SEMI Standards Doc



Background Statement for SEMI Draft Document 4517

NEW STANDARD: SEMI Statistical Guidelines for Ship to Control

Note: This background statement is not part of the balloted item. It is provided solely to assist the recipient in reaching an informed decision based on the rationale of the activity that preceded the creation of this document.

Note: Recipients of this document are invited to submit, with their comments, notification of any relevant patented technology or copyrighted items of which they are aware and to provide supporting documentation. In this context, “patented technology” is defined as technology for which a patent has issued or has been applied for. In the latter case, only publicly available information on the contents of the patent application is to be provided.

The Statistical Methods Task Force (SMTF) – Liquid Chemicals Committee has developed the attached ballot for the Guide: SEMI Statistical Guidelines for Ship to Control. This effort started in December 2005 and involved weekly teleconferences along with three to four longer face-to-face meetings annually. The motivating force for this intensive development effort is that there has been a growing push in the industry to require material suppliers to only ship materials that are in statistical control. This extension of using statistical control limits as either reporting limits or as additional specifications has profound consequences. Material suppliers and Independent Device Manufacturers (IDMs) will not calculate the same control limits unless all computational aspects are strictly defined, e.g., which data, which time frame, and which method of control limit calculation. Additionally numerous differing methodologies for ship to control (STC) had been proposed or were in limited industrial use. Lack of standardization will cause significant product fragmentation as well as being a source of supplier and IDM friction.

The nature of much of the trace contamination data used in estimation of ship to control limits made the problem a difficult one. Typical materials have three data characteristics that make traditional ways of calculating control limits unsuitable. First, there are often many (>20) properties measured per sample. This dramatically inflates the Type I error (supplier’s risk) from the nominal 0.27% for a Shewhart type control chart to 5% or higher. Next, most trace contamination analytical data near to zero is skewed to the right and often has a low P/T ratio. If the skew (nonnormality) is not accounted for very high Type I errors can occur. Lastly, it is common for some trace contamination data to be partly or mostly censored to a method detection limit (MDL) and only reported as being Wl/3. (11)

After the yearly review the reference set is updated. The new reference set consists of the values for the parameters from the previous reference set that were not changed plus the values from the test set for the parameters whose STC limits did change.

Example—A complete set of calculations will be run through on a reference and test set each containing analytical results from 50 samples. It is recommended that the minimum sample size be 100. However, in order to keep the manipulations of the data tractable a smaller sample size will be used. There are 5 characteristics measured per sample. This sets the individual Type I error for each characteristic at:

(Ind = 1-0.991/5 = 0.002008.

The MDL’s, MDL designator strings and which control limits are to be calculated are shown below.

|  |A |B |C |D |E |

|MDL |0.01 |0.01 |1 |9 |1 |

|MDL designator string |ND |ND |ND |ND |ND |

|UCL ?(Y for yes) |Y |Y |Y |Y |Y |

|LCL ?(Y for yes) | |Y | | | |

The reference data is shown below.

