Method and apparatus for controlling a process
A computer-implemented method of monitoring a process includes obtaining a sample data distribution. The sample data represents one or more parameters of a process. The sample data is collected by one or a plurality of sampling units. The method further includes calculating a control limit based on an evaluation of at least one difference of percentiles near an upper edge of the sample data distribution or a lower edge of the sample data distribution.
1 . A computer-implemented method of monitoring controlling a process, the method comprising:
obtaining a sample data distribution, the sample data representing one or more parameters of the process, the sample data being collected by one or a plurality of sampling units;
calculating a control limit based on an evaluation of at least one difference of percentiles near an upper edge of the sample data distribution or a lower edge of the sample data distribution; and
controlling the one or more process parameters by varying one or more manufacturing equipment settings based on the calculated control limit.
2 . The method of claim 1 , wherein the percentiles near the upper edge of the sample data distribution are greater than a 70%-percentile of the sample data distribution and/or the percentiles near the lower edge of the sample data distribution are less than a 30%-percentile of the sample data distribution.
3 . The method of claim 1 , wherein calculating the control limit is not based on modelling the sample data distribution and/or on calculating a mean value and/or a standard deviation of the sample data distribution.
4 . The method of claim 1 , further comprising:
producing a cumulative sample data distribution of the sample data distribution, wherein calculating the control limit is based on an evaluation of the cumulative sample data distribution.
5 . The method of claim 4 , wherein the percentiles are a p1-percentile and a p2-percentile, wherein p1 and p2 are given percentages, and wherein the p1-percentile is calculated as the sample data value at p1 of the cumulative sample data distribution and the p2-percentile is calculated as the sample data value at p2 of the cumulative sample data distribution.
6 . The method of claim 4 , wherein in an upper control limit case, the cumulative sample data distribution is evaluated only in a region equal to or greater than 70%, and/or, in a lower control limit case, the cumulative sample data distribution is evaluated only in a region equal to or less than 30%.
7 . A computer-implemented method of controlling a process, the method comprising:
obtaining a sample data distribution, the sample data representing one or more parameters of the process, the sample data being collected by one or a plurality of sampling units;
calculating at least a p1-percentile P1 and a p2-percentile P2 of the sample data distribution, wherein p1 and p2 are given percentages, wherein either
in an upper control limit case, p1<p2 and p1≥70%, or
in a lower control limit case, p1>p2 and p1≤30%;
calculating an edge evaluation measure based on at least one difference of percentiles P2−P1;
calculating a control limit based on a sum of a ps-percentile Ps of the sample data distribution and the edge evaluation measure, wherein ps is a given percentage; and
controlling the one or more process parameters by varying one or more manufacturing equipment settings based on the calculated control limit.
8 . The method of claim 7 , wherein, in the upper control limit case, ps≥80%, or, in the lower control limit case, ps≤20%.
9 . The method of claim 7 , wherein P1, P2 and Ps are calculated as the sample data values at p1, p2 and ps, respectively, of a cumulative sample data distribution produced from the sample data distribution.
10 . The method of claim 7 , further comprising:
calculating a p3-percentile P3 of the sample data distribution, wherein p3 is a given percentage with p3>p2 in the upper control limit case, or p3<p2 in a lower control limit case; and
calculating the edge evaluation measure additionally based on an edge percentile difference P3−P2.
11 . The method of claim 10 , wherein the edge evaluation measure is based on a weighted sum of the edge percentile differences ΔP12=P2−P1 and ΔP23=P3−P2.
12 . The method of claim 11 , wherein the edge evaluation measure is EEM=A×ΔP12+(1−A)×ΔP23, with A being a weight between 0 and 1.
13 . The method of claim 12 , wherein the control limit (CL) is calculated by CL(EEM)=Ps+D×EEM, with D being a control limit adjustment factor.
14 . The method of claim 12 , wherein p1, p2, p3 are chosen such that ΔP23/ΔP12=1 for a normal distribution.
15 . The method of claim 12 , wherein A is a constant value at least for sample data distributions meeting the condition 1/x≤(ΔP23/ΔP12)≤x, with x being equal to or greater than 5.
16 . The method of claim 15 , wherein A is approximately 0.37.
17 . The method of claim 12 , wherein A is a non-constant function of (ΔP23/ΔP12) at least for sample data distributions meeting the condition (ΔP23/ΔP12)<1/x or (ΔP23/ΔP12)>x, with x being equal to or greater than 5.
18 . The method of claim 17 , wherein x is approximately 10.
19 . The method of claim 11 , further comprising:
classifying an edge progression comprising checking whether or not ΔP12≠0 and ΔP23≠0 is met; and
carrying out the method only if ΔP12≠0 and ΔP23≠0.
20 . A system comprising:
one or a plurality of sampling units configured to collect sample data representing one or more parameters of a process;
a data processing apparatus configured to obtain a distribution of the sample and calculate a control limit based on an evaluation of at least one difference of percentiles near an upper edge of the sample data distribution or a lower edge of the sample data distribution; and
a process control apparatus configured to control the one or more process parameters by varying one or more manufacturing equipment settings based on the calculated control limit.
21 . A non-transitory computer readable storage medium storing a computer program operable to implement a method of controlling a process, the computer program comprising:
program instructions to obtain a sample data distribution, the sample data representing one or more parameters of the process, the sample data being collected by one or a plurality of sampling units;
program instructions to calculate a control limit based on an evaluation of at least one difference of percentiles near an upper edge of the sample data distribution or a lower edge of the sample data distribution; and
program instructions to control the one or more process parameters by varying one or more manufacturing equipment settings based on the calculated control limit.