Some Research On Process Capability Analysis And Process Capability Indices

Statistical process control (SPC) is broadly used in controlling and improving process capability in modern industrial manufactures, and process capability indices (PCIs) are important tools applied by SPC. PCIs can provide numerical measure to whether a process is capable of producing items meeting the quality requirement preset in a factory, then the production department can trace and improve a poor process so that the quality level can be enhanced and the requirements of the customers can be satified. Traditional process capability analysis is based on three fundamental assumptions that a process under study is in statistical control, quality characteristic follows a normal distribution and process data are statistical independent.In this paper, we begin with a short history of process capability indices. Application areas for capability indices are summarized, and characteristics of the various indices are also discussed. Then we study PCIs from the following aspects:1. Some reviews on understanding and using PCIs are given, the relationship between the PCIs and the proportion nonconforming is established. The indices are grouped according to the loss function in their interpretation. Recommendations are made for selection of indices.2. Investigate the estimators of the PCIs and their statistical properties. The results obtained are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability. In order to obtain the more reliable result, based on the theory of statistical hypothesis testing, a procedure on assessing process capability is provided.3. The importance of normality assumption is analyzed. When the distribution of a process characteristic is non-normal, the normally-based PCIs often lead to erroneous interpretation of process capability. Several methods for the estimation of non-normal PCIs are categorized and discussed.4. when the observations are autocorrelated, not independent, the effect of autocorrelations on PCIs is investigate. Results show that autocorrelated time series may lead to a bised estimate of the true capability, and if positive autocorrelation is with observations, the PCIs calculated by traditional methods are overestimated. When observations satisfy an autoregressive model of order one AR(1), a method to calculate PCIs is introduced.