|A |B |C |D |E |

|3.26 |80.45 |ND |ND |ND |

|4.5 | |ND |ND |ND |

|2.02 |78.96 |ND |9.31 |ND |

|2.98 |80.04 |3.57 |ND |ND |

|4.22 | |ND |ND |ND |

|5.38 | |3.91 |9.11 |ND |

|0.75 |80.41 |3.06 |ND |ND |

|0.86 |79.17 |ND |ND |ND |

|0.09 |80.52 |1.71 |ND |ND |

|0.71 |79.29 |ND |ND |ND |

|1.42 |80.7 |4.09 |ND |ND |

|1.45 | |1.92 |ND |ND |

|0.75 |80.5 |1.87 |ND |ND |

|3.56 |78.37 |ND |ND |ND |

|0.9 |78.23 |ND |ND |ND |

|1.77 |79.63 |3.73 |ND |ND |

|0.14 |80.46 |2.65 |ND |ND |

|0.48 |78.32 |2.46 |ND |ND |

|0.58 |81.71 |ND |ND |ND |

|1.89 |80.34 |ND |ND |ND |

|1.06 |80.07 |ND |ND |ND |

|0.82 |79.02 |3.47 |ND |ND |

|0.95 |80.06 |2.87 |ND |ND |

|0.21 |79.87 |ND |ND |ND |

|3.14 |80.49 |ND |ND |ND |

|0.58 |79.6 |ND |ND |ND |

|2.13 |80.12 |ND |ND |ND |

|4.62 |81.8 |ND |ND |ND |

|1.85 |79.89 |2.21 |ND |ND |

|2.63 |80.98 |ND |ND |ND |

|1.54 |79.74 |ND |ND |ND |

|6.76 |79.47 |2.28 |ND |ND |

|1.37 |79.43 |ND |ND |ND |

|1.43 |79.78 |3.4 |ND |ND |

|0.87 |81.22 |4.86 |13.5 |ND |

|0.78 |78.23 |ND |ND |ND |

|1.56 |80.97 |2.56 |ND |ND |

|0.68 |79.42 |ND |ND |ND |

|3.47 |79.36 |ND |ND |ND |

|2.35 |79.73 |ND |ND |ND |

|1.22 |79 |7.14 |ND |ND |

|1.61 |80.61 |1.33 |ND |ND |

|1.76 |80.93 |ND |9.54 |ND |

|2.46 |79.77 |2.68 |ND |ND |

|0.79 |80.53 |3.44 |ND |ND |

|2.18 |79.26 |4.56 |ND |ND |

|1.4 |79.43 |ND |ND |ND |

|2.08 |78.8 |4.02 |ND |ND |

|1.12 |79.83 |1.52 |ND |ND |

|2.62 |78.9 |2.77 |ND |ND |

For characteristics A, C, D and E there is no missing data. For characteristic B there are 4 missing data points. Thus nA, nC, nD, and nE = 50 and nB = 46. Characteristics A, C, D and E require only upper control limits. For these the critical t value is

tcrit = t(αInd, nj-1) = t(0.002008, 49) = 3.0192.

Characteristic B requires two sided limits. For this case the critical t value is

tcritB = t(αInd/2, nB) = t(0.001004, 45) = 3.2801.

Note that if the TINV function in Excel is used to calculate tcrit it requires the user to supply a probability and degrees of freedom. It always assumes a two-tailed application. To make Excel provide the correct value for tcrit then enter twice the value of αInd in the Probability input box for a once sided limit (upper or lower STC) and αInd for a two-sided limit (upper and lower STC).

The a factor for characteristics A, C, D and E is given by:

p’=p=5

b0 = 4.151277(1-exp(-0.024273(500.478154))) = 0.60521

b1 = (9.804714/50)1.18041 + 0.246002 = 0.39216

a = (5/0.60521)0.39216 = 2.2889

For two sided control limits the a factor is calculated the same way except that p’ is

p’ = 2p

Thus, for characteristic B with two sided limits and nB = 46:

p’ = 2*5 = 10

b0 = 4.151277(1-exp(-0.024273(460.478154))) = 0.583303

b1 = (9.804714/46)1.18041 + 0.246002 = 0.407276

a = (10/0.583303)0.407276 = 3.182

Before the reference sample average ([pic]), standard deviation (Sj) and coefficient of skewness (k3j) can be calculated the dual value insertion must occur for each censored value. For each characteristic, the first time a censored value is encountered the value 0 is inserted. The second time the value of the MDL is inserted. Alternate between 0 and the MDL for succeeding censored values. The reference data set after dual value insertion is shown below.

|A |B |C |D |E |

|3.26 |80.45 |0 |0 |0 |

|4.5 | |1 |9 |1 |

|2.02 |78.96 |0 |9.31 |0 |

|2.98 |80.04 |3.57 |0 |1 |

|4.22 | |1 |9 |0 |

|5.38 | |3.91 |9.11 |1 |

|0.75 |80.41 |3.06 |0 |0 |

|0.86 |79.17 |0 |9 |1 |

|0.09 |80.52 |1.71 |0 |0 |

|0.71 |79.29 |1 |9 |1 |

|1.42 |80.7 |4.09 |0 |0 |

|1.45 | |1.92 |9 |1 |

|0.75 |80.5 |1.87 |0 |0 |

|3.56 |78.37 |0 |9 |1 |

|0.9 |78.23 |1 |0 |0 |

|1.77 |79.63 |3.73 |9 |1 |

|0.14 |80.46 |2.65 |0 |0 |

|0.48 |78.32 |2.46 |9 |1 |

|0.58 |81.71 |0 |0 |0 |

|1.89 |80.34 |1 |9 |1 |

|1.06 |80.07 |0 |0 |0 |

|0.82 |79.02 |3.47 |9 |1 |

|0.95 |80.06 |2.87 |0 |0 |

|0.21 |79.87 |1 |9 |1 |

|3.14 |80.49 |0 |0 |0 |

|0.58 |79.6 |1 |9 |1 |

|2.13 |80.12 |0 |0 |0 |

|4.62 |81.8 |1 |9 |1 |

|1.85 |79.89 |2.21 |0 |0 |

|2.63 |80.98 |0 |9 |1 |

|1.54 |79.74 |1 |0 |0 |

|6.76 |79.47 |2.28 |9 |1 |

|1.37 |79.43 |0 |0 |0 |

|1.43 |79.78 |3.4 |9 |1 |

|0.87 |81.22 |4.86 |13.5 |0 |

|0.78 |78.23 |1 |0 |1 |

|1.56 |80.97 |2.56 |9 |0 |

|0.68 |79.42 |0 |0 |1 |

|3.47 |79.36 |1 |9 |0 |

|2.35 |79.73 |0 |0 |1 |

|1.22 |79 |7.14 |9 |0 |

|1.61 |80.61 |1.33 |0 |1 |

|1.76 |80.93 |1 |9.54 |0 |

|2.46 |79.77 |2.68 |9 |1 |

|0.79 |80.53 |3.44 |0 |0 |

|2.18 |79.26 |4.56 |9 |1 |

|1.4 |79.43 |0 |0 |0 |

|2.08 |78.8 |4.02 |9 |1 |

|1.12 |79.83 |1.52 |0 |0 |

|2.62 |78.9 |2.77 |9 |1 |

Values for[pic], Sj and k3j can be calculated using Excel or other spreadsheet standard functions. If these are not available use the equations that define[pic], Sj and k3j in ¶ 8.1. A summary of these statistics is shown below along with the critical t values and the a factors.

