Method for determining the equivalency index of goods, processes, and services

A method for qualifying a first process based on an equivalency index associated with a characteristic parameter of a product, the product being manufactured with the first process, comprising:

• a. identifying at least one variable characteristic parameter of a product manufactured with the first process;
• b. measuring said parameter on a first group of products manufactured with the first process;
• c. recording the data of the measurement;
• d. constructing a first probability distribution from the data;
• e. repeat step b and c on a second group of products, the second group of products being manufactured with a second process and the second process being of known desirable quality;
• f. deriving an second average value and a second standard deviation from the data taken from the second group of products;
• g. performing an integration of first probability distribution over limits related to the second average values and the second standard deviations;
• h. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• i. setting a threshold value for the equivalency index;
• j. comparing the equivalency index to the set threshold value;
• k. declaring the first process as being of equivalent quality as the second process when the equivalency index of at least one identified characteristic parameter is not lower than the set threshold value.

A method for qualifying a process in a first semiconductor integrated circuit manufacturing facility (FAB) based on an equivalency index associated with a parameter characteristic to an integrated circuit product, the integrated circuit product being manufactured with said process, comprising:

• a. identifying at least one variable parameter characteristic to an integrated circuit product manufactured with said process in a first FAB;
• b. measuring said parameter on a first group of integrated circuit products manufactured with said process in the first FAB;
• c. recording the data of the measurement;
• d. constructing a first probability distribution curve from the data;
• e. providing a second probability distribution of said parameter, said second probability distribution being derived from measurements of said parameter on a second group of integrated circuit products, said second group of integrated circuit products being manufactured with said process in a second facility, the second facility being possessive of said process of desirable quality;
• f. providing a second average value and a second standard deviation of said second probability distribution;
• g. integrating the area under said first probability distribution curve;
• the lower limit of the integration being the difference between the second average value and three times the value of the second standard deviation value;
• the upper limit of the integration being the sum of the second average value and three time the value of the second standard deviation value;
• h. dividing the result of step h by a weighing factor 99.7% and designating the quotient as the equivalency index of said parameter of said process of said first FAB;
• i. setting a pass threshold of the equivalency index at 98% and a reject threshold of the equivalency index at 90%;
• j. comparing the equivalency index of step i to the set thresholds;
• k. repeating steps b through i for all other identified parameters characteristic to the process;
• l. declaring said first FAB as possessive of said process of equivalent quality as said second facility when the equivalency indices of a predetermined number of identified parameters characteristic to said process are higher than the set pass threshold.

A method for qualifying a product based on an equivalency index associated with a characteristic parameter of the first product, comprising:

• a. identifying at least one variable characteristic parameter of the product;
• b. measuring said parameter on a group of the products;
• c. recording the data of the measurement;
• d. constructing a first probability distribution from the data;
• e. providing a desired target average value and a desired standard deviation value;
• f. performing an integration of the first probability distribution over limits related to the desired target average value and the desired standard deviation value;
• g. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• h. setting a threshold value for the equivalency index;
• i. comparing the equivalency index to the set threshold value;
• j. declaring the product as being of quality meeting the average and standard deviation targets when the equivalency index of at least one identified characteristic parameter is not lower than the set threshold value.

A method for qualifying a first process based on an equivalency index associated with a characteristic parameter of a product, the product being manufactured with the first process, comprising:

• a. identifying at least one variable characteristic parameter of a product manufactured with said process;
• b. measuring said parameter on a first group of products manufactured with said process;
• c. recording the data of the measurement;
• d. constructing a first probability distribution from the data of the measurements;
• e. providing a desired target average value and a desired standard deviation value;
• f. performing an integration of the first probability distribution over limits related to the desired target average value and the desired standard deviation value;
• g. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• h. setting a threshold value for the equivalency index;
• i. comparing the equivalency index to the set threshold value;
• j. declaring the first process as being of quality meeting the average and standard deviation targets when the equivalency index of at least one identified characteristic parameter is not lower than the set threshold value.

