Publicado

2015-07-01

Design of SkSP-R Variables Sampling Plans

Diseño de planes de muestreo SkSP-R

DOI:

https://doi.org/10.15446/rce.v38n2.51669

Palabras clave:

Acceptable Quality Level, Acceptance Sampling, Average Sample Number, Limiting Quality Level, Quality Control (en)
Características de calidad medibles, Control de calidad, Muestreo Skip-lot, Nivel de calidad aceptable, Nivel de calidad límite, Muestreo de aceptación. (es)

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Autores/as

  • Muhammad Aslam King Abdulaziz University, Saudi Arabia
  • Saminathan Balamurali Departments of Mathematics institution, Krishnankoil, India
  • Chi-Hyuck Jun Pohang University of Science and Technology, Republic of Korea
  • Batool Hussain Kinnaird College for Women, Pakistan
In this paper, we present the designing of the skip-lot sampling plan including the re-inspection  called SkSP-R. The plan parameters of the proposed plan are determined through a  nonlinear optimization problem by minimizing the average sample number satisfying both the producer's risk and the consumer's risks. The proposed plan is shown to perform better than the existing sampling plans in terms of the average sample number. The application of the proposed plan is explained with the help of illustrative examples.

En este artículo, se presenta el diseño de un plan de muestreo de lotes incluyendo reinspección llamado SkSP-R. Los parámetros del plan propuesto se determinan a través de un problema de optimización no lineal que minimiza el número de muestras promedio óptimo que satisface el riesgo del productor a un nivel de calidad aceptable y el riesgo del consumidor a un nivel de calidad límite. El plan propuesto se desempeña mejor que otros planes de muestreo existentes en términos del número de muestras promedio. Se presenta una aplicación del plan propuesto con la ayuda de tabulados.

https://doi.org/10.15446/rce.v38n2.51669

Design of SkSP-R Variables Sampling Plans

Diseño de planes de muestreo SkSP-R

MUHAMMAD ASLAM1, SAMINATHAN BALAMURALI2, CHI-HYUCK JUN3, BATOOL HUSSAIN4

1King Abdulaziz University, Faculty of Sciences, Department of Statistics, Saudi Arabia. Associate Professor. Email: aslam_ravian@hotmail.com
2Departments of Mathematics institution Kalasalingam University, Krishnankoil, India. Professor. Email: sbmurali@rediffmail.com
3Pohang University of Science and Technology, Department of Industrial and Management Engineering, Republic of Korea. Professor. Email: chjun@postech.ac.kr
4Kinnaird College for Women, Department of Statistics, Pakistan. Ph.D. Student. Email: bhjafri@gmail.com

Abstract

In this paper, we present the designing of the skip-lot sampling plan including the re-inspection called SkSP-R .The plan parameters of the proposed plan are determined through a nonlinear optimization problem by minimizing the average sample number satisfying both the producers risk and the consumers risks. The proposed plan is shown to perform better than the existing sampling plans in terms of the average sample number. The application of the proposed plan is explained with the help of illustrative examples.

Key words: Acceptable Quality Level, Acceptance Sampling, Average Sample Number, Limiting Quality Level, Quality Control.

Resumen

En este artículo, se presenta el diseño de un plan de muestreo de lotes incluyendo reinspección llamado SkSP-R. Los parámetros del plan propuesto se determinan a través de un problema de optimización no lineal que minimiza el número de muestras promedio óptimo que satisface el riesgo del productor a un nivel de calidad aceptable y el riesgo del consumidor a un nivel de calidad límite. El plan propuesto se desempeña mejor que otros planes de muestreo existentes en términos del número de muestras promedio. Se presenta una aplicación del plan propuesto con la ayuda de tabulados.

Palabras clave: características de calidad medibles, control de calidad, muestreo Skip-lot, nivel de calidad aceptable, nivel de calidad límite, muestreo de aceptación.

Texto completo disponible en PDF

References

1. ANSI/ASQC Standard A2-1987, (1987), Terms, symbols, and definitions for acceptance sampling, American Society for Quality Control, Milwaukee.

2. Aslam, M., Balamurali, S., Jun, C.-H. & Ahmad, M. (2010), 'Optimal designing of a skip-lot sampling plan by two point method', Pakistan Journal of Statistics 26(4), 585-592.