|  |A |B |C |D |E |

|Sample Size |50 |46 |50 |50 |50 |

|critical t value |3.019 |3.280 |3.019 |3.019 |3.019 |

|skewness equation factor |2.289 |3.182 |2.289 |2.289 |2.289 |

|Sample Average |1.875 |79.857 |1.802 |4.969 |0.500 |

|Sample Standard Deviation |1.415 |0.863 |1.640 |4.676 |0.505 |

|Sample Skewness Coefficient |1.421 |0.089 |0.887 |-0.093 |0.000 |

Calculations for the STC control limits for characteristics A and B are shown below.

UCLA = 1.875 + (3.019 + 2.289*1.421)*1.415*(1 + 1/50)1/2 = 10.84

UCLB = 79.857 + (3.280 + 3.182*0.089)*0.863*(1+1/46)1/2 = 82.97

LCLB = 79.857 + (-3.280 + 3.182*0)*0.863(1+1/46)1/2 = 76.99

The complete set of values for the STC limits for all five characteristics are shown below.

|  |A |B |C |D |E |

|UCL |10.84 |82.97 |10.16 |19.23 |2.04 |

|LCL | |76.99 | | | |

For this example none of the reference values were OOC. If a value was flagged as OOC then it can be removed from the data set if and only if a special cause was identified that was responsible for the OOC value and if that cause has been removed. Otherwise OOC points should remain in the reference data set.

The test data set is shown below.

|A |B |C |D |E |

|5.38 |78.63 |1.67 |ND |ND |

|0.62 |77.48 |ND |ND |6.1 |

|0.17 |78.17 |ND |11.72 |2.2 |

|5.13 |77.97 |2.86 |ND |ND |

|2.12 |78.22 |ND |ND |ND |

|4.5 |79.7 |1.24 |ND |ND |

|5.24 |81.32 |ND |13.43 |ND |

|5.59 |81.52 |ND |10.94 |ND |

|2.32 |79.36 |3.34 |ND |ND |

|1.62 |80.8 |ND |ND |ND |

|2.02 |80.8 |1.16 |9.86 |ND |

|0.86 |78.39 |1.04 |ND |ND |

|2.04 |78.47 |ND |ND |ND |

|0.24 |78.35 |2.31 |10.71 |4.7 |

|1.37 |77.51 |1.71 |ND |ND |

|2.98 |79.33 |1.01 |ND |ND |

|0.55 |78.59 |1.42 |ND |2.4 |

|0.79 |78.86 |ND |ND |ND |

|1.49 |79.45 |ND |ND |ND |

|1.3 |77.81 |ND |9.38 |ND |

|4.22 |79.28 |1.04 |ND |ND |

|3.77 |78.91 |1.19 |12.78 |ND |

|1.39 |80.63 |ND |ND |ND |

|1 |79.58 |ND |ND |ND |

|4.67 |78.18 |ND |9.67 |ND |

|3.26 |78.83 |1.03 |ND |ND |

|3.66 |80.35 |ND |ND |ND |

|0.64 |79.89 |ND |ND |ND |

|0.53 |78.13 |1.15 |ND |5.5 |

|4.49 |77.25 |ND |ND |ND |

|0.75 |78.56 |ND |ND |ND |

|2.66 |77.71 |1.18 |ND |ND |

|0.93 |80.74 |ND |ND |ND |

|2.3 |77.84 |ND |ND |ND |

|0.41 |77.83 |ND |ND |3.1 |

|0.86 |76.86 |ND |13.36 |ND |

|1.55 |77.73 |ND |ND |ND |

|1.87 |79.49 |ND |ND |ND |

|4.99 |78.8 |ND |ND |ND |

|0.58 |78.11 |ND |ND |3.3 |

|0.09 |78.14 |ND |ND |1.5 |

|0.71 |78.05 |ND |ND |ND |

|1.08 |80.58 |2.94 |ND |ND |

|2.64 |80.4 |1.83 |ND |ND |

|3.5 |78.81 |1.4 |10.11 |ND |

|0.71 |78.1 |2.15 |15.05 |ND |

|2.42 |80 |1.38 |ND |ND |

|1.09 |78.47 |1.46 |12.91 |ND |

|3.19 |78.86 |ND |ND |ND |

|2.22 |79.18 |1.4 |9.05 |ND |

All of the values in bold are flagged as OOC based on the STC limits calculated from the reference set. Assuming that each sample came from a unique lot then 8 of the 50 lots would contain OOC values and would not be shippable under the strictest interpretation of the STC limits.

