This document discusses control charts for attributes data, specifically p charts and np charts. It provides information on how p charts and np charts are constructed and how they can be used to monitor processes where the quality characteristic is classified as conforming or non-conforming. Examples are given to illustrate how to set up p charts and np charts and how to interpret them to check if a process is in control.

1. CONTROL CHARTS FOR ATTRIBUTES

2. CONTROL CHARTS FOR ATTRIBUTES
It is often inconvenient, impractical, or impossible to take numerical measurements of
the type necessary to set up variables control charts.
In these cases, the quality characteristic of a unit is judged, or classified, as either
conforming or non-conforming based on whether or not it has certain attributes
(leaks/does not leak, works/does not work, etc.).
There are four special control charts for analyzing attribute data:
p chart — Plots the fraction non-conforming per sample
np chart — Plots the number non-conforming per sample
c chart — Plots the number of non-conformities per inspection unit
u chart — Plots the average number of non-conformities per
inspection unit

3. One advantage of using attributes charts is that they can handle multiple
characteristics.
Therefore, attributes charts typically require more inspec- tion.
The inspection is less precise (no measurements to be taken and recorded) and is
usually cheaper (no special training needed).
Advantages of ATTRIBUTES CHARTS

4. CONTROL CHART FOR FRACTION NON-
CONFORMING (p CHART)
The control chart for fraction non-conforming is also known as the p chart.
The “p” stands for proportion because it measures the proportion of non-conforming
units in a group of units being inspected.
The p chart monitors the fraction non-conforming of a process by plotting sample
fraction non-conforming over time.
The p chart is based on the binomial distribution.

5. The binomial distribution assumes that:
1. For every trial there are only two possible outcomes (e.g., pass/fail,
conforming/non-conforming).
2. The same trial is repeated any number of times.
3. The repeated trials are independent of one another. For example, the outcome of
the second trial is not affected by (or dependent on) the first trial, and the
outcome of trial n is not affected by the outcomes of trial 1 through trial n – 1.
4. The probability of a specific outcome remains constant from trial to trial.

6. The control limits for the p chart to be determined from:
where Di = number of non-conforming units in sample i
ni = number of units in sample i
m = number of samples

7. This allows the control limits for the p chart to be determined from:
Note: The LCL may give a value less than zero. Whenever this occurs, a lower control limit
of zero is used.

8. A manager wants to keep track of the number of non-conforming circuit testers being
produced. There are six types of defects that can cause a circuit tester to be considered
defective or non-conforming:
1. Mechanical defect
2. Short
3. Open
4. Peak inverse voltage (PIV)
5. Voltage forward (VF)
6. Reverse polarity (RP)
The manager sets up a data collection sheet and begins to collect the information on the
defective circuit testers being produced. The manager sets the sample size at 2000. The data
collected for a period of 23 days are given in Table.

10. The control limits for the p chart are:
- 0.1048

11. The process appears to be in-control, and the average fraction non- conforming is 12.72%.

12. ROL CHART FOR NUMBER NON-CONFORMING (np C
If the sample size can be kept constant, then the p chart can be simplified.
With a constant sample size, there is really no need to convert the number non-
conforming to fraction non-conforming. Simply plot the number non- conforming.
The np chart is also based on the binomial distribution. The control limits for the np
chart can be found using the following equations:

13. As with the p chart, if the LCL equation gives a value less than zero for the lower
control limit, then the lower control limit is set to zero.
A small sheet-metal part is shaped through a series of processes. When the shaping is
completed, the part is inspected. If any defect is found, the part is considered defective
and is scrapped. The shop foreman has decided to track the number of defective sheet-
metal parts produced. The parts are produced and shaped in batches of size 100. Since
the sample size is constant, the foreman decides to use an np chart. The inspection
results of the last 26 batches are shown in Table.

16. The np chart is given in Figure.
The chart appears to be in-control as no points fall outside the control limits.
However, an average of 16 non-conforming pieces per batch is too high. The foreman
has decided further investigation is needed.