Process capability indices when two sources of variability present, a tolerance interval approach

The sound tolerance interval–based method and two Pp–based approximations are compared on the proportion of nonconforming parts. As output distribution of the process, one possible model is examined here: two sources of variations are in a one‐way structure. It was found that the uncertainty of variance components estimates plays the major role in the goodness of the three calculation methods. Summary Statistical indices – like process capability (CP) or process performance (PP) index – make the relationship between the width of the specification interval and the extent of the process variability illustrative. The latter is characterized by the tolerance interval, which contains the major part of the population with high confidence. In the original concept this tolerance interval is calculated using oversimplified models. In practice this model is not conform with reality. As improvement two sources of variation is assumed in a one‐way structure. The proportion of non‐conforming parts of the population is the quantity of interest. Non‐conforming means that the characteristic is beyond the specification limits. According to this, the quantile of the distribution shall be determined that is equal to the specification limits. Thus, the task is to calculate the tolerance interval for the NμσA2+σe2 distribution. In practical cases the variance components are unknown and are to be estimated. To estimate the ratio of non‐conforming parts, two approximate calculation methods which are coherent with the definition of PP are investigated, as well. The aim of this work is to compare the results of the two PP based approximate methods with the tolerance interval based (theoretically sound) calculation method. Two situations from the practice are considered – datasets from process validation and process monitoring environment are evaluated during which the effect of the number of experiments is given. Our study indicated that the main difference of the goodness of the approximations is from the uncertainty of parameter estimates. The sound tolerance interval‐based method and two Pp‐based approximations are compared on the proportion of nonconforming parts. As output distribution of the process, one possible model is examined here: two sources of variations are in a one‐way structure. It was found that the uncertainty of variance components estimates plays the major role in the goodness of the three calculation methods.