Data processing: measuring – calibrating – or testing – Measurement system – Statistical measurement
Reexamination Certificate
1999-09-28
2002-08-13
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system
Statistical measurement
C702S033000, C702S081000, C702S113000, C702S182000
Reexamination Certificate
active
06434511
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates generally to physical processes, such as industrial processes and, more particularly, to a processor and method for determining the statistical equivalence of the respective mean values of two of such processes.
Engineers and scientists are often interested in comparing the mean values of two processes with the objective of demonstrating a statistically (and practically) significant difference between them. In some cases, it may be of interest to determine that two process means are not different, or at least close enough to be considered equivalent. For example, an engineer may be interested in determining if the mean productivity, &mgr;
x
, of a standard process X, is equivalent to the mean productivity, &mgr;
y
, of a new state of the art process Y, which costs considerably more than process X.
During the planning stage of an experiment for determining the equivalence of two process means, the investigator may be faced with the fundamental question of “How many samples do I truly need to demonstrate statistical equivalence?” As suggested in many statistical textbooks, see for example, textbooks by Devore, J. L. (1987),
Probability and Statistics for Engineering and the Sciences
, Monterey: Brooks/Cole Publishing, or by Ott, Lyman (1988),
An Introduction to Statistical Methods and Data Analysis
, Boston: PWS-Kent, prior techniques have employed a somewhat cumbersome formula or algorithm to determine the sample size, n, when conducting a two-sided test of no difference between two process means at a level of significance, &agr;. In order to achieve a power of 1−&bgr; when the true difference between the process means is |&mgr;
x
−&mgr;
y
|≧&Dgr;, the required sample size (from each process) is approximately,
n
=
2
σ
2
(
z
α
/
2
+
z
β
)
2
Δ
2
,
(
1
)
where &sgr;
2
denotes the common variance of the two processes. Here, Z
k
denotes the 100(1−k) percentile of the standard normal distribution. Unfortunately, application of this formula yields an infinite sample size when &Dgr;=0 (i.e., no difference of two population means). Even if a very small difference (e.g., &Dgr;=0.001) between the two means is specified, this formula often yields a sample size too large to be practical in industrial processes generally subject to substantially tight budgetary and/or scheduling constraints in order to successfully compete in today's global economy.
In view of the foregoing drawbacks of known algorithms for computing sample sizes having a sufficiently small magnitude so as to be of practical use to a user in an industrial setting, it is desirable to provide a method and processor that advantageously allows the user for determining the mean equivalence of respective processes without sacrificing the statistical accuracy of the determination of equivalence and without requiring relatively large sample sizes. It is further desirable that such algorithm be computationally friendly, that is, an algorithm that is computationally straight forward to compute without the user having to spend any inordinate amount of programming time and without having to allocate any significant computational resources to its solution.
BRIEF SUMMARY OF THE INVENTION
Generally speaking, the present invention fulfills the foregoing needs by providing a computer-based method for determining the equivalence of the respective mean values of two physical processes, X and Y, generally used in the production of predetermined goods. The method allows for inputting respective values for upper and lower limits [&thgr;
L
,&thgr;
U
] of a range for testing the difference or ratio of mean equivalence of two respective processes. The method further allows for inputting a value for a parameter &agr; indicative of a probability of falsely declaring equivalence in the equivalence range and for inputting a value for a parameter 1−&bgr; indicative of a probability of correctly declaring equivalence in the equivalence range. Additional inputting steps allow for inputting a value indicative of an externally-derived standard deviation a that is mutually shared by the respective processes and for inputting a value for a parameter &Dgr; indicative of a planned location shift between the respective mean values of the respective processes. A storing step allows for storing each inputted value from the foregoing inputting steps into a memory unit, and a computing step allows for computing, based on the stored values, respective sample sizes, n
x
, and n
y
, required by the respective processes X and Y to determine whether the respective mean values of the respective processes are equivalent to one another at least within the selected equivalence range and within the respective probabilities, the magnitude of the respective sample sizes being sufficiently small to allow a user to experimentally demonstrate the equivalence of the respective mean values of the respective processes.
The present invention further fulfills the foregoing needs by providing a processor for determining the equivalence of the respective mean values of two physical processes, X and Y, generally used in the production of predetermined goods. The processor includes, for example, a suitable input/output unit that conveniently provides means for inputting respective upper and lower limits [&thgr;
L
,&thgr;
U
] of a range for testing the mean value equivalence of the respective processes; means for inputting a value &agr; indicative of a probability of falsely declaring equivalence in the equivalence range; means for inputting a value 1−□ indicative of a probability of correctly declaring equivalence in the equivalence range, means for inputting an externally-derived standard deviation value &sgr; being mutually shared by the respective processes; and means for inputting a value &Dgr; indicative of a planned location shift between the respective mean values of two processes, X and Y. A memory unit is used for storing each inputted value. A computing module is coupled to the memory unit to receive each stored value. The computing module is configured to determine respective sample sizes, n
x
, and n
y
, required by the respective processes X and Y to determine whether the respective mean values of the respective processes are equivalent to one another at least within the selected equivalence range and within the respective probabilities. In one key advantage of the present invention, the magnitude of the respective sample sizes is sufficiently small to allow a user to experimentally demonstrate the equivalence of the respective mean values of the respective processes.
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Patent Cooperation Treaty Written Opinion on Attorney Docket 26,872, Ser. No. 09,407,310 Filed Sep. 28, 1999.
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Doganaksoy Necip
Stein Jeffrey William
Breedlove Jill M.
General Electric Company
Goldman David C.
Hoff Marc S.
Tsai Carol S.
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