Acceptance Single Sampling Plan with Fuzzy Parameter with The Using of Poisson Distribution

This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (oc) curves of the plan is like a band having a high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the oc bands of using of binomial with the oc bands of using of Poisson distribution.

• Ezzatallah Baloui Jamkhaneh
• Bahram Sadeghpour-Gildeh
• Gholamhossein Yari

• Statistical quality control
• acceptance single sampling
• fuzzy number.

[1] J. J. Buckley (2003) fuzzy probability: new approach and application, physica-velage, Hidelberg ,Germany.
[2] J.J. Buckley (2006) fuzzy probability and statistics, springer-verlage Berlin Hidelberg.
[3] D. Dubis , H. Prade (1978) Operations of fuzzy number, Int. J. syst.
[4] B.P.M. Duate, P.M. Saraiva, "An optimization basd approach for
designing attribute acceptance sampling plans, " Int. journal of quality &
reliability management.vol. 25 no. 8,2008.
[5] P. Grzegorzewski(1988) A soft design of acceptance sampling by attributes, in: proceedings of the VIth international workshop on intelligent statistical quality control Wurzburg, September 14-16 , PP.29-38.
[6] P. Grzegorzewski (2001 b) Acceptance sampling plans by attributes with
fuzzy risks and quality levels, in: Frontiers in frontiers in statistical quality
control. Vol. 6, Eds. Wilrich P. Th. Lenz H. J. Springer, Heidelberg, PP. 36-46.
[7] P. Grzegorzewski (2002) A soft design of acceptance sampling plans by
variables, in: technologies for contrueting intelligent systems, Eds, speringer,
vol. 2. pp. 275-286.
[8] O. Hryniewisz (1992) statistical acceptance sampling with uncertain
information from a sample and fuzzy quality criteria working paper of SRI
PAS, Warsow, (in polish).
[9] A. Kanagawa,H. Ohta (1990), A design for single sampling attribute plan
based on fuzzy set theory, fuzzy sets and systems, 37. 173-181.
[10] D. C. Montgomery (1991), introduction to statistical quality control,
wiley New york.
[11] H. Ohta ,H. Ichihashi (1998), Determination of single-sampling attribute
plans based on membership function, Int. J. Prod, Res 26, 1477-1485.
[12] J. L. Romeu, Understanding binomial sequential testing, Rac start,
Volume 12, Number 2.
[13] E.G. Schiling (1982), acceptance sampling quality control, Dekker, Newyork.
[14] F. Tamaki , A. Kanagawa, Ohta H. (1991), A fuzzy design of sampling
inspection plans by attributes, Japanese journal of fuzzy theory and systems, 3,
315-327