PARAMETRIC TEST IN PARTIAL LINEAR REGRESSION MODELS

Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.

Testing for Normality from the Parametric Seven-Number Summary

The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.

Processing of Rainfall Time Series Data in the State of Rio de Janeiro

The goal was to perform the filling,consistency and processing of the rainfall time series data from 1943 to 2013 in five regions of the state.Data were obtained from several sources(ANA,CPRM,INMET,SERLA and LIGHT),totaling 23 stations.The time series(raw data)showed failures that were filled with data from TRMM satellite via 3B43 product,and with the climatological normal from INMET.The 3B43 product was used from 1998 to 2013 and the climatological normal over the 1947-1997 period.Data were submitted to descriptive and exploratory analysis,parametric tests(Shapiro-Wilks and Bartlett),cluster analysis(CA),and data processing(Box Cox)in the 23 stations.Descriptive analysis of the raw data consistency showed a probability of occurrence above 75%(high time variability).Through the CA,two homogeneous rainfall groups(G1 and G2)were defined.The group G1 and G2 represent 77.01%and 22.99%of the rainfall occurring in SRJ,respectively.Box Cox Processing was effective in stabilizing the normality of the residuals and homogeneity of variance of the monthly rainfall time series of the five regions of the state.Data from 3B43 product and the climatological normal can be used as an alternative source of quality data for gap filling.

Improving the Reliability of a Domestic Refrigerator Compressor Subjected to Repetitive Loading

As a reliability quantitative specification, parametric accelerated life testing was used to assess the reliability of a newly designed compressor of a commercial refrigerator subjected to repetitive stresses. A generalized life-stress failure model and new sample size equation with a new load concept were derived starting with the basic refrigeration cycle. The sample size equation with the acceleration factor also enabled the parametric accelerated life testing to quickly evaluate the expected lifetime. The design of this testing should help an engineer uncover the design parameters affecting reliability during the design process of the compressor system. Consequently, it should help companies improve product reliability and avoid recalls due to the product failures in the field. A newly designed compressor in a commercial refrigerator was used as a test case.

Reliability Design of Ice-Maker System Subjected to Repetitive Loading

Parametric Accelerated Life Testing (ALT) was used to improve the reliability of ice-maker system with a fractured helix upper dispenser in field. By using bond graphs and state equations, a variety of mechanical loads in the assembly were analyzed. The acceleration factor was derived from a generalized life-stress failure model with a new load concept. To reproduce the failure modes and mechanisms causing the fracture, new sample size equation was derived. The sample size equation with the acceleration factor also enabled the parametric accelerated life testing to quickly reproduce early failure in field. Consequently, the failure modes and mechanisms found were identical with those of the failed sample. The design of this testing should help an engineer uncover the design parameters affecting the reliability of fractured helix upper dispenser in field. By eliminating the design flaws, gaps and weldline, the B1 life of the redesign of helix upper dispenser is now guaranteed to be over 10 years with a yearly failure rate of 0.1% that is the reliability quantitative test specifications (RQ).