Theoretical Research On Process Capability Index Under Non-normal Conditions

Process capability refers to the uniformity of the process.It also means the ability of a process to produce output within specification limits which considered international standards,national standards,industry standards and customer requirements.The process capability index is an important index to measure the processing capability of the production process.The enterprises can use statistical control theory to improve the quality of product by the research.When we use process capability index to analyze process capability,it is usually assumed that the data obey the normal distribution.However,due to the existence of the non normal distribution in production practice,it is necessary to define a new process capability index for the non normal data.The process capability indices(PCIs)indicate the extent to which a process can satisfy a specification,the research on the process capability indices is of great theoretical and practical values.This dissertation introduces the basic principle of the traditional process capability index first,analyzes the advantages and disadvantages of the common process capability index under non normal conditions.A new process capability index is constructed based on Cornish Fisher expansion and Clements method.Then,three non normal processes,viz.the Weibull distribution,the Poisson distribution and the Gamma distribution,are simulated by R language,the new process capability index are calculated and the confidence interval of percentile bootstrap are obtained by using bootstrap sampling method.This is very important to enhance the quality and strengthen market competitiveness.From the simulation results,the new process capability index can solve the problem of process capability well under the non normal conditions.Finally,analysis the process capability by using a set of data obtained from production practice,it is proved that the new process capability index can be well applied in the production practice.