ACCEPTANCE SINGLE SAMPLING PLAN WITH FUZZY PARAMETER

Document Type: Research Paper

Authors

1 Department of Statistics, Faculty of Basic Science, University of Mazandaran, P.O. Box 311, Babolsar, Iran

2 PhD student, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran

3 Iran University of Science and Technology, Tehran, Iran

Abstract

The acceptance sampling plan problem is an important topic in
quality control and both the theory of probability and theory of fuzzy sets may
be used to solve it. In this paper, we discuss the single acceptance sampling
plan, when the proportion of nonconforming products is a fuzzy number. We 
show that the operating characteristic (𝑂𝐶) curve of the plan is a band having
high and low bounds and that for fixed sample size and acceptance number,
the width of the band depends on the ambiguity proportion parameter in the
lot. When the acceptance number equals zero, this band is convex and the
convexity increases with 𝑛 Finally, we compare the 𝑂𝐶 bands for a given value of 𝑐.

Keywords


[1] J. J. Buckley, Fuzzy probability: new approach and application, Physica-Verlag, Heidelberg,
Germany, 2003.

[2] J. J. Buckley, Fuzzy probability and statistics, Springer-Verlag, Berlin Heidelberg, 2006.
[3] T. K. Chakraborty, A class of single sampling plans based on fuzzy optimization, Opsearch,
29(1) (1992), 11-20.
[4] T. K. Chakraborty, Possibilistic parameter single sampling inspection plans, Opsearch, 31(2)
(1994a), 108-126.
[5] D. Dubois and H. Prade, Operations of fuzzy numbers, Int. J. of Systems Science, 9 (1978),
613-626.
[6] M. H. Fazel Zarandi, I. B. Turksen and A. H. Kashan, Fuzzy control chart for variable and
attribute quality characteristics, Iranian Journal of Fuzzy Systems, 3(1) (2006), 31-44.
[7] P. Grzegorzewski, A soft design of acceptance sampling by attributes, Proceedings of the VIth
International Workshop on Intelligent Statistical Quality Control. W¨urzburg, September 14-
16, (1998), 29-38.
[8] P. Grzegorzewski, Acceptance sampling plans by attributes with fuzzy risks and quality levels,
Frontiers in Statistical Quality Control, 6: eds., Wilrich P. Th. Lenz H. J. Springer,
Heidelberg, (2001), 36-46.
[9] P. Grzegorzewski, A soft design of acceptance sampling by variables, Technologies for Constructing
Intelligent Systems, eds., Springer, 2 (2002), 275-286.
[10] O. Hryniewisz, Statistical acceptance sampling with uncertain information from a sample
and fuzzy quality criteria, Working Paper of SRI PAS, Warsaw, (in Polish), 1992.
[11] O. Hryniewisz, Statistical decisions with imprecise data and requirements, In: R. Kulikowski,
K. Szkatula and J. Kacprzyk, eds., Systems Analysis and Decisions Support in Economics
and Technology. Omnitech Press, Warszawa, (1994), 135-143.
[12] O. Hryniewisz, Statistics with fuzzy data in statistical quality control, Soft Computing, 12
(2008), 229-234.
[13] A. Kanagawa and H. Ohta, A design for single sampling attribute plan based on fuzzy sets
theory, Fuzzy Sets and Systems, 37 (1990), 173-181.
[14] D. C. Montgomery, Introduction to statistical quality control, Wiley, New York, 1991.
[15] H. Ohta and H. Ichihashi, Determination of single sampling attribute plans based on membership
function, Int. J. of Production Research, 26 (1998), 1477-1485.
[16] E. Pasha, A. Saiedifar and B. Asady, The percentiles of fuzzy numbers and their applications,
Iranian Journal of Fuzzy Systems, 6(1) (2009), 27-44.
[17] S. Sampath, Hybrid single sampling plan, World Applied Science Journal, 6(12) (2009),
1685-1690.
[18] E. G. Schiling, Acceptance sampling quality control, Dekker, New York, 1982.
[19] M. Taheri and M. Mashinchi, Introduction to fuzzy probability and statistics, Shahid Bahonar
University of Kerman Publication, Iran, (in Persian), 2008.
[20] F. Tamaki, A. Kanagawa and H. Ohta, A fuzzy design of sampling inspection plans by attributes,
Japanese Journal of Fuzzy Theory and Systems, 3 (1991), 315-327.