  Control charts are important tools to monitor quality of products. One of
useful applications is to monitor the proportion of non-conforming products.
However, in practical applications, measurement error is ubiquitous and may
occur due to false records or misclassification, which makes the observed
proportion different from the underlying true proportion. It is also well-known
that ignoring measurement error effects provides biases, and is expected that
the resulting control charts may incur wrong detection. In this paper, we study
this important problem and propose a valid method to correct for measurement
error effects and obtain error-eliminated control chart for the proportion of
non-conforming products. In addition, unlike traditional approaches, the
corrected EWMA $p$-control chart provides asymmetric control limits and is
flexible to handle the data with small sample size. Numerical results are
conducted to justify the validity of the corrected EWMA $p$-control chart and
verify the necessity of measurement error correction.
