Question

Define the "center line", "LCL" and "UCL" for an p chart and a p bar chart.

Answer 1

P CHART:

P chart is one of the attribute control chart which is used to evaluate process stability when counting the number or fraction defective. The P chart is used when the sample size varies.

Let samples of size be taken randomly from the production process or output at different time intervals. If is the number of defectives in a sample, then the fraction defective in the sample.

= Number of defective unit in a sample / Total number of unit or items in a sample

  

The actual number of defectives

If is the proportion of defectives produced by the entire processing or the average fraction defective and it is given by

= Total number of defective items in all the samples inspected/Total number of items in all samples.

The p-chart is based on binomial distribution. The binomial distribution has the standard deviation which is given by the relation,

Thus the central line and control limits for P chart are as follows:

CENTRAL LINE:

LOWER CONTROL LIMIT (LCL):

  

UPPER CONTROL LIMIT (UCL):

  

NP CHART:

NP chart is one of the attribute control chart which is used to evaluate process stability when counting the number of defective. The np chart is useful when it's easy to count the number of defective items and the sample size is always the same.

= Total number of defective items in all the samples inspected/Total number of items in all samples.

Using the same notations as in p-chart the standard deviation and control limits of np-chart are as follows:

CENTRAL LINE:

LOWER CONTROL LIMIT (LCL):

  

UPPER CONTROL LIMIT (UCL):