STC limits can be calculated for the test set exactly the same way as for the reference set. This is necessary for the yearly review to determine if the new STC limits are applicable. First the dual value insertion has to be performed. The results of this are shown below.

| A| B | C | D | |

| | | | |E |

|5.38 |78.63 |1.67 |0 |0 |

|0.62 |77.48 |0 |9 |6.1 |

|0.17 |78.17 |1 |11.72 |2.2 |

|5.13 |77.97 |2.86 |0 |1 |

|2.12 |78.22 |0 |9 |0 |

|4.5 |79.7 |1.24 |0 |1 |

|5.24 |81.32 |1 |13.43 |0 |

|5.59 |81.52 |0 |10.94 |1 |

|2.32 |79.36 |3.34 |9 |0 |

|1.62 |80.8 |1 |0 |1 |

|2.02 |80.8 |1.16 |9.86 |0 |

|0.86 |78.39 |1.04 |9 |1 |

|2.04 |78.47 |0 |0 |0 |

|0.24 |78.35 |2.31 |10.71 |4.7 |

|1.37 |77.51 |1.71 |9 |1 |

|2.98 |79.33 |1.01 |0 |0 |

|0.55 |78.59 |1.42 |9 |2.4 |

|0.79 |78.86 |1 |0 |1 |

|1.49 |79.45 |0 |9 |0 |

|1.3 |77.81 |1 |9.38 |1 |

|4.22 |79.28 |1.04 |0 |0 |

|3.77 |78.91 |1.19 |12.78 |1 |

|1.39 |80.63 |0 |9 |0 |

|1 |79.58 |1 |0 |1 |

|4.67 |78.18 |0 |9.67 |0 |

|3.26 |78.83 |1.03 |9 |1 |

|3.66 |80.35 |1 |0 |0 |

|0.64 |79.89 |0 |9 |1 |

|0.53 |78.13 |1.15 |0 |5.5 |

|4.49 |77.25 |1 |9 |0 |

|0.75 |78.56 |0 |0 |1 |

|2.66 |77.71 |1.18 |9 |0 |

|0.93 |80.74 |1 |0 |1 |

|2.3 |77.84 |0 |9 |0 |

|0.41 |77.83 |1 |0 |3.1 |

|0.86 |76.86 |0 |13.36 |1 |

|1.55 |77.73 |1 |9 |0 |

|1.87 |79.49 |0 |0 |1 |

|4.99 |78.8 |1 |9 |0 |

|0.58 |78.11 |0 |0 |3.3 |

|0.09 |78.14 |1 |9 |1.5 |

|0.71 |78.05 |0 |0 |1 |

|1.08 |80.58 |2.94 |9 |0 |

|2.64 |80.4 |1.83 |0 |1 |

|3.5 |78.81 |1.4 |10.11 |0 |

|0.71 |78.1 |2.15 |15.05 |1 |

|2.42 |80 |1.38 |9 |0 |

|1.09 |78.47 |1.46 |12.91 |1 |

|3.19 |78.86 |1 |0 |0 |

|2.22 |79.18 |1.4 |9.05 |1 |

tcrit, the a factor, [pic], Sj, k3j, UCL and LCL are all calculated the same as for the reference set. A table that summarizes the results is shown below.

|  |A |B |C |D |E |

|Sample Size |50 |50 |50 |50 |50 |

|critical t value |3.019 |3.264 |3.019 |3.019 |3.019 |

|skewness equation factor |2.289 |3.004 |2.289 |2.289 |2.289 |

|Sample Average |2.170 |78.920 |0.998 |6.219 |0.996 |

|Sample Standard Deviation |1.612 |1.124 |0.813 |5.099 |1.387 |

|Sample Skewness Coefficient |0.702 |0.568 |0.716 |-0.258 |2.234 |

|UCL |9.70 |84.56 |4.82 |21.77 |12.39 |

|LCL | |75.22 | | | |

Next, two nonparametric (NP) tests are applied to determine statistically significant differences between the STC limits from the reference and test sets. For upper limits the 90’th percentile and the maximum from each set (for each characteristic) have to be determined. Determining the maximums is straightforward. The determination of the 90’th percentile for characteristic A in the reference set is illustrated below.

Sort the data from lowest to highest.

Let pt90 = 0.9 * (nA + 1) = 0.9*(50 + 1) = 45.90

Let ipt90 = the integer part of pt90 = 45

Let fpt90 = the fractional part of pt90 = 0.90

Let ipt91 = ipt90 + 1 = 46

Let A90 be the value of characteristic A with rank ip90 = A45 = 3.56

Let A91 be the value of characteristic A with rank ip91 = A46 = 4.22

Then, the 90’th percentile, A90%, is given by:

A90% = A90 + (A91 – A90)* fpt90 = 3.56 + (4.22 – 3.56)*0.90 = 4.15

Note that if the censoring is high enough then the maximum and/or the 90’th percentile can be the value of the MDL.

For lower control limits separate calculations have to be done for the 10’th percentile and minimum for each set. The calculations for the 10’th percentile are essentially the same as the 90’th percentile case and are illustrated below for characteristic B in the reference set.

Sort the data from lowest to highest.

