Quality Reporting for Attributes
Control Charts for attributes cover the things that can be counted verses continuous variables modeled by X-Bar and R-Bar Charts. Continuous variables, for example, consists of sample measurements of different parts being produced on a manufacturing line within a certain time frame. Quality attributes often include things like surface flaws on sheet metal panels, cracks in drawn wire, color inconsistencies on a painted surface, etc.
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A p-chart is one of the many attribute control charts commonly used for determining the fraction defective using a constant or varying sample size, or in other words the percent defective within a lot of parts. Governed by the normal distribution approximation to the binomial distribution, p-charts typically are good for a single evaluation for a large number of parts. In other words, they are used to determine the “acceptability” of a lot of parts either on the manufacturing line, getting delivered by a supplier, or any similar situation where the outcome is pass or fail, always with two distinct outcomes.
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The binomial distribution is efficient in this case where the sample size is known but the entire population is unknown. It allows computation of the probability of observing a specified number of successes when the process is repeated a specific number of times and the outcome is success or failure. That alludes to the benefits that any manufacturing process can experience by knowing this methodology.
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Np-charts, opposed to p-charts, plot the actual number defective per subgroup in contrast to the p-chart which only plots the fraction defective. These are more useful when in direct contact with operators on the manufacturing line because it is the most straightforward pictorial reference that distinguishes the number of nonconforming parts within the manufacturing line. It is important not to confuse these with C-charts which are used for counting the number of nonconformities in single unit verses a lot of units for the np/p-charts.
For this p/np-chart representation, the count of surface nonconformities in 1000m2 of 20-kg paper. The central line and control limits are plotted. The center line represents the average fraction of nonconforming parts to the total lot within the data group. The control limits are set according to the relationship between the average fraction defective and the subgroup as follows:
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Where:
p bar is the average fraction defective
np = the number defective
n = subgroup size
The np chart just plots the number of nonconforming with the control limits having somewhat of a different relationship with the average fraction defective and the subgroup size, a follows:
Where:
p bar = the average fraction defective
n = subgroup size
