## Attributes Control Charts in SPC

## Attributes

## Control

## Charts

Provide verification for the impact of any change made and help ensure that the process remains stable over time. Without the use of controls charts, there’s a greater chance of wasting time and resources chasing false alarms, while being unsure of the impact of any change that’re made to the process and the process’ sustainability.

When it isn’t possible to measure things, you are limited to counting / tallying the results, e.g. whenever there’s an all or none inspection like go / no-go, acceptable / unacceptable, etc., this is where attributes control charts become important.

In a factory environment the common situations where attributes are the only choice are when yes/no decisions need to be made, for example,

- Evaluating packaging appearance
- Checking the accuracy of package labeling
- Checking label locations on packages
- Making sure that packaging is free of grease marks and forklift tracks

Another great use for attributes control charts is to analyze historical data. Many companies already collect inspection data before they ever start using SPC. This data is almost always attribute data such as number of defects detected in a unit / sample / batch, etc.

Variables data provides more detailed and helpful information for troubleshooting and process improvements, therefore it is favored wherever it’s feasible to collect variables data. For example, a go / no-go gauge only tells you whether a part passed inspection or not, it doesn’t tell you whether it was over the upper tolerance value or lower than the lower tolerance value and by how much. This information can be critical when trying to troubleshoot or improve a process.

Another key advantage of using variables data to construct control charts is that they require significantly less data to construct. Sample sizes for attributes data are not only lager but also the amount of data required increases inversely with the rate of nonconformities, that is to say, the lower the rate of nonconformities the larger the sample size for a attributes control chart must be. For example, if the rate of nonconformity is 1 in 100 but you take a sample of size 10. Then the chances of coming across an out-of-spec part are very low. This means that the chart will indicate that there were 0 out-of-spec parts, it will be a flat horizontal line at 0, which is not very helpful.

* This especially troublesome because companies usually want to spend as little time collecting samples as possible.

**Types of Attributes Control Charts**

**p charts:**Reflect the ratio of nonconforming units in a sample to the conforming units in the sample. Given that it’s a fraction the actual sample size may vary.**np charts:**Like ‘*p charts*‘ but instead of the ratio,*np charts*show the number of nonconforming units in a sample, because it charts the number of nonconforming samples, the sample size must remain constant.**u charts:**Reflect the ratio of nonconformities per unit in a given sample, because it’s a ratio, the sample size may vary.**c charts:**Like ‘*u charts*‘ but instead of a ratio,*c charts*show the number of nonconformities for all the units in a sample, therefore the sample size must stay the same.

**Collecting Data**

* Like *variables control charts*, *attributes control charts *are graphs that display the value of a process variable over time. Therefore, the order of production matters even though, it’s not always tracked while collecting attributes data which is not meant to be used for constructing control charts.

A good place to start collecting attributes data is while conducting experiments, but extra care must be taken to record the order of production as well, which isn’t always the case because of the randomized nature of experiments.

Historical data is often a good source of attributes data as well, because most companies tend to keep a record of inspections that’ve occurred in the past.

Inspections, of all sorts, are also a good place to collect attributes data. Especially, when the attribute being evaluated has no objective unit of measurement.

Also, any situation where a binary decision needs to be made like acceptable / unacceptable or go / no-go, etc. is good place to collect attributes data for control charts.

* FSWorks, by Factory Systems, offers an intuitive data collection solution for attributes data along with automatic and real-time attributes control chart generation for all types of attributes control charts such as p-charts, np-charts, u-charts, and c-charts.

If you want to leverage the powerful, yet easy-to-use, suite of tools offered by FSWorks in order to gain a deeper understanding from the data being collected in your factory or the historical data you’ve collected in the past, please click here.

**Analyzing Data**

Data analysis for attributes control charts is simpler than that for variables control charts.

We need to keep a track of the number of nonconformities (*for np and c charts*) or the fraction of nonconformities (*for p and u charts*), for each sample (*in p and np charts*) or each inspection unit (*in c and u charts*).

**Constructing Control Charts**

#### I. Centerline

The centerlines for attributes control charts are per sample/unit averages of total number/fraction of nonconformities, usually denoted by p-bar, c-bar, and u-bar.

#### II. Control Limits

‘*p*‘ and ‘*np*‘ control charts are known to follow a Binomial Distribution, and from statistical theory we know that the standard deviation of a binomial variable is,

therefore the upper and lower control limits for *p* and *np* *control charts *are as follows,

where p-bar and np-bar are the estimate of the long-term process mean established during control-chart setup.

*u* and *c charts *are known to follow a Poisson distribution, and from statistical theory we know that the standard deviation for a poisson variable is,

Therefore the upper and lower control limits for *c *and *u *control *charts* are as follows,

where c-bar and u-bar are the estimate of the long-term process mean established during control-chart setup.

**Analyzing Attributes Control Charts**

In analyzing the attributes control charts, our primary interest is process stability and consistency. With that in mind, if there’s only evidence of inherent variability, then the process can be thought of being in-control / stable. However, if there is evidence of assignable-cause variability, then the process can be thought of as being out-of-control / unstable, in which case you must take action to return stability to the process before proceeding further.

Some of the trends in attributes control charts that indicate if a process is out-of-control are,

- Any point outside of the control limits.
- 9 points in a row above or below centerline.
- 6 points in a row steadily increasing or decreasing.
- 14 points in a row alternating up and down.

**Conclusion**

Attributes control charts help you ensure that the process remains stable and predictable, when collecting variable measurements is either infeasible or impossible. That being said, variables data is always preferred and should be used wherever possible. Also, control charts, of either kind, don’t help you decide when to be satisfied with the current state of the process, they only tell you if it’s stable and provide you with the value that the process is centered on and the amount of variability in the process.

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