zero, which makes no sense in the context of fractions; in this instance, the lower control limit is set to zero.
The control limits are usually set by the following equations:
LCL\ =\ \overline{P}-3\cdot\sqrt{\frac{\overline{P}\left(1-\overline{P}\right)}{n}}Center is at \overline{P}
UCL=\overline{P}+3\cdot\sqrt{\frac{\overline{P}\left(1-\overline{P}\right)}{n}}with P¯ being the mean of n proportions considered. Note that the band of tolerance
is given by + 3 standard deviations of the distribution of proportions (binomial
distribution).
Note that:
(a) p=\frac{f}{n} is the number of defectives in the sample f, divided by the sample size n.
(b) {\overline{P}=\sum_{n=1}^p}\frac{P}{m }
Sum of the number of defectives, divided by the total number of sample items
or groups.
with P¯ being the mean of m proportions considered. Note that the band of tolerance is given by + 3 standard deviations of the distribution of proportions (binomial
distribution).