Unbiased process capability estimation for autocorrelated data using exhaustive systematic sampling

Abstract

It is well known that process control index estimators are inflated when naively applied to positively autocorrelated data. The autocorrelation is a nuisance and not a feature that is captured in the process capability indices. This paper proposes exhaustive systematic sampling to create a pooled variance estimator that replaces the biased estimator of the process data standard deviation when data are autocorrelated. The proposed method is effective because the observations within a systematic sample are spread out in time and should be less correlated with each other as a result. It is similar to Bayesian thinning as a strategy for reducing the impact of autocorrelation except no observations are dropped. Properties of estimated process control indices are derived using quadratic forms and large sample theory that is nonparametric in the sense no distribution or time series model is assumed. Approximately unbiased estimates can be achieved for sufficiently large systematic sampling interval. The proposed method is compared to the time series method in a simulation study that demonstrates similar performance. The proposed method is applied to two examples that use because the target is not the midpoint of the specification limits and the mean differs from the target.