The Np Chart

Tool #7 - The Np Attribute Control Chart

The use of attribute control charts arises when items are compared with some standard and then are classified as to whether they meet that standard or not. The Np control chart is used to determine if the rate of nonconforming product is stable, and will detect when a deviation from stability has occurred. There are those who argue that there should only be an Upper Control Limit (UCL), and NOT a Lower Control Limit (LCL) since rates of nonconforming product outside the LCL is actually a good thing. However, if we treat the LCL violations as another search for an assignable cause, we could learn where lower nonconformity rates lie and perhaps eliminate them further.

There is a difference between a "P Chart" and an "Np Chart". A P chart is one that shows the fraction defective (p), whereas the Np chart shows the NUMBER of defectives (Np). They are practically the same thing with the exception that an Np chart is used when the size of the subgroup (N) is constant, and a P chart is used when it is NOT constant.

Steps In Constructing An Np Chart

STEP #1 - Collect the data recording the number inspected (N) and the number of defective products (Np). Divide the data into subgroups. Usually, the data is grouped by date or by lot numbers. The subgroup size (N) should be over 50, and it is strongly recommended you stick with the constant sample size of 100 for subgroups.

STEP #2 - Record the number of defectives on a chart or spreadsheet, along with the subgroup size. An example of a chart such as this, is shown below:

STEP #3 - Record the number of defectives for each subgroup and record on the data sheet. Then total both columns, from our example above you can see we had 272 defects, and 25 groups of 100 = 2500 total parts.

_ Use the following formula to determine your Pbar, (P) and to determine the percentage defective:
_ NP = number of defectives = Np Total Parts Inspected N
To indicate as a percentage, multiply your answer by 100.
From our chart, you can see that the formula is:
272 / (divided by) 2500 = 0.1088 and this answer is Pbar
Multiply this answer by 100 and you get 10.88%.

STEP #4 - Compute the Control Limits using the formula below:

Thus, with our example: 10.88 + 3 * square root of 10.88 * (1 - .1088)

10.88 + 3 * the square root of 10.88 (.89)

10.88 + 3 * 3.11 = 10.88 + 9.34 = 20.22

With our example: 10.88 - 3 * square root of 10.88 * (1 - .1088)

10.88 - 3 * 3.11 = 10.88 - 9.34 = 1.54

STEP #5 - Draw in the Control Limits and plot the number of defective parts listed in our chart above. Connect the dots and observe the chart to determine if there are any points out of the control limits.

So that you can fully understand what the graph looks like as plotted, I have attached the actual graph of this exercise for you, using the data from the chart above. Notice that there is one point that is actually over the Upper Control Limit and thus indicates a point "out-of-control". Example Graph
If you take a close look at the Graph Example attached, it really is not that difficult for you to duplicate with paper and pencil. At this time, I have not found a suitable blank form to provide you with.

CLOSING COMMENTS & THANK YOU
If you have made it this far, I certainly congratulate you on your efforts and sincerity to learn everything within this web site. Quality is not only an exciting and challenging aspect of today's manufacturing world, it's also a vital function for survival in today's global world. What's more interesting, I believe, is that the Quality arena has expanded into service areas as well as manufacturing. The Health Care world has also embraced Quality concepts, so you see, this is not just a manufacturing concept.
There is a whole world of Quality out there to explore, and thanks to the wonderful world of the Internet, it's just a finger touch away from you. KNOWLEDGE IS POWER, Learn everything you can, while you can!
Best wishes to you all, your comments and criticisms are openly welcomed. Feel free to contact me at qualityspctools@yahoo.com. Thanks for visiting my web site.
Professor Frank E. Armstrong