Acceptance sampling is a statistical technique which contains the procedure, to reach a decision on either to accept or to reject the lots based on the quality of the sampled units inspected. The variable sampling inspection plan, one of the acceptance sampling techniques, is applicable when the quality characteristic of sampled items is measured on a continuous scale and functional form of the probability distribution is known. When the lots are submitted substantially in the order of their production from a process having a constant proportion of non-conforming, one of the conditional sampling plans, called multiple dependent state sampling inspection plan, is implemented. In this article, a multiple dependent state sampling plan is proposed for sentencing lots of products with quality characteristic following symmetric distributions. The proposed plan is designed by considering two points on the OC curve, namely, (AQL, 1 – α) and (LQL, β), by formulating it as a non-linear optimization problem. A comparative study is carried out for three symmetric distributions, namely, Laplace, logistic and normal distributions.

multiple dependent state sampling plan, symmetric distribution, operating characteristic curve, acceptable quality level, limiting quality level.

Received: April 21, 2022; Accepted: June 14, 2022; Published: August 4, 2022

How to cite this article: S. Geetha and S. Saranya, Construction of multiple dependent state sampling plan for variables on symmetric distributions, Far East Journal of Theoretical Statistics 65 (2022), 115-124. http://dx.doi.org/10.17654/0972086322009

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] Aijun Yan, Sanyang Liu and Xiaojuan Dong, Designing a multiple dependent state sampling plan based on the coefficient of variation, SpringerPlus 5 (2016), Article number: 1447. DOI: 10.1186/s40064-016-3087-3.
[2] S. Balamurali and C. H. Jun, Multiple dependent state sampling plan for lot acceptance based on measurement data, European J. Oper. Res. 180 (2007), 1221-1230. DOI: 10.1016/J.EJOR.2006.05.025.
[3] A. J. Dunkan, Quality Control and Industrial Statistics, 5th ed., Richard D. Irwin, Homewood, Illinois, 1986.
[4] K. Govindaraju and K. Subramani, Selection of multiple deferred state MDS-1 sampling plan for given acceptable quality level and limiting quality level involving minimum risks, J. Appl. Stat. 17 (1990), 427-434. DOI: 10.1080/03610929208830851.
[5] K. Govindaraju and K. Subramani, Selection of multiple deferred [dependent] state sampling plans for given acceptable quality level and limiting quality level, J. Appl. Stat. 20(3) (1993), 423-428. DOI: https://doi.org/10.1080/02664769300000041.
[6] K. Kuralmani and K. Govindaraju, Selection of multiple deferred [dependent] state sampling plans, Comm. Statist. Theory Methods 21(5) (1992), 1339-1366. DOI: 10.1080/03610929208830851.
[7] J. Nocedal and Stephen J. Wright, Numerical Optimization, 2nd ed., Springer, USA, 2000.
[8] V. Soundararajan and R. Vijayaraghavan, On designing multiple deferred state sampling [MDS-1] [0, 2] plans involving minimum sum of risks, J. Appl. Stat. 16(1) (1989), 87-94. DOI: 10.1080/02664768900000010.
[9] V. Soundararajan and R. Vijayaraghavan, Construction and selection of multiple dependent [deferred] state sampling plan, J. Appl. Stat. 17 (1990), 397-409. DOI: 10.1080/02664769000000012.
[10] S. Geetha and S. Saranya, Construction of multiple dependent state sampling plan for variables based on logistic distribution, International Journal of Statistics and Applied Mathematics 7(1) (2022), 112-117. DOI: https://doi.org/10.22271/maths.2022.v7.i1b.780.
[11] R. Varest, A procedure to construct multiple deferred state sampling plan, Methods of Operation Research 37 (1982), 477-485.
[12] A. W. Wortham and R. C. Baker, Multiple deferred state sampling inspection, International Journal of Production Research 14 (1976), 719-731. DOI: 10.1080/00207547608956391.