1. http://www.paa-web.de Part Average Analysis PAA Rev. 2.0 / 2005 2. Mathematics part A Calculation rules for anomalies detection P AA

2. http://www.paa-web.de Definition / 1 Notes: 1. High qualified PAA results will be attained by considering the measuring resolution. Please be carefully to evaluate anomalies those are indicated inside of a 5% area of full scale range. 2. The PAA may be accomplished only with good examined parts without any use of out of range data. 3. It`s allowed to use data from abnormal parts for calculating local mean and standard deviation. 1.Specify the total quantity of a lot N; N  13 N = total number of the parts in one lot (observation set). Example: Yield of a manufacturing lot by a day or in one shift. Typical numbers for Automotive series production are 400... 10000 parts. For small serious production there are at least 13 parts required. 2. Specify the number of representatives in the M local set Within the observation set N the observed element is compared to the elements in it`s local set. The number of parts in the comparative set M local will be calculated by: (Gl.I) M local = MAX(12, RND((  N) / 2) x 2), RND: round up / down The typical numbers of comparative sets in automotive domains are 20...100 parts about. For small serious production there are at minimum 12 parts required.

3. http://www.paa-web.de Definition / 2 3. Measuring parameters, classification of measured data, figure up frequency distribution To every component of the comparative set parameters X j are measured. The typical number (j) of measured parameters related to automotive components are about 20... 400. (Gl.II) Number of classes K L = M local (Gl.III) Statistical resolution A stat = 1/K L * 100% (Gl.IV) Class range Y L : Y L = 1/K L * ( Y USL – Y LSL ) (Gl. V) Frequency distribution: K Histogram = K L + 2 4. Local characteristics, recognition threshold The PAA is carried out as a dynamic test. For each parameter value of the tested component there must be calculated the local average and the local standard deviation from the comparative set. (Sliding average, sliding standard deviation) Exclusion: Binary data (1-0, good-bad, black-and-white).

4. http://www.paa-web.de Definition / 3 5. Local average and standard deviation for linear PAA Applications are linear serial production processes In the following there are i and n integer numbers and N is the observation set. Calculating regulation for the first parts, e.g. with process start up routines: Remark: In case, that  i = 0 or negative, caused by the limited calculation performance of your computer, set  i =  i-1

5. http://www.paa-web.de Definition / 4 Calculating regulation for the continously running process Calculating regulation for final processing, e.g. the stop mode

6. http://www.paa-web.de Definition / 5 6. Calculating regulation for the two-dimensional PAA Select a circular area with the radius R around the center point which is given by the defined part Xi Incremental enlargement of the surroundings until the quantity of parts inside this area is filled up to: n (Xi)  M lokal List all parts inside the circle with new index k Local area X

7. http://www.paa-web.de Definition / 6 7. Dynamical PAA-Limits, 6  - outlier detection figure 8. „Dortmunder“ model There is a possiblity to deviate from the formulas Gl. VI… VIII by calculating the local average and the local standard deviation from X (i-1) to X (i-  N ) indices. However, this is only possible by stable symmetrical parameter distributions. Then with parameter shifts depending on different lots of used parts the quality of the PAA decreases necessarily. The „Dortmunder“ model may be applied only after a qualified evaluation. The advantage of this model is to safe costs for a fifo-stack (first in first out storage) in serious production, to storage parts between test and select stations.