Two Methods For Calculating The Small Sample Of Process Capability Index

Process capability index has been proposed as the concept to measure the quality ofthe production process. It has been widespread concern because of its Practicability. Withthe continuous improvement of living standards and the material culture is constantlyenrich, the production by large quantities of the original production turn to personalizedand small scale gradual. Because of the decrease in the number of products, the calculationof process capability index cannot get enough data from the small sample. The solution tothe problem is the use of interval to estimate the process capability index.The article is structured as follows:First of all, discuss the limitations of traditional methods in calculating small sampledata. When using small sample data, the traditional calculation method cannot avoid thehuge influence of random samples. This paper try to improve national standard GB/T13264-2008in small sample data sampling, although get a certain extent less risk ofpurchase, but it did not solve the problem in essence. Maximum likelihood of fourcommon types of process capability index estimation of small sample data operationcannot get rid of the random effects, the problems encountered in calculation. Try toimprove the Bootstrap method from the principle in two ways, through the numericalexamples show that the method of using three degree polynomial improved is better thanthe original method.Secondly, using the Bootstrap method to solve the small sample problem of therandom, taking on the small sample of repeated sampling method and enlarge the samplesize, increase the reliability of the calculating of Process capability index by confidenceinterval calculation. We can get the conclusion by comparing the calculated results of fourkinds of bootstrap method which is the most suitable method to calculate the confidenceinterval of process capability index. Then try to improve Bootstrap methods in principle intwo ways, through numerical examples illustrate the use of cubic polynomial Bootstrapmethods is better than the original method.Finally, the Bias estimator is applied to process capability index calculation processof the lower confidence interval confidence. The prior distribution is the key to the application of Bayes formula, because the use of Bayesian method is to make use of priorinformation to reduce the impact of random data. No Bayesian prior distribution has nopractical significance in the process of calculation. We may encounter difficulties whenusing the existing information such as: a priori information form complex to calculate, orthe image cannot give specific distribution expression of the problem, we can use thefinite mixture gamma distribution to fit the prior distribution, make full use of existinginformation.