Resarch And Quality Control Of The Goodness Of Fit Test Statistic

The goodness of fit test is one kind of nonparametric test in statistics. Sinceχ~2testaroused by Pearson. The general test methods includeχ~2test and test based on theempirical distribution function (EDF). In this paper, the goodness of fit test statistics wasstudied and its application in quality control was discussed. The main contents are asfollows:First, the paper summarizes the research significance and research progress of thegoodness of fit test. Through maximizing Pearsonχ~2test statistics and dividing the space,the new grouping principle was proposed. According to stochastic simulation method,effectiveness simulation map of two statistics was presented, which proved that theefficacy of the new statistics is higher than the original statistics.Secondly, based on one-dimensional skewness and kurtosis test, this paper proposeda type of comprehensive test(R test), and a correction of the Jarque-Bera test. TheJarque-Bera test statistic and its correction statistics(AJB empirical quantile) wereexhibited in table. According to the simulation result of probability of test statisticcommitted the error of the first and second kind, the JB statistics and AJB statistics wereconsidered in priority for the one-dimensional normality test.Again, this paper demonstrated the consistency of spherical uniform distribution ofthe goodness of fit test. Then, based on the unit spherical uniform distribution of goodnessof fit test, this paper studied the probability distribution of multivariate normality teststatistic. Through constructing multivariate normality test statistic(χ~2n), asymptoticdistribution ofχ~2nis the distribution of degrees of freedom for k1forH0exiting.Finally, according to hypothesis test, the improvement of M700stirred tankautomatic feeding equipment realized the goal of cost saving and aided in quality controlin the Qinhuangdao Starter Special Vehicle Manufacturing Company Limited.