On Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions

Anwer Khurshid, Ashit B Chakraborty

Abstract


The negative binomial distribution (NBD) is extensively used for the
description of data too heterogeneous to be fitted by Poisson
distribution. Observed samples, however may be truncated, in the
sense that the number of individuals falling into zero class cannot be
determined, or the observational apparatus becomes active when at
least one event occurs. Chakraborty and Kakoty (1987) and
Chakraborty and Singh (1990) have constructed CUSUM and
Shewhart charts for zero-truncated Poisson distribution respectively.
Recently, Chakraborty and Khurshid (2011 a, b) have constructed
CUSUM charts for zero-truncated binomial distribution and doubly
truncated binomial distribution respectively. Apparently, very little
work has specifically addressed control charts for the NBD (see, for
example, Kaminsky et al., 1992; Ma and Zhang, 1995; Hoffman, 2003;
Schwertman. 2005).

The purpose of this paper is to construct Shewhart control charts
for zero-truncated negative binomial distribution (ZTNBD). Formulae
for the Average run length (ARL) of the charts are derived and studied
for different values of the parameters of the distribution. OC curves
are also drawn.


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DOI: http://dx.doi.org/10.22555/pjets.v4i1.521

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