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Statistics for Quality
Published in K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur, A First Course in Quality Engineering, 2018
K. S. Krishnamoorthi, V. Ram Krishnamoorthi, Arunkumar Pennathur
Most statistical software packages provide a routine to make the normal probability plot for a given set of data. Figure 2.28 shows a normal probability plot made using the Minitab software. The computer software plots each point in the data against its cumulative probability, the cumulative probabilities for individual values being estimated by the mean rank of the value in the data. To calculate the mean rank, the data are first arranged in ascending order. Then, the mean rank of the observation that has the i-th rank in the data is i/(n + 0.5), where n is the total number of observations in the data. The mean ranks of a few values for the data in Table 2.1 are shown in Table 2.4. An alternative method to estimate the cumulative probabilities is to use the median rank calculated as (i − 0.3)/(n + 0.4).
Process Capability
Published in Gisi Philip, Sustaining a Culture of Process Control and Continuous Improvement, 2018
The proper interpretation of a capable process, using capability analysis, requires that the data approximates a normal distribution, which is characteristic of many industrial processes. Data collection may require a minimum sample size of 30 data points before sample means can be evaluated for normality. The Anderson–Darling normality test is often used to determine data normality with an understanding of its limitations. Data that is normally distributed will be exhibited as a straight line when using a normal probability plot and have a p-value >0.05. If the data is not normal (p < 0.05), consider options for transforming the data set into a normal distribution or an alternate method for assessing process capability. Sometimes, a simple visual display of distributed data will justify a normality assessment.
Desensitized control charts with operational importance for autocorrelated processes
Published in Quality Technology & Quantitative Management, 2022
Samrad Jafarian-Namin, Mohammad Saber Fallahnezhad, Reza Tavakkoli-Moghaddam, Ali Salmasnia
Figure 8 indicates that the data fluctuate around the mean, and the variance is not unstable. From Figure 9(a), the ACF plot shows exponential decay with tails off, indicating the stationarity and no need for differentiation. However, the PACF plot has a significant spike at the first lag and then cuts off. It means that the observation of the current period only depends on one of the previous periods, and thus, AR(1) is selected for modeling. Table 3 shows the results of estimating the model by Minitab software. The significant coefficient is ϕ = 0.55. Since |ϕ|<1, the stationarity is deduced. The constant term should be considered in the model. To evaluate the adequacy of the model, Figure 9(b) shows no significant spikes for the ACF and PACF values. In addition, the independence assumption of residuals is not rejected from Table 3(b). Therefore, there is no remaining pattern among the residual. Further investigations are followed via Figure 10. The data points mainly lie on a straight line in the normal probability plot. The symmetrical feature is identified around zero by the histogram. Figure 10(b) indicates a random scatter between residuals and fitted values. Figure 10(d) shows no patterns among residuals versus time.
A Four-Pillared Holistic Model for Improving Performance in Engineering Virtual Project Teams
Published in Engineering Management Journal, 2020
Minitab Statistical Software, Version 17, by Minitab, Inc. is used to conduct the analysis. In order to perform the statistical analyses, several assumptions are validated, including related pairs, absence of significant outliers, normality, no multicollinearity, homoscedasticity, and linearity (Hair et al., 2016). To ensure no multicollinearity (i.e., high correlation between multiple predictor variables), variance inflation factor (VIF) values are calculated to ensure values less than 10 (Hair et al., 2016). Review of residual plots and normal probability plots are performed to assess normality of the residuals and homoscedasticity, indicating the residuals are equally distributed and not grouped together. The normal probability plot illustrates a straight line while the histograms illustrate an even distribution, indicating the residuals are normally distributed. A scatterplot and fitted line plot are used to plot the values of the holistic model pillars vs. project performance in order to assess absence of outliers and linearity.
Relationship between pore coarsening and mass loss during supersolidus liquid phase sintering of alpha brass
Published in Powder Metallurgy, 2019
Abbas Sabahi Namini, Maziyar Azadbeh, Ahad Mohammadzadeh, Herbert Danninger, Shirin Rezapasand
Here it must however be considered that these models have been given for impact test bars with a dimension of 55 × 10 × 10 mm. The Zn evaporation depends on the specific surface of the sample; therefore varying the dimensions of the specimen means that the specific surface of the sample is changed and the value of the ML must be calculated for the other dimensions. Equations (9)–(11) predict ML of the sintered samples. The Equation (9) is given in the coded values of parameters for both sintering atmospheres, and the Equations (10) and (11) are given in the form of actual values of parameters for N2 and Ar sintering atmospheres, correspondingly. The normal plot of residuals and the predicted versus actual response plot are, respectively, demonstrated in Figure 5(a,b), for the response ML. The normal probability plot indicates whether the residuals follow a normal distribution, in which case the points will follow a straight line. Figure 5(a) reveals that errors are extended normally because the residuals follow a straight line. Figure 5(b) exposes that the predicted ML values are in good agreement with the actual ones within the ranges of the parameters, because the slope of data points are split evenly by the x = y line.