3. Aslam, M., Balamurali, S., Jun, C.-H. & Ahmad, M. (2013), 'Optimal design of skip lot group acceptance sampling plans for the weibull distribution and the generalized exponential distribution', Quality Engineering 5(3), 237-246.

4. Aslam, M., Wu, C. W., Azam, M. & Jun, C.-H. (2013), 'Variable sampling inspection for resubmitted lots based on process capability index C_pk for normally distributed items', Applied Mathematical Modeling 37, 667-675.

5. Balamurali, S., Aslam, M. & Jun, C.-H. (2014), 'A new system of product inspection based on skip-lot sampling plans including resampling', The Scientific World Journal, 1-6. ID 192412.

6. Balamurali, S. & Jun, C.-H. (2006), 'Repetitive group sampling procedure for variables inspection', Journal of Applied Statistical Science 33(3), 327-338.

7. Balamurali, S. & Jun, C.-H. (2011), 'A new system of skip-lot sampling plans having a provision for reducing normal inspection', Applied Stochastic Models in Business and Industry 27(3), 348-363.

8. Balamurali, S. & Subramani, J. (2012), 'Optimal designing of skip-lot sampling plan of type sksp-2 with double sampling plan as the reference plan', Journal of Statistical Theory and Practice 26, 354-362.

9. Bennett, G. K. & Callejas, C. J. (1980), The economic design of skip-lot sampling plans, Transactions on Spring Annual Conference, p. 349-355.

10. Besterfield, D. H. (2004), Quality Control, 7 edn, Pearson Prentice Hall.

11. Cao, Y. & Subramaniam, V. (2013), 'Improving the performance of manufacturing systems with continuous sampling plans', IIE Transactions 45(6), 575-590.

12. Carr, W. E. (1982), 'Sampling plan adjustment for inspection error and skip-lot plan', Journal of Quality Technology 14(1), 10-18.

13. Collani, E. V. (1990), 'A note on acceptance sampling for variables', Metrika 38, 19-36.

14. Cox, D. C. (1980), 'Skip-lot sampling plans', Quality 21(8), 26-27.

15. Deros, B. M., Peng, C. Y., Ab Rahman, M. N., Ismail, A. R. & Sulong, A. B. (2008), 'Assessing acceptance sampling application in electrical and electronic product', Journal of Achievements in Materials and Manufacturing Engineering 31(2), 622-628.

16. Dodge, H. F. (1943), 'A sampling inspection plan for continuous production', Annals of Mathematical Statistics 14(3), 264-279.

17. Dodge, H. F. (1955), 'Skip-lot sampling plan', Industrial Quality Control 11(5), 3-5.

18. Duffuaa, S. O., Turki, U. M. & Kolus, A. A. (2009), 'Process-targeting model for a product with two dependent quality characteristics using acceptance sampling plans', International Journal of Production Research 47(14), 4031-4046.

19. Duncan, A. J. (1986), Quality Control and Industrial Statistics, 5 edn, R. D. Irwin, Homewood, Illinois.

20. Fu, H., Tsai, H., Lin, C. & Wei, D. (2004), 'Application of a single sampling plan for auditing medical-claim payments made by taiwan national health insurance', Health Policy 70(2), 185-95.

21. Gharaibeh, N., Liu, L. & Wani, S. (2012), 'Skip-lot acceptance sampling plans for highway construction and materials', Journal of Construction Engineering Management 138(7), 791-796.

22. Govindaraju, K. & Ganesalingam, S. (1997), 'Sampling inspection for resubmitted lots', Communications in Statistics- Simulation and Computation 26, 1163-1176.

23. Hsu, J. I. S. (1980), 'A cost model for skip-lot destructive testing', IEEE Transactions on Reliability 26(1), 70-72.

24. Lee, S-H., Aslam, M. & Hun, C.-H. (2012), 'Repetitive group sampling plans with double specification limits', Pakistan Journal of Statistics 28(1), 41-57.

25. Liebesman, B. S. (1987), 'The development of an attribute skip-lot sampling standard', Frontiers in Statistical Quality Control 3, 3-33.

26. Liebesman, B. S. & Saperstein, B. (1983), 'A proposed attribute skip-lot sampling program', Journal of Quality Technology 15(3), 130-139.

27. MIL-STD 105D , (1963), Sampling procedures and tables for inspection by attributes, Government Printing Office, Washington D.C..