Let pt10 = 0.1 * (nB + 1) = 0.1*(46 + 1) = 4.7

Let ipt10 = the integer part of pt10 = 4

Let fpt10 = the fractional part of pt10 = 0.70

Let ipt11 = ipt10 + 1 = 5

Let B10 be the value of characteristic B with rank ip10 = B4 = 78.37

Let B11 be the value of characteristic B with rank ip11 = B5 = 78.80

Then, the 10’th percentile, B10%, is given by:

B10% = B10 + (B11 – B10)* fpt10 = 78.37 + (78.80 – 78.37)*0.70 = 78.67

Note that with even moderate censoring the 10’th percentile can be buried in the censored values. In that case the MDL is an upper bound of the 10’th percentile. Values for the required percentiles, maximums and minimums are shown below.

|  |A |B |C |D |E |

|Ref n |50 |46 |50 |50 |50 |

|Test n |50 |50 |50 |50 |50 |

|Ref 90%tile |4.154 |80.973 |4.009 |9 |1 |

|Test 90%tile |4.958 |80.729 |2.118 |12.674 |3.03 |

|Ref Max |6.76 |81.8 |7.14 |13.5 |1 |

|Test Max |5.59 |81.52 |3.34 |15.05 |6.1 |

|Ref 10%tile | |78.67 | | | |

|Test 10%tile | |77.71 | | | |

|Ref Min | |78.23 | | | |

|Test Min | |76.86 | | | |

Next, critical values for the 90’th percentile and the Tukey tests need to be determined. These are the same for both upper and lower control limits. This will be worked out in detail for characteristics A and B. For characteristic A note that the 90’th percentile for the test set is greater than the reference set. Let:

n3 = ntest –1 = 50 – 1 = 49

S = (0.9*0.1/nref)1/2 = (0.9*0.1/50)1/2 = 0.042426

p3 = 0.1 + 2.326*S = 0.1 + 2.326*.0424 = 0.1986

Next, starting at i=0 find the value of i such that the cumulative binomial distribution function first becomes greater than 0.943. The critical value is then i + 1. It is recommended that this be done in a spreadsheet that supports the binomial function. The binomial function in Excel was used in this example. The arguments for the function are:

Number = cell location for value of i

Trials = n3 = 49

Probability = p3=0.1986

Cumulative = true

|i |Bn(i,49,0.19,true) | |

|0 |0.000 | |

|1 |0.000 | |

|2 |0.002 | |

|3 |0.007 | |

|4 |0.023 | |

|5 |0.057 | |

|6 |0.120 | |

|7 |0.216 | |

|8 |0.341 | |

|9 |0.482 | |

|10 |0.621 | |

|11 |0.744 | |

|12 |0.840 | |

|13 |0.908 | |

|14 |0.951 |=> i=14 and critical value = 15 |

|15 |0.976 | |

If software is not available to do this calculation then it can be done by hand using the binomial density function given by:

[pic], (12)

where x! = 1*2*…*(x-1)*x and 0! = 1.

Thus for, say, i=10 and n3 and p3 defined above we get:

[pic]= 0.140

The cumulative distribution value for i from 0 to r is:

[pic] (13)

For characteristic B start with the critical value for the upper control limit. The 90’th percentile for the reference data is greater than for the test data. For this case:

n3 = nref –1 = 46 – 1 = 45

S = (0.9*0.1/ntest)1/2 = (0.9*0.1/50)1/2 = 0. 042426

p3 = 0.1 + 2.326*S = 0.1 + 2.326*.0447 = 0.1986

Values for the cumulative binomial distribution function are shown below.

|i |Bn(i,45,0.1986,true) | | |

|0 |0.000 | | |

|1 |0.001 | | |

|2 |0.003 | | |

|3 |0.014 | | |

|4 |0.040 | | |

|5 |0.094 | | |

|6 |0.183 | | |

|7 |0.306 | | |

|8 |0.450 | | |

|9 |0.597 | | |

|10 |0.729 | | |

|11 |0.832 | | |

|12 |0.905 | | |

|13 |0.951 |=> critical value=14 |

|14 |0.976 | | |

|15 |0.990 | | |

Next, calculate the critical value for the lower control limit for characteristic B. When both the reference and test data have about the same number of observations the critical values for the upper and lower control limits will be the same. If the sample sizes are different then the critical values will probably be different. This is the case for characteristic B. Note that the 10’th percentile for the reference is greater than the 10% percentile for the test. For this case:

n3 = ntest –1 = 50 – 1 = 49

S = (0.9*0.1/nref)1/2 = (0.9*0.1/46)1/2 = 0. 04423

p3 = 0.1 + 2.326*S = 0.1 + 2.326*.04423 = 0.2029

Values for the cumulative binomial distribution function are shown below.

|i |Bn(i,49,0.2029,true) | | |

|0 |0.000 | | |

|1 |0.000 | | |

|2 |0.001 | | |

|3 |0.006 | | |

|4 |0.019 | | |

|5 |0.050 | | |

|6 |0.106 | | |

|7 |0.195 | | |

|8 |0.314 | | |

|9 |0.452 | | |

|10 |0.592 | | |

|11 |0.718 | | |

|12 |0.820 | | |

|13 |0.894 | | |

|14 |0.942 | | |

|15 |0.971 |=>critical value=16 |

Next the critical values for the Tukey test are calculated. This will be done for characteristics A and D. For characteristic A the maximum of the reference set is greater than the test. For this case

pcrit = 0.99*nref/(nref+ntest) = 0.99*50/(50+50) = 0.495.