A method for qualifying a process in a first semiconductor integrated circuit manufacturing facility (FAB) based on an equivalency index associated with a parameter characteristic to an integrated circuit product, the integrated circuit product being manufactured with said process, comprising:

• a. identifying at least one variable parameter characteristic to an integrated circuit product manufactured with said process in a first FAB;
• b. measuring said parameter on a first group of integrated circuit products manufactured with said process in the FAB;
• c. recording the data of the measurement;
• d. constructing a first probability distribution curve from the data;
• e. determining a first average value and a first standard deviation of said first probability distribution;
• f. providing a second probability distribution of said parameter, said second probability distribution being constructed with a desired target average value and a acceptable standard deviation;
• g. integrating the area under said first probability distribution curve;
• the lower limit of the integration being the difference between said desired target average value and three times the value of said acceptable standard deviation value;
• the upper limit of the integration being the sum of said target average value and three time the value of said acceptable standard deviation value;
• h. dividing the result of step g by a weighing factor 99.7% and designating the quotient as the equivalency index of said parameter of said process of said first FAB;
• i. setting a pass threshold of the equivalency index at 98% and a reject threshold of the equivalency index at 90%;
• j. comparing the equivalency index of step h to the set thresholds;
• k. repeating steps b through h for all other identified parameters characteristic to the process;
• l. qualifying said first FAB as possessive of said process of desired quality when the equivalency indices of a predetermined number of identified parameters characteristic to said process are higher than the set pass threshold.

A method for declaring two products, a first product and a second product, as being equal, based on an equivalency index associated with a characteristic parameter common to the two products, comprising:

• a. identifying at least one variable characteristic parameter common to the two products;
• b. measuring said parameter on a group of the first product;
• c. recording the data of the measurement;
• d. constructing a first probability distribution from the data;
• e. determining a first average value and a first standard deviation of said first probability distribution;
• f. repeating steps b through c with a group of the second product;
• g. constructing a second probability distribution from the data of measurements taken from the group of the second product;
• h. determining an second average value and a second standard deviation of the second probability distribution;
• i. performing an integration of the sum of the two probability distributions over limits related to the first and second average values and the first and second standard deviations;
• j. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• k. setting a threshold value for the equivalency index;
• l. comparing the equivalency index to the set threshold value;
• m. declaring said two products as being equivalent in quality when the equivalency index of at least one identified characteristic parameter is not lower than the set threshold.

A method for declaring two processes, a first process and a second process, as being equal, based on an equivalency index associated with a characteristic parameter to a product manufactured with the two processes, comprising:

• a. identifying at least one variable characteristic parameter of the product, the product being manufactured with the two processes;
• b. measuring said parameter on a first group of the product, the first group of the product being manufactured with the first process;
• c. recording the data of the measurement;
• d. constructing a first probability distribution from the data in step c;
• e. determining a first average value and a first standard deviation of said first probability distribution;
• f. repeating steps b and c on a second group of the product, the second group of the product being manufactured with a second process;
• g. constructing a second probability distribution from the data taken from the second group of product;
• h. determining an second average value and a second standard deviation of said second probability distribution;
• i. performing an integration of the sum of the two probability distributions over limits related to the first and second average values and the first and second standard deviations;
• j. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• k. setting a threshold value for the equivalency index;
• l. comparing the equivalency index to the set threshold value;
• m. declaring said two facilities as possessive of said process of equivalent quality when the equivalency index of at least one identified characteristic parameter is not lower than the set threshold.

A method for declaring a process in two semiconductor integrated circuit manufacturing facilities (FABs), a first FAB and a second FAB, as being equal, based on an equivalency index associated with a parameter characteristic to an integrated circuit product, the integrated circuit product being manufactured with said process, comprising:

• a. identifying at least one variable parameter characteristic to an integrated circuit product, the integrated circuit product being manufactured with said process in the two FABs;
• b. measuring said parameter on a first group of integrated circuit products, the integrated circuit products being manufactured with said process in the first FAB;
• c. recording the data of the measurement;
• d. constructing a first probability distribution curve from the data;
• e. determining a first average value and a first standard deviation of said first probability distribution;
• f. repeating steps b through d on a second group of integrated circuit products, the integrated circuit products being manufactured with said process in the second FAB;
• g. determining an second average value and a second standard deviation of said second probability distribution;
• h. integrating the sum of the areas under the first probability distribution curve and the second distribution curve;
• the lower limit of the integration being the greater of two values, the first value being the difference between said first average and three times said first standard deviation, the second value being the difference between said second average and three times said second standard deviation, the upper limit of the integration being the lesser of two values, the first value being the sum of said first average and three times said first standard deviation, the second value being the sum of said second average and three times said second standard deviation;
• i. dividing the result of step h by a weighing factor of two times 99.7% and designating the quotient as the equivalency index of said parameter of the two FABs;
• j. setting a pass threshold of the equivalency index at 98% and a reject threshold of the equivalency index at 90%;
• k. comparing the equivalency index of step i to the set thresholds;
• l. repeating steps b through i for all other identified parameters characteristic to the process;
• m. declaring said two FABs as possessive of said process of equivalent quality when the equivalency indices of a predetermined number of identified characteristic parameters of the process are higher than the set pass threshold.