28. Okada, H. (1967), 'Skip-lot sampling inspection plan combined with MIL-STD 105D', Reports of Statistical Application Research 14(4), 13-20.

29. Parker, R. D. & Kessler, L. (1981), 'A modified skip-lot sampling plan', Journal of Quality Technology 13(1), 31-35.

30. Perry, R. L. (1970), A System of Skip-lot Sampling Plans for Lot Inspection, PhD thesis, Rutgers-The State University.

31. Reetz, D. (1984), 'Optimal skip-lot sampling plans for Markov chains - theoretical foundation', Frontiers in Statistical Quality Control 2, 25-36.

32. Schilling, E. G. (1982), Acceptance Sampling in Quality Control, American Society for Quality, Milwaukee.

33. Seidel, W. (1997), 'Is sampling by variables worse than sampling by attributes? A decision theoretic analysis and a new mixed strategy for inspecting individual lots', Sankhya B 59, 96-107.

34. Stephens, K. S. (1979), How to perform continuous sampling (csp), 'ASQC Basic References in Quality Control, Statistical Techniques', Vol. 2, American Society for Quality Control, Milwaukee.

35. Taylor, W. A. (2005), 'Selecting statistically valid sampling plans'. http://www.variation.com/techlib/as-7.html.

36. Vijayaraghavan, R. (1994), 'Construction and selection of skip-lot sampling inspection plans of type sksp-2 indexed by indifference quality level and maximum allowable percent defective', Journal of Applied Statistics 21(5), 417-423.

37. Wu, C.-W., Aslam, M. & Jun, C.-H. (2012), 'Variables sampling inspection scheme for resubmitted lots based on the process capability index c_pk', European Journal of Operational Research 217(3), 560-566.

[Recibido en febrero de 2014. Aceptado en enero de 2015]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv38n2a07,
    AUTHOR  = {Aslam, Muhammad and Balamurali, Saminathan and Jun, Chi-Hyuck and Hussain, Batool},
    TITLE   = {{Design of SkSP-R Variables Sampling Plans}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2015},
    volume  = {38},
    number  = {2},
    pages   = {413-429}
}

Referencias

ANSI/ASQC Standard A2-1987 (1987), Terms, symbols, and definitions for acceptance sampling, American Society for Quality Control, Milwaukee.

Aslam, M., Balamurali, S., Jun, C.-H. & Ahmad, M. (2010), ‘Optimal designing of a skip-lot sampling plan by two point method’, Pakistan Journal of Statistics 26(4), 585–592.

Aslam, M., Balamurali, S., Jun, C.-H. & Ahmad, M. (2013), ‘Optimal design of skip lot group acceptance sampling plans for the weibull distribution and the generalized exponential distribution’, Quality Engineering 5(3), 237–246.

Aslam, M., Wu, C. W., Azam, M. & Jun, C.-H. (2013), ‘Variable sampling inspection for resubmitted lots based on process capability index cpk for normally distributed items’, Applied Mathematical Modeling 37, 667–675.

Balamurali, S., Aslam, M. & Jun, C.-H. (2014), ‘A new system of product inspection based on skip-lot sampling plans including resampling’, The Scientific World Journal pp. 1–6. ID 192412.

Balamurali, S. & Jun, C.-H. (2006), ‘Repetitive group sampling procedure for variables inspection’, Journal of Applied Statistical Science 33(3), 327–338.

Balamurali, S. & Jun, C.-H. (2011), ‘A new system of skip-lot sampling plans having a provision for reducing normal inspection’, Applied Stochastic Models in Business and Industry 27(3), 348–363.

Balamurali, S. & Subramani, J. (2012), ‘Optimal designing of skip-lot sampling plan of type sksp-2 with double sampling plan as the reference plan’, Journal of Statistical Theory and Practice 26, 354–362.

Bennett, G. K. & Callejas, C. J. (1980), The economic design of skip-lot sampling plans, Transactions on Spring Annual Conference, pp. 349–355.

Besterfield, D. H. (2004), Quality Control, 7 edn, Pearson Prentice Hall.

Cao, Y. & Subramaniam, V. (2013), ‘Improving the performance of manufacturing systems with continuous sampling plans’, IIE Transactions 45(6), 575–590.

