Sains Malaysiana 49(5)(2020): 1145-1152

http://dx.doi.org/10.17576/jsm-2020-4905-20

 

The Application of Lognormal Distribution on the New Two-Sided Group Chain Sampling Plan

 

(Pengaplikasian Taburan Lognormal ke atas Plan Persampelan Berangkai Dua Sisi secara Kumpulan yang Baharu)

 

MUHAMMAD FAROUK*, NAZRINA AZIZ & ZAKIYAH ZAIN

 

School of Quantitative Sciences, College of Arts and Science, Universiti Utara Malaysia, 06010 Sintok, Kedah Darul Aman, Malaysia

 

Received: 18 April 2019/Accepted: 24 January 2020

 

ABSTRACT

This paper gives emphasis on the technical aspect of acceptance criteria in acceptance sampling plans, more specifically the family of two-sided group chain sampling plans. The new two-sided complete group chain sampling plan (NTSCoGCh) operates with five acceptance criteria, while the two-sided group chain sampling plan (TS-GCh) operates with three acceptance criteria. Generally, the number of acceptance criteria has a direct influence on the probability of lot acceptance; the more criteria being accepted leads to higher probability of lot acceptance. This paper suggests a new, balanced plan for the family of two-sided group chain sampling plans. The plan, named the new two-sided group chain sampling plan (NTSGCh), operates with four acceptance criteria. The Lognormal distribution is used to represent the production sequence of manufactured products in this study. A time truncated life test simulation is carried out to obtain the minimum number of groups required and the probability of lot acceptance. The findings show that the NTSGCh outperformed its predecessors. In conclusion, the NTSGCh is a viable alternative for implementation in the industry.

Keywords: Acceptance sampling; lognormal distribution; truncated life test

ABSTRAK

Makalah ini memberi penekanan kepada aspek teknikal iaitu kriteria penerimaan di dalam persampelan penerimaan, terutamanya kepada gugusan pelan persampelan berangkai dua sisi secara berkumpulan. Pelan persampelan lengkap berangkai dua sisi secara berkumpulan yang baru (NTSCoGCh) beroperasi dengan menggunakan lima kriteria penerimaan, manakala pelan persampelan berangkai dua sisi secara berkumpulan (TS-GCh) beroperasi dengan menggunakan tiga kriteria penerimaan. Umumnya, bilangan kriteria penerimaan mempunyai pengaruh langsung pada kebarangkalian penerimaan lot; lebih tinggi bilangan kriteria penerimaan, maka kebarangkalian penerimaan lot juga meningkat. Makalah ini mencadangkan pendekatan baru dan lebih seimbang dalam persampelan penerimaan yang dinamakan pelan persampelan berangkai dua sisi secara berkumpulan yang baru (NTSGCh). Pelan ini beroperasi menggunakan empat kriteria penerimaan. Serakan Lognormal telah digunakan di dalam kajian ini. Simulasi ujian hayat terpenggal telah dijalankan untuk mendapatkan jumlah minima kumpulan dan juga kebarangkalian penerimaan lot. Keputusan kajian menunjukkan bahawa NTSGCh memberikan keputusan yang lebih baik berbanding kedua-dua pelan persampelan terdahulu. Kesimpulannya, NTSGCh merupakan satu alternatif yang baik untuk digunakan dalam proses pemeriksaan lot di industri.

Kata kunci: Persampelan penerimaan; taburan Lognormal; ujian hayat terpenggal

REFERENCES

Aslam, M. 2007. Double acceptance sampling based on truncated life tests in Rayleigh Distribution. European Journal of Scientific Research 17: 605-611.

Aslam, M. & Jun, C.H. 2010. A double acceptance sampling plan for Generalized Log-Logistic Distribution with known shape parameters. Journal of Applied Statistics 37(3): 405-414.

Aslam, M. & Jun, C.H. 2009. A group acceptance sampling plan for truncated life test having Weibull Distribution. Journal of Applied Statistics 36(9): 1021-1027.

Aslam, M., Jun, C.H. & Ahmad, M. 2009. A double acceptance sampling plan based on truncated life test in the Weibull distribution. Journal of Statistics Theory and Applications 8(2): 191-206.

Deva Arul, S. & Rebecca, I.E.K. 2012. Two-sided complete chain sampling plans for attribute quality characteristics (CChSP-0,1). Karunya Journal of Research 3(1): 8-16.

Dodge, H.F. 1955. Chain sampling inspection plan. Industry Quality Control 11(4): 10-13.

Goode, H.P. & Kao, J.H.K. 1961. Sampling plans based on the Weibull Distribution. Proceedings of the Seventh National Symposium on Reliability and Quality Control. pp. 24-40.

Kantam, R., Rosaiah, K. & Rao, G.S. 2001. Acceptance sampling based on life tests: Log- logistic model. Journal of Applied Statistics 28(1): 121-128.

Montgomery, D.C. 2009. Introduction to Statistical Quality Control. 6th ed. New Jersey: John Wiley & Sons.

Montgomery, D.C. & Runger, G.C. 2003. Applied Statistics and Probability for Engineers. 3rd ed. New Jersey: John Wiley & Sons.

Mughal, A.R. 2018. A family of group chain acceptance sampling plans based on truncated life test. Doctoral Thesis. Ph.D.  Universiti Utara Malaysia, Sintok (Unpublished).

Mughal, A.R., Zain, Z. & Aziz, N. 2016. Time truncated efficient testing strategy for Pareto distribution of the 2nd kind using Weighted Poisson and Poisson Distribution. Sains Malaysiana 45(11): 1763-1772.

Mughal, A.R., Zain, Z. & Aziz, N. 2015. New two-sided complete group chain sampling plan for Pareto distribution of the 2nd kind. Research India Publication 10(12): 31855-31860.

O'Connor, A.N., Modarres, M. & Mosleh, A. 2016. Probability Distributions Used in Reliability Engineering. Maryland: University of Maryland.

Ramaswamy, A.R.S. & Jayasri, S. 2014. Time truncated chain sampling for Generalized Rayleigh distribution. International Refereed Journal of Engineering and Sciences 3(2): 49-53.

Ramaswamy, A.R.S. & Jayasri, S. 2015. Time truncated chain sampling for Weibull Distribution. International Journal of Engineering Research and General Science 3(2): 59-67.

Rosaiah, K. & Kantam, R. 2005. Acceptance sampling based on the Inverse Rayleigh Distribution. Economic Quality Control 20(2): 277-286.

 

*Corresponding author; email: faroukzainolkamal@gmail.com

 

 

 

 

 

previous