Iterate through the following loop until p3 is greater than pcrit.

p1=1

p3=0

i = -1

do until p3>pcrit

i=i+1

p1 = p1*(nref-i)/(nref + ntest –i)

p3 = p3 + p1*ntest/( nref + ntest –i-1)

loop

The Tukey critical value is then i + 2. The iteration for characteristic A is shown below. This was done in Excel. Recall that pcrit = 0.495.

|i |p1 |p3 | | | |

|0 |0.5 |0.252525 | | | |

|1 |0.247475 |0.378788 | | | |

|2 |0.121212 |0.441268 | | | |

|3 |0.058732 |0.471858 | | | |

|4 |0.028142 |0.486669 | | | |

|5 |0.013331 |0.49376 | | | |

|6 |0.00624 |0.497115 |=>i=6 and critical value =8 |

|7 |0.002885 |0.498683 | | | |

|8 |0.001317 |0.499406 | | | |

|9 |0.000593 |0.499736 | | | |

For characteristic D the maximum of the test set is larger than the reference. For this case the role of nref and ntest switch places with each other for all the above calculations. Since nref = ntest = 50 the same result is obtained for the Tukey critical value, 8.

Tukey’s test is not applied to lower control limits. If Tukey’s test can be applied then so can the 90’th percentile test. Since the latter is has more power the 90’th percentile test is used.

A table of all the critical values for all the characteristics for both NP tests is shown below.

|  |A |B |C |D |E |

|CV for 90%tile Test for Upper CL |15 |14 |15 |15 |15 |

|CV for 90%tile Test for Lower CL |15 |16 |15 |15 |15 |

|CV for Tukey Test |8 |7 |8 |8 |8 |

The critical values can now be applied to each characteristic to determine if there is sufficient statistical evidence to conclude that the STC limits have changed. This will be done for each characteristic. The NP tests do not directly test the equivalency of STC limits, but test for statistically significant differences in the tail region nearest the control limit between the reference and test distributions. Such a difference in distribution, when statistically significant, indicates the potential need for updated STC limits. In this testing context, the null hypothesis is that the STC limits are the same and the alternative hypothesis is that the reference and test STC limits differ.

Characteristic A

For both sets the 90’th percentiles are greater than the MDL so we can apply the 90’th percentile test. Since the reference set has the smaller value for the 90’th percentile we count how many values in the test set are greater than 4.154. There are 9 such values. Since 9 Wu/3, or (16)

Abs(LCLref – LCLtest) > Wl/3. (17)

The calculations are illustrated for characteristics A and B. For characteristic A

Wu = ((3.019 + 2.289*1.421)*1.415*(1+1/50)1/2)/3 = 2.99

Abs(UCLref – UCLtest) = Abs(10.84 – 9.70) = 1.14 < 2.99.

Thus the observed difference is of no practical significance.

Characteristic B has both an upper and a lower control limit.

Wu = ((3.280 +3.182*0.089)*0.863*(1 + 1/46)1/2 )/3= 1.04

Wl = Abs(((-3.280 +3.182*0)*0.863*(1 + 1/46)1/2)/3) = 0.95

Abs(UCLref – UCLtest) = Abs(82.97-84.56) = 1.59 > 1.04

Abs(LCLref – LCLtest) = Abs(76.99 – 75.22) = 1.77 > 0.95

It is sufficient for just one of these inequalities to hold in order to deem the observed difference to of practical significance. For characteristic B the difference is of practical concern.

Shown below is a summary of the tests for statistical and practical differences. A blank indicates that there was no significant difference. An “*” in the practical significance test row means that there was a practically significant difference. X>Y in the NP significance test row indicates that X was shown to be statistically significantly greater than Y.

|  |A |B |C |D |E |

|Ref UCL |10.84 |82.97 |10.16 |19.23 |2.04 |

|Test UCL |9.70 |84.56 |4.82 |21.77 |12.39 |

|NP Stat Sig. Test | | |Ref>Test | |Test>Ref |

|Practical Sig. Test | |* |* | |* |

|Ref LCL | |76.99 | | | |

|Test LCL | |75.22 | | | |

|NP Stat Sig. Test | |Ref>Test | | | |

|Practical Sig. Test | |* | | | |

Note:

1. The upper control limits and the lower control limits are tested separately.

2. In order to change the STC limit from that calculated by the reference set to that calculated by the test set the observed difference has to be both statistically and practically significant.

3. In the case where there is both an upper and a lower control limit it is sufficient for either of them to be statistically and practically different to cause the STC to change. Even if only one control limit changed both would revert to the new STC limits.

For this example characteristics B, C and E were both statistically and practically different. Thus, their STC limits would be changed at the yearly review. The STC limits for characteristics A and D would remain the same.

SEMI STC Methodology

NOTICE: The material in this appendix is an official part of SEMI [insert designation, without publication date (month-year) code] and was approved by full letter ballot procedures on [dd-mm-yyyy]. This Appendix is intended to provide additional background information on issues related to the SEMI STC Methodology. More detailed information can be found in the Ship to Control Workshop which was provided at SEMICON West 2007. Use the following link () on the SEMI website to obtain a copy of this presentation.

