Attribute Charts for Zero-Inflated Processes |
| |
Authors: | C. H. Sim M. H. Lim |
| |
Affiliation: | 1. Faculty of Science , University of Malaya , Kuala Lumpur, Malaysia simch@um.edu.my;3. Faculty of Science , University of Malaya , Kuala Lumpur, Malaysia |
| |
Abstract: | The classical Shewhart c-chart and p-chart which are constructed based on the Poisson and binomial distributions are inappropriate in monitoring zero-inflated counts. They tend to underestimate the dispersion of zero-inflated counts and subsequently lead to higher false alarm rate in detecting out-of-control signals. Another drawback of these charts is that their 3-sigma control limits, evaluated based on the asymptotic normality assumption of the attribute counts, have a systematic negative bias in their coverage probability. We recommend that the zero-inflated models which account for the excess number of zeros should first be fitted to the zero-inflated Poisson and binomial counts. The Poisson parameter λ estimated from a zero-inflated Poisson model is then used to construct a one-sided c-chart with its upper control limit constructed based on the Jeffreys prior interval that provides good coverage probability for λ. Similarly, the binomial parameter p estimated from a zero-inflated binomial model is used to construct a one-sided np-chart with its upper control limit constructed based on the Jeffreys prior interval or Blyth–Still interval of the binomial proportion p. A simple two-of-two control rule is also recommended to improve further on the performance of these two proposed charts. |
| |
Keywords: | Blyth–Still interval c J -chart Control rule Jeffreys prior interval np J -chart np BS -chart Zero-inflated count |
|
|