On Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions
| Autor: | Anwer Khurshid, Ashit B. Chakraborty |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
021103 operations research
0211 other engineering and technologies Negative binomial distribution 02 engineering and technology Poisson distribution Binomial distribution symbols.namesake Beta-binomial distribution Statistics symbols Econometrics Multinomial distribution Control chart Shewhart individuals control chart Mathematics Count data |
| Zdroj: | Pakistan Journal of Engineering, Technology & Science. 4 |
| ISSN: | 2224-2333 2222-9930 |
| DOI: | 10.22555/pjets.v4i1.521 |
| Popis: | The negative binomial distribution (NBD) is extensively used for thedescription of data too heterogeneous to be fitted by Poissondistribution. Observed samples, however may be truncated, in thesense that the number of individuals falling into zero class cannot bedetermined, or the observational apparatus becomes active when atleast one event occurs. Chakraborty and Kakoty (1987) andChakraborty and Singh (1990) have constructed CUSUM andShewhart charts for zero-truncated Poisson distribution respectively.Recently, Chakraborty and Khurshid (2011 a, b) have constructedCUSUM charts for zero-truncated binomial distribution and doublytruncated binomial distribution respectively. Apparently, very littlework has specifically addressed control charts for the NBD (see, forexample, Kaminsky et al., 1992; Ma and Zhang, 1995; Hoffman, 2003;Schwertman. 2005).The purpose of this paper is to construct Shewhart control chartsfor zero-truncated negative binomial distribution (ZTNBD). Formulaefor the Average run length (ARL) of the charts are derived and studiedfor different values of the parameters of the distribution. OC curvesare also drawn. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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