Commercial Issues: A limited discussion of some of the commercial issues that will be associated with the application of a STC methodology

Product Fragmentation: Product fragmentation occurs when there are multiple product grades originating from a single product production process. From a product management standpoint, as product grades become more fragmented, this implies a greater cost for managing the supply system. Product fragmentation can also negatively impact product availability and typically drives requirements for higher overall levels of product inventory as compared to materials with less product fragmentation. Keeping with SEMI terminology a supplier produces a product and a producer (often an IDM) consumes the product.

Prior to STC, product fragmentation was typically driven by producer product requirements or the interplay with producer product requirements, differential pricing of product grades and the capability of a supplier’s process. Different product grades result whenever a producer requires a non-standard product container, requires a non-standard specification (only one product property specification needs to differ for this to occur), requires a material quality level that can not be consistently met by the supplier’s process or requires any existing specialized data treatment that uses additional data evaluation to determine product suitability over and above the nominal product specification.

The motivation of suppliers in allowing existing product fragmentation typically originates from having to satisfy their customer’s requirements. It also can originate, to a more limited extent, when a supplier finds a market opportunity when the creation of one or two additional differential product grades with differential pricing more than offsets the costs of managing these additional grades.

With implementation of STC, when used for anything other than notification, it is likely, that initially, there will be increased product fragmentation. Even if a supplier chooses to offer only one STC product grade in a single container type; such a grade is likely to be initially offered as an alternative to the existing product grades. Eventually, if STC achieves enough success, such an STC grade may displace some of the current product grades.

Existing product fragmentation may not go away. If a unique container is still required by a producer, an STC version of this product grade would replace one unique grade with another. If a supplier must still meet a customer specific set of nominal product specifications as part of an STC product grade again this product grade would replace one unique grade with another. In this latter case, there is an opportunity for STC to reduce product fragmentation if the STC product grade’s nominal specifications can be changed to levels that are no longer customer specific.

There is potential for greatly increased future product fragmentation for any STC product grade that is purchased by multiple producers. STC limits are not rigid; they can change as part of the Annual Review Process. Unless suppliers and producers consistently accept all changes in STC limits required by the STC methodology and allow use of a consistent date for Annual Review process, there is potential for massive future product fragmentation and all its undesirable consequences. The focus in devising the STC methodology was to define the method and data requirements in a manner that leads to a unique result. Any future customer specific deviation(s) will immediately result in increased product fragmentation.

STC Limits Change Impact: STC limits have the characteristic that they are likely to change more rapidly than traditional nominal specifications have historically. STC product that requires anything more than notification will require substantially more change management. The Annual Review (4.14, 8.2) process’s timing provides a tradeoff in that it does not require too frequent changes in what can be immediately shipped or the statistical specifications versus the STC limits being locked into place ad infinitum. Section 7.4 of the Guide is intended to smooth any transition to new limits.

The Annual Review portion ¶ 8.2, of the Guide uses the philosophy that STC limits should only be changed on Annual Review when there is both a statistically significant difference between the test and reference data sets and this difference is also judged to be of practical significance (4.6, 4.7, and 4.9). In this respect, the SEMI STC method is biased to only change STC limits when there is strong evidence of meaningful change (8.2). The exception to this are STC limits which are provisional (4.10, 5.7, 7.2, 8.2) and always change upon Annual Review.

Based on industry data on 34 products studied by the TF in developing the Guide, about 25% of STC parameters are likely to require modification upon Annual Review. Since the statistical tests in ¶ 8.2 were tuned to the ( ≤ 1% level on a per test parameter basis, this discrepancy implies that typical industry processes have some real degree of time instability.

When STC limits change there is high potential for product fragmentation (A1-1.1 ) if the entire package of required changes is not accepted (6.3, 6.4, and 6.5). The driving psychology for potential trouble with STC limit changes will originate from two sources; suppliers wanting the looser STC limits and not the tighter STC limits and producers wanting the tighter STC limits and not the looser STC limits. The method does not equivocate on this matter (6.5); all data indicated required changes (8.2) are implemented without exception. In order to protect producer processes, section 7.5 maintains traditional nominal specification requirements for the product grade. In this manner, STC product can never be worse than the nominal product grade it originated from.

Impact of Alternative STC Methodologies

The short version of the impact of this is product fragmentation (A1-1.1 ). Any difference in methodology (data selection, statistical rules, time frames, or additional rules) results in a different specific product grade. Additionally the operational characteristics of what alternative STC methodologies actually accomplish with respect to typical electronics product data, other than that which is provided below, are not well known. To the knowledge of the TF there is no prior unified product level statistical methodology for control limit calculation that simultaneously deals with sample size, number of parameters for which limits are desired, skewed (non-normal) data distributions, and censored data handling.

These are the reasons why the SEMI methodology was developed. It handles a broad range of issues while providing a rigorous data definition and computational methodology.

