1 SMU EMIS 7364 NTU TO-570-N Control Charts for Attributes Data Updated: Statistical Quality Control Dr. Jerrell T. Stracener, SAE Fellow

2 Attributes Data Definition - Attributes are quality characteristics for which each inspected item can be classified as conforming or nonconforming to the specification on that quality characteristic Types Fraction nonconforming Number nonconforming Number of nonconformities per unit Average number of nonconformities per unit

3 Attributes Data Are best used where subjective characteristics must be checked (presence or absence of nicks, for example) Tend to emphasize defect reduction as the end goal (vs. variability reduction) defects (count) percentage non-conforming (or percentage) defect per unit Measurements that depend on counting are called attributes measurements.

4 Fraction Nonconforming Statistical Basis - For a stable process producing identical and independent items with probability p that an item will not conform to spec where D is the number of items nonconforming in a random sample of size n, and

5 Sample Fraction Nonconforming The sample fraction non-conforming is defined as the ratio of the number of nonconforming in the sample, D, to the sample size n, i.e. and

6 Control Chart for Fraction Nonconforming p-chart

7 where Fraction nonconforming in the i th sample for i = 1, 2,..., m

8 Test for Shift in Process Fraction Nonconforming Hypothesis: H 0 : p 1 = p 2 H 2 : p 1 > p 2 Test statistic:

9 Test for Shift in Process Fraction Nonconforming where Decision rule: reject H 0 if Z > Z  ; otherwise accept H 0

10 The p-chart - instructions 1. Obtain a series of samples of some appropriate size. Convenient sample sizes are 50 and 100. The ‘sample’ may actually be the complete lot if the entire lot has been checked. Have 20 or more groups if possible, but not less than 10 groups. 2. Count the number of defective units (warped, undersize, oversize, or whatever the characteristics may be in which you are interested). Calculate the value of p for each sample.

11 The p-chart - instructions 3. Calculate p (the average percentage defective). This is the centerline for the p-chart. 4. Calculate upper and lower control limits for the p-chart.

12 Uses of a p-chart Characteristics on which it is difficult or impractical to obtain variables measurement. Studies of defects produced by machines or operators which are directly under the machine operators control. Direct studies of the amount of dropouts, shrinkage, or scrap at specific operations

13 Uses of a p-chart - continued Can cover all defects and all characteristics, Can be a valuable capability study in itself Will also provide a good measure of the effectiveness of changes, corrections or improvements which have been made as a result of other studies

14 p-charts vs. x - R-charts The p-chart is less powerful than x and R charts. It provides less information With the x - R chart, we can study the process without regard to the specifications - the p-chart requires specs. The p-chart cannot tell us whether non- conformances are caused by poor centering, excessive variability, or out-of-control conditions.

15 p-charts vs. x - R-charts The p-chart cannot warn of trends or shifts unless they are so pronounced that they actually resulted in a change in the number of defective units produced.

16 Number of Nonconformities c - the total number of nonconformities in a unit

17 Number of Nonconformities Statistical Basis - The number of opportunities for nonconformities is infinitely large and the probability of occurrence of a nonconformity at any location is small and constant. Samples are of a constant size and the inspection unit is the same for each sample. X = number of nonconformities in the sample where c = expected number of nonconformities

18 Control Chart for Nonconformities - The c-chart C - is the count of defects in a sample c = count c = average of the counts

19 Average Number of Nonconformities Per Unit - u Where c is the total nonconformities in a sample of n inspection units

20 Control Chart - The u-chart Occasionally, it is useful to work with defects per unit, particularly when the inspection unit consists of several physical units of product. Then if n = sample size, defined as a consistent area of opportunity U

21 Control Chart - The u-chart where