BlueKaizen QuEst
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Product Presentation
Motivation
In a manufacturing facility, quantile estimation is a strategic Process Control function, used for capability index and control limit calculations.
In both cases, the objective is to detect problems that should be corrected, e.g. a drift in the process capability, or the occurrence of out-of-control products. The accuracy of the estimation of quantile is thus a key to focus engineering efforts on real problems and avoid wasting their time on the analysis of false alarms.
While standard quantile estimation techniques are either relying on strong hypothesis about the data (normal distribution, Johnson fits), or need a lot of data to be accurate (empirical quantiles), BlueKaizen QuEst is a statistical learning solution aimed at delivering accurate quantile estimation for a broad range of distribution types.
Principle
BlueKaizen QuEst is a fully automatic quantile estimation tool based on modern non-parametric density estimation techniques as opposed to 6-sigma-like rules that strongly rely on the Normal assumption.
The only underlying assumption BlueKaizen QuEst makes is that samples are drawn from the same (unknown) probability distribution. Any quantile between 0% and 100% can be accurately estimated.
MASA has conducted a comparative study on the quantile estimation accuracy of three different estimation algorithms: using the Gaussian assumption (six-sigma), using the empirical quantiles (EQ) and using BlueKaizen QuEst.
The study reveals that, when the target distribution is not a Normal distribution, the six-sigma estimation is strongly biased, even if a large amount of samples is available (in other words, the study shows the lack of consistency of the quantile estimation based on the Gaussian assumption when the target distribution is not Gaussian).
In the same study, it is shown that both EQ estimation and BlueKaizen QuEst are unbiased and consistent.
BlueKaizen QuEst outperforms all technologies when the sample size is small (less than 200 values)
Main Characteristics
- Much more accurate on small data samples (<200)
- Outperforms the six-sigma method for the parameters having a non-Gaussian distribution
- Similar to the six-sigma approach for Gaussian distributions
- Provides, in standard, confidence intervals
- Provides, in standard, PPM computation
Benefits
Accurate quantile estimation enables the user to focus process control effort on the real problems, and avoid wasting a lot of time on the treatment of false alarms! The capability indices and control limits computed using BlueKaizen QuEst are more accurate than indices obtained by standard techniques such as sigma-based or empirical quantiles for a wide variety of real-world data distributions (namely multi-modal, asymmetric, heavy queued, etc).
The additional confidence intervals and PPM computation standard features also make BlueKaizen QuEst a very powerful tool that can be either used standalone, as a Microsoft Excel Macro or fully integrated in the customers IT infrastructure.
Using BlueKaizen Quest as part of his standard toolkit, you will drastically improve the accuracy of your whole process control scheme and in the end, improve the quality of the product to be delivered to your own customers.
Application examples
Control Limit Use Case
The histogram below represents a distribution of semiconductor product measurements:
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Standard Gaussian 2% control limits = [-1.418, 0.6974]
BlueKaizen QuEst 2% control limits = [-0.8002, 0.4953]
The distribution is not Normal and the standard limits defined by the 6-sigma rule lead to an irrelevant acceptance interval (especially the lower limit). As a consequence, no alarm will be raised, and out-of-control lots will not be detected.
In this case, the Normal hypothesis must be dropped. In contrast, the limits computed using BlueKaizen QuEst are accurate and will raise the requested number of alarms.
CpK Calculation Use Cases
Estimation of the 0.0014 and 0.9986 quantiles (eq to -+ or - 3 sigma)
Example 1:
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- QuEst estimation:
- Lower Quantile: -0.7785
90% Confidence interval: (-0.9454, -0.6117)
Upper Quantile: 0.8275
90% Confidence interval: (0.7301, 0.9248)
Gaussian estimation:
- Lower Quantile: -0.8620
90% Confidence interval: (-1.0635, -0.6605)
Upper Quantile: 0.9743
90% Confidence interval: (0.7728, 1.1759)
CPK estimation:
- QuEst value : 1.2114
90% Confidence interval: (1.0824, 1.3755)
Gaussian value : 1.0266
90% Confidence interval: (0.8490, 1.2983)
Example 2:
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- QuEst estimation:
- Lower Quantile: -1.0377
90% Confidence interval: (-1.1142, -0.9613)
Upper Quantile: 0.7388
90% Confidence interval: (0.6000, 0.8775)
Gaussian estimation:
- Lower Quantile: -1.8297
90% Confidence interval: (-2.1379, -1.5216)
Upper Quantile: 0.9783
90% Confidence interval: (0.6702, 1.2865)
CPK estimation:
- QuEst value : 0.8857
90% Confidence interval: (0.7193, 1.1524)
Gaussian value : 0.2607
90% Confidence interval: (0.2045, 0.3594)
PPM Calculation Use Cases
Objective: Compute the probability of being out of specification.
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Out of Specification probability estimation (in DPPM – Defective Part per Million):
- QuEst values:
- lower: 3,900
upper: 0
TOTAL: 3,900
Gauss values:
- lower: 111,400
upper: 1,200
TOTAL: 112,600
Contact
If you would like more information about BlueKaizen QuEst, please Contact us
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