Construction And Selection Of A Bayesian Single Sampling Scheme With A Gamma Prior Distribution Using Weighted Poisson Distribution
Abstract
The purpose of this paper present a method for creating and choosing a Bayesian single sampling scheme with a gamma prior distribution using weighted Poisson distribution. The weighted Poisson function is used to derive the average probability of lot acceptance based on defective random defective products. Gamma distribution is considered as a suitable prior for weighted Poisson distribution. It is discussed with i) Acceptance Quality Level and Limiting Quality Level, ii) control point and the relative slope at that point and iii) MAPD. Tables are provided for the easy selection of the plans.
References
WISE, M.E. (1946). ‘The use of the Negative Binomial distribution in an industrial sampling procedure’, Journal of Royal Statistical Society, Vol.8, pp.202-211.
HAMAKER, H.C. (1960). ‘Attribute Sampling in Operation’, Bulletin of the International Statistical Institute, Vol.37, No.2, pp.265-281.
HALD, A. (1967). ‘The Determination of Single Sampling Attribute Plans with Given Producer's and Consumer's Risk’, Taylor & Francis Ltd , Academic Press, New York, U.S.A., Vol. 9, No. 3 (Aug., 1967), pp. 401-415 (15 pages).
OLIVER, L.R. AND SPRINGER, M.D. (1972). ‘A general set of Bayesian attribute acceptance plans’, American Institute of Industrial Engineers, Norcross, G.A.
LAWER, N.G. (1979). ‘Acceptance Probabilities for sampling plans where the proportion defective has a Beta distribution’, Journal of quality Technology, Vol.10, pp.52-55.
CALIVIN, T.W. (1984). "How and When to Perform Bayesian Acceptance Sampling," Edwards and Broughton, 2nd Ed., Raleigh, NC, U.S.A.
SURESH, K. K. AND LATHA . M (2002). ‘Selection of Bayesian Single Sampling Plan with Gamma Prior Distribution’, Statistical Methods, Vol.4, No.l, pp.64-74.
SURESH, K. K. AND PRADEEPA VEERAKUMARI, K. (2007). ‘Construction and Evaluation of Performance Measures for Bayesian Chain Sampling Plan (BChSP-1)’, Acta Ciencia Indica , Vol. 33, No. 4, pp. 16-35.
MOHANA PRIYA, L. (2008). “Construction and Selection of Acceptance Sampling Plans based on Weighted Poisson Distribution”, Ph.D., Dissertation, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India.
SURESH, K. K., UMAMAHESWARI AND PRADEEPA VEERAKUMARI, K. (2013). ‘Bayesian Repetitive Deferred Sampling Plan Indexed Through Relative Slopes’, Mathematical Journal of Interdisciplinary Sciences, Vol. 1, No. 2, pp. 41–5.
YUVARAJ V (2016). ‘Selection of Bayesian single sampling plan for attributes based on prior binomial distribution’, International Journal of Applied Research, 2(2), pp 303-305.
PALANISAMY, A AND LATHA M (2018). ‘Construction of Bayesian Single Sampling Plan by Attributes under the Conditions of Gamma Zero – Inflated Poisson Distribution’ International Research Journal of Advanced Engineering and Science, Vol 3( 1), pp 67-71,
WAQARHAFEEZ1 AND NAZRINA AZIZ (2021). ‘Designing Bayesian Two-Sided Group Chain Sampling Plan for Gamma Prior Distribution’, Computer Systems Science and Engineering 2023, 44(2), pp.1069-1079.