The long version of this involves what the Statistical Methods Task Force, (Guide developers) called the calibration study. The calibration study involved the use of data from many suppliers and many products to evaluate the actual performance characteristics of both the incremental and final versions of the draft Guide as well as some simple alternative methodologies (two 3 sigma approaches, 99th percentile, and historical high). The incremental calibration studies performed on the evolving draft statistical methodology allowed identification of problem areas. These problem areas, once identified, indicated where the draft methodology needed further improvement. After each modification, the performance of the entire methodology was checked again. Through this iterative process the methodology evolved until it was found to provide sufficiently reliable performance. The final calibration study involved data from 34 products and 16 suppliers. Some of these results were reported in A1-1.2 and A1-3 .

The Statistical Methods Task Force attempted to err on the side of simplicity in this evolutionary process. Many of the earlier changes made to the draft methodology via the calibration process involved discovering that the earliest attempts at method simplicity exacted too high a price on method performance. The later, more incremental, changes to the draft methodology involved detecting and resolving more subtle, but still important, issues that were only detected through iterating the calibration process.

A major calibration sub-study examined four simple statistical approaches to defining STC limits. These were:

• Three sigma control limits using the sample std. dev. (s) as estimate of sigma

• Three sigma control limits using the moving range estimate of sigma (2.66x[pic])

• Maximum (UCL=maximum in training set, LCL=minimum in training set)

• 99’th Percentile (UCL=99’th percentile, LCL=1’st percentile)

The calibration study used two years of data from processes believed to be unchanged. The first year’s data was used to set the STC limits (reference data), the second to test the performance of the STC limits (test data). This study used data submitted by 11 suppliers from 18 products. Upper control limits were applied whenever there was an upper specification, lower control limits were applied whenever there was a lower specification and both were applied whenever there was both an upper and lower specification. The average percentage of product failing to meet the historical STC limits from the first year in the second year of data is provided as a percentage.

• 25.4% (Three sigma control limits using the sample std. dev. (s))

• 42.0% (Three sigma control limits using 2.66x[pic])

• 20.7% (UCL=Maximum, LCL=Minimum)

• 25.5% (UCL=99’th Percentile, LCL= 1’st percentile)

These results were judged to be unacceptable in terms of their performance in that they would institute a statistical cherry picking mechanism with their high rejection rates. Statistical theory would also indicate that these results are largely expected rather than being unusual in nature. The draft SEMI methodology provided an average 2.6% product rejection rate when processed with the identical product data. This result is close to the average 2.8% result reported in A1-1.4 which is based on data from a total of 34 products from 16 companies.

Likely Future STC Product Rejection Rates

The SEMI STC Methodology was tested with data from 34 products submitted by 16 companies. Typically two years of data were used from processes believed to be unchanged. The first year’s data was used to establish the limits, the second year’s data to evaluate performance to the limits. This resulted in an estimated future average STC product rejection rate of 2.8%. The SEMI Method was constructed in a manner such that for a perfectly in-control process, the future average failure rate will be about 1%. The difference between the 1% target and the 2.8% observed result with actual industry data is likely to be due to real industrial processes not being in perfect statistical control. This conclusion was verified by extensive simulation studies which showed the target 1% rate is achieved for mixtures of normal and non-normal distributed properties with varying degrees of data censoring, sample sizes and number of parameters.

What an individual company experiences with STC can vary from the average 2.8% product rejection rate that was observed in the calibration study. A given product may do better or worse than the average. A collection of truly in-control processes will average 1%. An OOC process, if sufficiently OOC, can reject all future product. The SEMI Methodology does not limit the future failure rate of an OOC process.

Measurement Issues: A limited discussion of some of the measurement related issues that impact implementation of STC or any other statistical methodologies.

Censored Data and Method Detection Limits (MDLs)

Censored data reflects a reported value that conveys a data range rather that a single reported value. Censored data may be left censored, right censored, or interval censored in nature. For example, a censored measured result may be reported as 500, or between 10 and 25. Typical electronics data includes all these possibilities; although left censored data is the dominant type in practice. Left censored data typically occurs when data is censored to a MDL. Measured or otherwise unobtainable results less than the MDL are typically reported as upper limit. Interval censoring occurs when the measurement instrument only provides a range rather than a measured value. For example, an optical particle counter provides a particle count within a particle size range. For example 15 particles were counted in the 0.1 to 0.2 micron range. Particle size is interval censored; particle count is not.

The remainder of this discussion will focus on the most commonly encountered censored data case in electronics industry data used for STC; that of MDL censored data. The STC methodology makes use of multiple statistical procedures to deal with or otherwise limit the impact of MDL censored data (8.1, 8.2). These include use of the dual value substitution methodology in STC computation (8.1) and the use of non-parametric statistical methodologies to limit the impact of censored data in the annual review process (8.2).

There are numerous detection limit concepts and definitions found in the literature. The concept focused on herein, is that of a Method Detection Limit (MDL). An MDL is a statistically derived figure of merit for a measurement method. Results below an MDL are in some statistical sense (the measured result is not statistically significantly different from zero) less reliable than data which is above the MDL. For the SEMI MDL definition, see SEMI C10 – Guide for Determination of Method Detection Limits. MDLs are, in common practice, often applied to uncensored below MDL data values in the following manner: Suppose the MDL=10 ppb and 8.1 ppb is measured, this result would be reported as ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download