Notation The control chart for Exercise 1 shows a value of \(\bar p\) = 0.0975. What does that value denote, and how is it obtained? What do UCL and LCL indicate?

A p-chart is plotted to examine if the process is under control or not.

Here, the p-chart depicts the proportion of defective quarters manufactured for a series of times.

On referring to the p-chart, the value of\(\bar p\)is obtained to be equal to 0.0975.

The value of\(\bar p\)indicates the estimated proportion of defectives in the entire process.

It is obtained using the given formula:

\(\bar p = \frac{{{\rm{Total}}\;{\rm{number}}\;{\rm{of}}\;{\rm{defective}}\;{\rm{quarters}}\;{\rm{in}}\;{\rm{all}}\;{\rm{samples}}}}{{{\rm{Total}}\;{\rm{sample}}\;{\rm{size}}}}\)

Here, UCL stands for upper control limit and LCL stands for lower control limit.

The limits define a boundary within which the value of the characteristic under study must fall so that the process is statistically stable.

Here, the value of UCL is equal to 0.1865, and the value of LCL is equal to 0.0085. This implies that the value of the proportion of defects should fall within these limits for the process to be under statistical control.