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Screening
Published in Michael G. Pecht, Riko Radojcic, Gopal Rao, Guidebook for Managing Silicon Chip Reliability, 2017
Michael G. Pecht, Riko Radojcic, Gopal Rao
A 3-sigma process, with +/-3 sigma process distribution fitting within the specification limits, is a well-known “threshold of excellence” that ensures 99.73% yield [Mikel 1990] to that specification. This process results in approximately 2700 failures per one million parts, which is generally unacceptable. Effective screens must detect those 2700 failures. A higher sigma process, e.g., a 6-sigma process, reduces the number of failures to 0.002 failures per one million parts, at which point screens may be considered uneconomical and may be eliminated.
Merchandising planning and order execution
Published in R. Rathinamoorthy, R. Surjit, Apparel Merchandising, 2017
Activity 3=σ2=4-162=0.25 $ 3 = \sigma^{2} = \left( {\frac{4 - 1}{6}} \right)^{2} = 0.25 $ weeks,
Intrusion Detection and Tolerance for 6LoWPAN-Based WSNs Using MMT
Published in Georgios Kambourakis, Asaf Shabtai, Constantinos Kolias, Dimitrios Damopoulos, Intrusion Detection and Prevention for Mobile Ecosystems, 2017
In general, our detection algorithm consists of two phases: learning phase and monitoring phase. Learning phase: We assume that Wi(t)∼N(μi,σi2), that is, Wi is distributed normally with mean μi and variance σi. N(μ,σ2) is the normal (or Gaussian) distribution in probability theory [12].According to 3-sigma rule, approximately 95% and 99.7% of values drawn from a normal distribution lie correspondingly within two and three standard deviations σ away from the mean μ. This percentage increases according to the gap away from the mean. In case of 7σ, the percentage approaches up to 99.99999999974%. In other words, the probability that X is within [(μ−7σ),(μ+7σ)] is high up to 0.9999999999974.In the learning phase, we assume that every node functions normally. This phase should be performed right after the sensor network starts operating. In fact, multiple attempts in learning phase could be useful to identify “the most common normal status of the network,” thus, to determine the best values for μi and σi for the node ni. We then define [(μi − ɛi),(μi + ɛi)] as the promising interval that Wi should lie within. ɛi is a customizable parameter, which defines the frontier between normal and abnormal behaviors. Its value is generally from 3σ to 7σ.Monitoring phase: In this phase, we listen to the network and calculate Wi(t) for every node. We evaluate whether a node ni is normal or abnormal by comparing Wi(t) with μi defined in the learning phase.
Monitoring univariate processes using control charts: Some practical issues and advice
Published in Quality Engineering, 2023
I. M. Zwetsloot, L. A. Jones-Farmer, W. H. Woodall
The Shewhart chart control limits are usually computed to be plus and minus three standard errors from the mean of the chart statistics, where the mean and variance correspond to an in-control, stable baseline process. Using Chebyshev’s inequality, as Shewhart (1931, p. 95) did with 3-sigma control limits, means that no more than about eleven percent of the observations from a stable process will fall outside of the control limits, regardless of the in-control distribution of the data. However, a connection between the 3-sigma control limits and normal distribution theory quickly took root. For example, Shewhart (1939, p. 36) noted that if the control chart statistics are uncorrelated and follow a normal distribution, the probability of a false alarm with a control chart statistic falling outside of the 3-sigma control limits when the process is in control is 0.003. In our view, the normal distribution assumption is not appropriate for initial Phase I analysis, but is sometimes useful as an approximation in Phase II to investigate performance metrics. In addition, probability-based limits usually yield charts with better detection ability for processes with non-normal in-control distributions compared to the use of 3-sigma limits.
Semi-automatic road extraction from high resolution satellite images by template matching using Kullback–Leibler divergence as a similarity measure
Published in International Journal of Image and Data Fusion, 2022
Xiangguo Lin, Wenhan Xie, Libo Zhang, Huiyong Sang, Jing Shen, Shiyong Cui
in which, is the grey value of some a pixel, is the mean value of the grey values, and is the standard deviation of the grey values. Moreover, according to the 68–95-99.7 (empirical) rule or the 3-sigma rule (Pukelsheim 1994), about 68% of values drawn from a normal distribution are within one standard deviation away from the mean; about 95% of the values lie within two standard deviations; and about 99.7% are within three standard deviations. Thus, we just focus on the region with grey values ranging from to in the histogram in this paper.
Use of meteorological data for identification of drought
Published in ISH Journal of Hydraulic Engineering, 2021
Ravi Kiran Karinki, Sanat Nalini Sahoo
Drought-prone areas can be identified by SPI which is based on precipitation data alone. SPI expresses the precipitation values as a standardized deviation with respect to rainfall probability function and hence this index got more importance in recent years as potential drought indicator. SPI is calculated (Homdee et al. 2016) in different time scales (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 etc. months). Among these time scales, 1, 3, 6, 9, 12, 24, 48 give better variations to reflect agricultural and hydrological drought/impacts (Karavitis et al 2011; Zargar et al. 2011). Time scales of 1, 2 and 3 months are useful for agriculture purpose and time scales of 6, 9 and 12 months are useful for hydrological purpose (Bergman 2009). Rest are useful for interannual aridity classification (Hayes 2010; Zargar et al. 2011; Svoboda et al. 2012). In the current study, 1-month time scale of SPI for the time period 1971–2016 of precipitation is used to identify the agriculture drought. The SPI was obtained by fitting a gamma distribution function (Equation (1)) to a given frequency distribution of precipitation and then transforming the gamma distribution to a normal distribution (the values lie in one standard deviation approximately 68% of time, 2 sigma within 95% of time, 3 sigma within 98% of time) with mean 0 and variance of 1 (Dutta et al. 2015). The gamma distribution function is normally defined by Equation (1).