Attribute Control Charts

Q.E.R II: Control Charts for Attributes.

P & NP charts.

What are the above charts?

Above we see a P and NP attribute control charts. The P chart displays the fraction of defective units in a sample group. The NP chart directly displays the direct count of defective units, . Attribute control charts are based on pass/fail discrete data generally from a visual or sensory measurement; paint defects, go/nogo gauge, surface cracking, mold flashing, etc. They are based on the binomial distribution, a probability distribution for which there are just two possible outcomes, with fixed probabilities summing to one. [cite onlinestatsbook].

What do the above charts mean?

Both of the above charts are generated by discrete data (pass/fail).

P-chart: The greater the y-axis value, the greater the proportion defective there is. The horizontal line at 0.0419 is the upper control limit, calculated. The control limits are used to track the performance of the part. For P-charts, the control limit will vary if the subgroup size varies. We can see that sample group 19 is out of control, as it is above the control limit.

NP-chart: A direct count of the defective parts. This chart gives us a direct amount of how many parts failed, and should only be used when the sample group size is constant.

When Do I use a P-chart or an NP chart?

When there is one defect per unit, P or NP-charts are used.

P-charts should be used when sample group size varies or is constant. NP- charts should be used only when the sample group size is constant.

P and NP charts are used when there are multiple samples per sample group, and each sample has only one pass/fail measurement.

What about the control limits?

Larger sample sizes are better for these Attribute charts. If only two samples are taken and one is defective, the proportion is immediately .5, a poor performance value. For attribute data, the applicability of the control limits is related to the process under measurement. For Control limits are used as a standard to compare future performance. The aim is to keep the process within the control limit. Consideration should be taken that the sample group size affects the control limits. For P-charts, if the sample group size varies, the control limits will be stepped.

See appendix for data table.

What is the above chart?

The above is a C-chart. C-charts are used when a single sample may have multiple defects, such as the count of surface defects per unit area of paper.

What does the above chart mean?

Each sample represents 1000m2 of paper. The greater the y-axis value, the more defects there were for the sample number. If the Sample number is beyond the Upper Control Limit, the process is out of control.

When do I use a C-chart or a U-chart?

C-charts are used when there is a sample size is constant. This means either a single item per sample, or a constant unit area per sample. U-charts (discussed later) are used when the number of defects per unit area is reported, and the unit area is subject to change.

C charts

About Attribute Control Charts.

Definition of a Control Chart

Control charts plot a quality characteristic with respect to time. The characteristic is compared to control limits to determine if the characteristic is within acceptable limits. If the characteristic is outside acceptable limits, the process is out of control.

Control Data Categories: Variables Data vs. Quality Attributes.

Quality attribute data is discrete, separated into one of two bins; go/no-go, Yes/No type data. Specimens are assessed visually or by a sensory device. The control chart data is used to determine the presence of attributes in question; Color inconsistency, surface cracking, mold defects (flashing, pitting) etc.

Variable data is continuous; weight, height, position, thickness. Parts are gauged by measuring equipment such as calipers, micrometer, scales. Variable control charts interpret the performance of a process. Variable Control chart data can be used to assign a cause to an out of control processes, or monitor a process over time.

Typical applications:

Quality Attribute: surface flaws, cracks, color inconsistency, go/no-go measurements.

Measured Variable: Weight, thickness, position, number of defects.

Attribute control charts & their distributions

P-Chart: Used to determine the fraction of defective parts in a subgroup. Uses the binomial distribution approximation of the normal distribution.

Np-chart: Determines the total number of defective units within a constant sample size. Uses the binomial distribution approximation of the normal distribution.

c-charts: Used when counting number of defects per unit. Applies Poisson’s Distribution.

u-charts: Used to count total defects per unit during a sampling period, and is able to track more than one defect per unit. Used when number of samples per period varies.

Variable control chart types & their distributions:

xbar-charts: shows the average of multiple sets over a certain subgroup

R-charts: shows the range of multiple sets over a certain subgroup

What probability distribution is the p-chart based on?

A p-chart is used to determine the fraction defective, or non-conforming parts within a group. It is based on the binomial distribution approximation of the normal distribution.

When to use an NP a P chart.

Np-charts determine the total number of defective units within a constant sample size. P-charts are used when the sample size is not constant, NP-charts are used when the sample size is constant. Applying a P-chart to a constant sample size is fine, however applying an NP-chart to a varying sample size may be misleading.

Control Chart Selection

Data Type:Quality Attribute
Differentiating between Quality attribute or Variable data will differentiate the type of chart to be used. Surface cracks, color consistency, flashing in injection molds are quality attributes, measured visually or by sensors. Measurement is discrete, pass or fail. This type of data may be applied to part dimensions by means of a go/nogo gauge. Pin Gauges are a type of GO/NOGO gauge utilized for limit dimensions. The GO gauge checks the low limit; if the hole is too small, the go gauge does not enter. The larger NOGO gauge checks the upper limit. If the hole is too large, the NOGO gauge will not enter.

GO: low limit. NOGO: upper limit.

Figure 1: A Flow Chart for selecting Control chart types, credit to Carl Berardinelli on isixsigma.com. <https://www.isixsigma.com/tools-templates/control-charts/a-guide-to-control-charts/>

Data Type: Variable Data
Variable Data is on a continuous measurement. Weight, thickness, position. This is often associated with part tolerances; Bilateral and Unilateral Tolerances being common types. The data can be any variable measured by a device such as calipers, micrometer, cmm, weight scale.

Continuous data: x-bar & R chart, x-bar and s chart, R charts.

Variable data: C-chart, u-chart, np-chart, p-chart.