Apple Sanity School > Attribute Charts
Nominal Data for P-Charts, NP-Charts, Nonconforming Items
Welcome to the school for Apple Sanity, Sunshine Ecstasy. This page describes
attribute charts and the process measurement for nominal and ordinal data, with p-charts, np-charts,
control limits, 6-sigma rule: shows if there are any special causes of error based on failure rates,
and identifies if these special causes are nonconforming items.
Information from Dr. Shewhart and Dr. Deming
All articles are original and the express, exclusive property of www.applesanity.com.
Background
During WWII, measurement of quality was applied with means, standard deviations and ranges based on a normal distribution. The enormous requirements and production levels, along with the demands of war, necessitated the need for quality control.
A process is any activity or set of activities that produces an output, which can be a product or service.
Process Measuring Charts (a.k.a. "control Charts") - used to determine whether the observed variation is from chance or due to a special cause.
Attribute Charts were invented by Dr. Walter Shewhart to help the Western Electric Company reduce problems with manufacturing telephones
Attribute Chart Data
In many service applications, the measure of quality is whether the execution is correct or not. An incorrect execution was known as a "defect." Today, manufacturers define an incorrect execution as a " nonconforming item " as a euphemism.
Attribute Charts ( or Process Measuring Charts ) are vital in measuring quality - conformance to specifications and fitness for use.
Conformity vs Conformance
Dr. Shewhart found that making a decision about the quality of a sample of telephones could lead to two mistakes: 1) Claim that defective telephones are okay or 2) claim that a batch of telephones are defective when in fact, they are okay
The model that gives the best economic decision between these two mistakes is the use of the normal distribution with plus or minus three standard deviation limits.
If a plot of series of observations over time shows a random pattern within these upper and lower bounds, then future observations will also fall within the limits as long as the process is unchanged.
Calculating p:
In attribute process control, the number of nonconforming items (r) is measured in a sample of (n) items. The "fraction of nonconforming items , " or (p), is simply (r) divided by (n). (P) multiplied by 100 yields a percentage of nonconforming items .
Plotting these fractions over an interval of time creates the basis for an attribute chart . These plots tend to fluctuate randomly and with a normal distribution.
Example of p-Chart Data
Four issues when regarding subgroups are 1) the nature of the subgroups, 2) the size of the sample for each subgroup, 3) how frequently to take samples during a day, week, etc., and 4) how many subgroups should be sampled before determining if special causes exist.
The generally accepted number of subgroups to take before one can be reasonably sure that a Process Measuring Chart lies within control limits is 25. Dr. Shewhart recommended 30 subgroups while Dr. Deming favored 60 before performing an analysis.
The easiest way to compile a Process Measurement Chart is to create relevant subgroups of equal sample size. For example a company can collect sample of 100 widgets from the set of goods produced each day, for every day during an interval of time. Each widget is counted as an observation, and each defective widget is counted as a non-conforming item or error.
The p-Chart
In order to determine if the random fluctuations are inherent in the process, the plots are measured against three horizontal lines. The center line is the average of the data. The top and bottom lines are the "control limits," corresponding to three standard deviations above and below the average line. Keep in mind that six sigma's cover 99.8 percent of all data.
Any sample plot point that surpasses the control limits is considered a special cause, which must be identified and remedied.
Computation
An unbiased average, which is known as "p-bar," is the sum of errors divided by the sum of observations. P-bar is the Center Line (CL) in a Process Measurement Chart. The upper (UCL) and lower (LCL) control limits are calculated by counting three standard deviations from the Center Line, based on p-bar and the sampling size.
Control Limits
If all the samples are the same size, then only one calculation is needed to find the upper and lower control limits. If the lower control limit turns out to be negative, then it is reset to zero because a negative control limit does not make sense. These calculations will create a "p-chart," which measures the fraction of nonconforming items over time.
If samples are of different sizes, then the unbiased average, or p-bar, is calculated the same way but the upper and lower control limits are calculated individually per sample, based on each sample's respective size.
A Special Case - the np-Chart
A similar chart, called an "np-chart," measures the number of errors over time. To calculate the Center Line, or np-bar, divide the sum of errors by the number of sample sets gathered. The upper and lower control Limits are calculated counting three standard deviations from the Center Line, based on np-bar.
np-charts can be used only when every sample is the same size. The advantage of an np-chart is that it offers a more tangible visualization of errors when compared to a p-chart.
