Analise de dados

Control Charts for Attributes
By the attribute method we mean the measurement of quality through noting the presence or absence of some characteristic in each of the units, and counting how many units do not posses the quality characteristic. The advantage of the attribute method is that a single chart can be set up for several characteristics, whereas a variables chart must be set up for each of the characteristics with an accompanying chart for controlling variability. p-Chart for Fraction Nonconforming
This is also known as the proportion chart. The p-chart configuration is intended to evaluate the process in terms of the proportion or fraction of the total units in a sample in which a designated classification event occurs. This designated classification event may be a deviation more than the specified on a measurement scale, quasi-measurement scale, go or not-go gauge, judgment, etc. It could also be a nonconformity, defect, blemish, presence or absence of some characteristic, etc. The classification may also be based on several characteristics. Instead of proportions, if percents are used, then the p-chart will stand for percent chart.
Let p stands for the fraction nonconforming of the process and [pic] be the sample fraction nonconforming computed as the ratio of the number of nonconforming units d to the sample size n. That is, [pic]= d/n. Let d follows a binomial distribution with parameters n and p ie
[pic]
It is further known that the mean and variance of [pic] are p and p(1-p)/n respectively. If the true value of p is known, the control limits become
[pic]
with the central line being at p. Here p could be a standard value p'.
Suppose that the true fraction nonconforming is unknown. As usual, it is assumed that the total number of units tested from the process is subdivided into m rational subgroups consisting of n1, n2, n3...ni...nm units respectively and a value of the proportion defective is computed for each subgroup. For convenience, one