A method for declaring a plurality of products as being equivalent in quality, based on an equivalency index associated with a characteristic parameter common to the plurality of products, comprising:

• a. identifying at least one variable characteristic parameter common to the plurality of products;
• b. measuring said parameter on a group of a first product of the plurality of products;
• c. recording data of the measurement;
• d. constructing a first probability distribution from the data;
• e. determining a first standard deviation of said first probability distribution;
• f. repeating steps b and c on a group of a second product of the plurality of products;
• g. constructing a second probability distribution from the data;
• h. determining a second standard deviation of said second probability distribution;
• i. repeating steps f and g for the remaining of the plurality of products;
• j. providing a desired target value for said parameter;
• k. integrating the first probability distribution over a pair of limits, the pair of limits being related to the desired target value;
• l. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• m. setting a threshold value for the equivalency index;
• n. comparing the equivalency index to the set threshold value;
• o. repeating steps k, l, and n for each of the remaining plurality of products;
• p. declaring each of the plurality of products as having achieved the equivalency in quality and the quality being satisfactory when at least one equivalency index associated with the each of the plurality of products is not lower than the set threshold value.

A method for declaring a plurality of processes as being equivalent in quality, based on an equivalency index associated with a characteristic parameter of a product manufactured with said processes, comprising:

• a. identifying at least one variable characteristic parameter of the product manufactured with said processes;
• b. measuring said parameter on a first group of products, the products being manufactured with a first process of the plurality of processes;
• c. recording data of the measurement;
• d. constructing a first probability distribution from the data;
• e. determining a first standard deviation of said first probability distribution;
• f. repeating steps b and c on a second group of products, the second group of products being manufactured with a second process of the plurality of processes;
• g. constructing a second probability distribution from the data;
• h. determining a second standard deviation of said second probability distribution;
• i. repeating steps f through h for the remaining of the plurality of processes;
• j. providing a desired target value for said parameter;
• k. integrating the first probability distribution over a pair of limits, the pair of limits being related to the desired target value;
• l. deriving an equivalency index of said variable characteristic parameter based on the result of the integration;
• m. setting a threshold value for the equivalency index;
• n. comparing the equivalency index to the set threshold value;
• o. repeating steps k, l, and n for each of the remaining plurality of processes;
• p. declaring each of the plurality of processes as having achieved the equivalency in quality and the quality being satisfactory when at least one equivalency index associated with the each of the plurality of processes is not lower than the set threshold value.

A method for declaring a process in a plurality of semiconductor integrated circuit manufacturing facilities (FABs) as being equal, based on an equivalency index associated with a parameter characteristic to an integrated circuit product, the integrated circuit product being manufactured with said process, comprising:

• a. identifying at least one variable parameter characteristic to an integrated circuit product, the integrated circuit product being manufactured with said process in said plurality of FABs;
• b. measuring said parameter on a first group of integrated circuit products, the integrated circuit products being manufactured with said process in a first FAB;
• c. recording data of the measurement;
• d. constructing a first probability distribution curve from the data;
• e. determining a first average value and a first standard deviation of said first probability distribution;
• f. repeating steps b and c on a second group of integrated circuit products, the integrated circuit products being manufactured with said process in the second FAB;
• g. constructing a second probability distribution curve from the data;
• h. determining a second average value and a second standard deviation of said second probability distribution;
• i. repeating steps f and g for other of the plurality of FABs;
• j. providing a desired target value for said parameter;
• k. designating the smallest standard deviation derived from all said probability distributions as the minimum standard deviation;
• l. integrating the area under the first probability distribution curve, the lower limit of the integration being the difference between said first target average and three times said minimum standard deviation, the upper limit of the integration being the sum of said target average and three times said minimum standard deviation;
• m. dividing the result of step h by a weighing factor 99.7% and designating the quotient as the equivalency index of said parameter of the first FAB;
• n. repeat steps l through m for the probability distributions of other FABs;
• o. setting a pass threshold of the equivalency index at 98% and a reject threshold of the equivalency index at 90%;
• p. comparing the equivalency index of steps m and n to the set thresholds;
• q. repeating steps b through n for all other identified parameters characteristic to the process;
• r. declaring each FAB that has the equivalency indices of a predetermined number of the identified parameters higher than the set pass threshold as possessive of said process of equivalent quality.