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Designing for Customer Value
Published in James William Martin, Operational Excellence, 2021
Parametric analysis of repairable systems estimates the mean number of expected repairs to a system over time for units under test by assuming a specific probability distribution. In contrast, a nonparametric analysis of a repairable system is used to estimate the mean number of repairs to a system over time for units under test, but without assuming a specific probability distribution. Distribution assumptions are important when building accelerated testing models of time to failure versus several independent variables. The accelerated testing models are based on a model with linear or exponential relationships between time to failure and independent or accelerating variables. However, regression-based testing can also be used to build reliability models to predict time to failure versus several independent variables and covariates, nested variables, and variable interactions. Probit analysis is a method used to estimate survival probabilities of test units exposed to an experimental stress condition. Distribution analysis is used to determine the time-to-failure probabilities for design characteristics exposed to an experimental stress condition. Finally, all information gathered during reliability testing and analyses is incorporated into the DFMEA after several design alternatives have been evaluated using reliability testing the project moves into the optimize phase.
Local empowerment and irrigation devolution in Ethiopia
Published in International Journal of Water Resources Development, 2022
Rahel Deribe Bekele, Dawit Mekonnen
The analysis was implemented at the plot level to capture more spatial heterogeneity and minimize omitted variable bias. Due to a collinearity problem between water management systems and interaction terms, a separate effect of a water management system on empowerment indicators was omitted. Thus, only interactions of the various irrigation water management systems and complementary irrigation technologies are captured. We tested whether there is a problem of multicollinearity among explanatory variables, but it was found only among the climate variables as one would expect. The correlation between these variables was leading to high variance inflation factors (VIFs) of between 3.83 and 69.71. However, all the variables in the models are included since they are statistically significant coefficients. Moreover, omitting one of the variables would result in omitted variables bias. The other variables had a variance inflation factor of < 2.08, indicating that multicollinearity was not a major concern for these variables (Gujarati, 1995). The White heteroscedasticity-robust covariance matrix (White, 1980), which is robust to heteroskedasticity of unknown form, was used. It was also tested if there is a problem of incorrect functional form. The result demonstrated that there was no evidence of functional form misspecification. Furthermore, the Pearson goodness-of-fit test was performed; all four probit models fit reasonably well.
Regression: binary logistic
Published in International Journal of Injury Control and Safety Promotion, 2018
Simple and multiple linear regression models study the relationship between a single continuous dependent variable Y and one or multiple independent variables X, respectively (Bangdiwala, 2018a, 2018b). If the value of the dependent variable Y can be only one of two outcomes (i.e. a binary variable, such as dead/alive, injured/not injured, or crash/no crash), the linear predictor function (which equals when we have two independent variables X1 and X2) would need to map onto the two values. Typically we consider the dependent variable Y as an indicator variable and assign the value of 1 to the outcome one is trying to predict, and the value of 0 to the other outcome. Mapping a linear predictor to only two values is not possible, so we have it map to the range of values from 0 to 1. Since probabilities range from 0 to 1, we map the linear predictor to a probability. Two common methods are the logistic model and the probit model. In the logistic model, we assume that the probability of Y having the value of 1 is given by the inverse of the log-odds or logit function:
Explaining the supply of home repair and renovation services in the undeclared economy: lessons from Europe
Published in Construction Management and Economics, 2021
Colin C. Williams, Aysegul Kayaoglu
To analyse the data, probit regression analysis is used because the dependent variables in our empirical models are binary variables. The maximum likelihood method is used to estimate the objective function. The log-likelihood function for the probit model is: where ϕ is the standard cumulative normal distribution function which is numerically maximised with respect to Using probit analysis, the following model is adopted: