P Chart

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Control Chart - p Chart


Purpose

A p Chart is to observe and evaluate the behavior of a process over time, and against control limits, and take corrective action if necessary. The chart plots the proportion of nonconforming units collected from subgroups of equal or unequal size.

A p Chart differs from np Charts in that they plot the proportion of defective units, rather than the number of defective units


P Charts, or percent defective charts, measure discrete data. They are used to quantify defective units. Data is usually collected in samples that are not of constant sizes. Normally subgroup sizes should be larger than 50 and your average number of defects should be equal to or greater than 5.

The p-chart chart measures the output of a process as a percentage of defective items. Each item is recorded as either pass or fail, even if the item has more than one defect. This is the most sensitive attribute chart.

Anatomy

P Chart

Terminology

A. Proportion – Proportion of defective units observed, obtained by dividing the number of defective units observed in the sample, by the number of units sampled

B. Sample Number – The chronological index number for the sample, or subgroup, whose proportion of defective units is being referenced

C. Lower Control Limit (LCL) –Represents the lower limit of the variation that could be expected if the process were in a state of statistical control, by convention equal to the Mean minus three Standard Deviations. Since the sample size varies, the Lower Control Limit is recalculated each time, resulting in a "staircase" effect

D. Process Average Proportion Nonconforming – (p) Average value of the proportion of defective units in each subgroup, over the period of inspection being referenced

E. Upper Control Limit (UCL) – Represents the upper limit of the variation that could be expected if the process were in a state of statistical control, by convention equal to the Mean plus three Standard Deviations. Since the sample size varies, the Upper Control Limit is recalculated each time, resulting in a "staircase" effect

F. Plot of proportion nonconforming vs sample number. Any point in this plot above the UCL or below the LCL represents an out-of-control condition to be investigated

G. p Chart – The title "p" Chart refers to the proportion of defective units in a subgroup

H. Out of Control Point – By definition, any point that exceeds either the UCL or the LCL is out of control. Minitab has a number of tests available for out of control conditions, and normally labels each point with a number corresponding to the test which the point fails. If the sample size is not constant, however, the tests are not applied.


Major Considerations

The p Chart plots the proportion of units defective, and not the proportion of defects

The use of chart is preferred over the np Chart if using the rate of defective units is more meaningful than using the actual number of defective units, and the subgroup, or sample, size varies from period to period.

Large subgroup sizes should always be selected (n>50 is considered normal), and the np value should always be greater than 5

When To Use P Charts

  • Primarily used to follow trends and cycles over time
  • Used when the subgroup size changes from sample to sample
  • Used to evaluate progress after process changes and/or improvements
  • Used in cases to quickly and inexpensively gather data
  • When there are no specialized skills required to collect the data
  • The major assumptions in using P charts are that there are only 2 attributes (e.g. Pass/Fail) that you are measuring and the occurrence of an attribute is independent from item to item.

Application Cookbook

1. Determine purpose of the chart

2. Select data collection point

3. Establish basis for subgrouping

4. Establish sampling interval and determine sample size

5. Set up forms for recording and charting data and write specific instructions on use of the chart

6. Collect and record data. It is recommended that at least 20 samples be used to calculate the Control Limits

7. Compute p, the proportion nonconforming for each of the i subgroups

8. Compute the Process Average Proportion Nonconforming p

9. Compute Upper Control Limit UCLp

10. Compute Lower Control Limit LCLp

11. Plot data points

12. Interpret chart together with other pertinent sources of information on the process and take corrective action if necessary

*Note: as the subgroup size n changes, the UCL and LCL must be recalculated for each subgroup


Statistical Process Control Basics

Statistical Process Control

Control Charts

Control Chart Selection

Control Limits

Capability Indices - Cpk, Etc.

Process Capability Study

Statistical Process Control Control Charts

Xbar & R (Range) Chart

Xbar & s (Standard Deviation) Chart

I (Individuals) & MR (Moving Range) Chart

p Chart

np Chart

u Chart

From p Chart to Statistical Quality Control.

From p Chart to Free Six Sigma Tools.

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