Carr, W. E. (1982), ‘Sampling plan adjustment for inspection error and skip-lot plan’, Journal of Quality Technology 14(1), 10–18.

Collani, E. V. (1990), ‘A note on acceptance sampling for variables’, Metrika 38, 19–36.

Cox, D. C. (1980), ‘Skip-lot sampling plans’, Quality 21(8), 26–27.

Deros, B. M., Peng, C. Y., Ab Rahman, M. N., Ismail, A. R. & Sulong, A. B. (2008), ‘Assessing acceptance sampling application in electrical and electronic product’, Journal of Achievements in Materials and Manufacturing Engineering 31(2), 622–628.

Dodge, H. F. (1943), ‘A sampling inspection plan for continuous production’, Annals of Mathematical Statistics 14(3), 264–279.

Dodge, H. F. (1955), ‘Skip-lot sampling plan’, Industrial Quality Control 11(5), 3– 5.

Duffuaa, S. O., Turki, U. M. & Kolus, A. A. (2009), ‘Process-targeting model for a product with two dependent quality characteristics using acceptance sampling plans’, International Journal of Production Research 47(14), 4031–4046.

Duncan, A. J. (1986), Quality Control and Industrial Statistics, 5 edn, R. D. Irwin, Homewood, Illinois.

Fu, H., Tsai, H., Lin, C. & Wei, D. (2004), ‘Application of a single sampling plan for auditing medical-claim payments made by taiwan national health insurance’, Health Policy 70(2), 185–95.

Gharaibeh, N., Liu, L. & Wani, S. (2012), ‘Skip-lot acceptance sampling plans for highway construction and materials’, Journal of Construction Engineering Management 138(7), 791–796.

Govindaraju, K. & Ganesalingam, S. (1997), ‘Sampling inspection for resubmitted lots’, Communications in Statistics- Simulation and Computation 26, 1163– 1176.

Hsu, J. I. S. (1980), ‘A cost model for skip-lot destructive testing’, IEEE Transactions on Reliability 26(1), 70–72.

Lee, S.-H., Aslam, M. & Hun, C.-H. (2012), ‘Repetitive group sampling plans with double specification limits’, Pakistan Journal of Statistics 28(1), 41–57.

Liebesman, B. S. (1987), ‘The development of an attribute skip-lot sampling standard’, Frontiers in Statistical Quality Control 3, 3–33.

Liebesman, B. S. & Saperstein, B. (1983), ‘A proposed attribute skip-lot sampling program’, Journal of Quality Technology 15(3), 130–139.

MIL-STD 105D (1963), Sampling procedures and tables for inspection by attributes, Government Printing Office, Washington D.C.

Okada, H. (1967), ‘Skip-lot sampling inspection plan combined with mil-std 105d’, Reports of Statistical Application Research 14(4), 13–20.

Parker, R. D. & Kessler, L. (1981), ‘A modified skip-lot sampling plan’, Journal of Quality Technology 13(1), 31–35.

Perry, R. L. (1970), A System of Skip-lot Sampling Plans for Lot Inspection, PhD thesis, Rutgers-The State University.

Reetz, D. (1984), ‘Optimal skip-lot sampling plans for Markov chains – theoretical foundation’, Frontiers in Statistical Quality Control 2, 25–36.

Schilling, E. G. (1982), Acceptance Sampling in Quality Control, American Society for Quality, Milwaukee.

Seidel, W. (1997), ‘Is sampling by variables worse than sampling by attributes? A decision theoretic analysis and a new mixed strategy for inspecting individual lots’, Sankhya B 59, 96–107.

Stephens, K. S. (1979), How to perform continuous sampling (csp), in ‘ASQC Basic References in Quality Control, Statistical Techniques’, Vol. 2, American Society for Quality Control, Milwaukee.

Taylor, W. A. (2005), ‘Selecting statistically valid sampling plans’. http://www.variation.com/ techlib/ as-7.html.

Vijayaraghavan, R. (1994), ‘Construction and selection of skip-lot sampling inspection plans of type sksp-2 indexed by indifference quality level and máximum allowable percent defective’, Journal of Applied Statistics 21(5), 417–423.

Wu, C.-W., Aslam, M. & Jun, C.-H. (2012), ‘Variables sampling inspection scheme for resubmitted lots based on the process capability index cpk’, European Journal of Operational Research 217(3), 560–566.

Cómo citar

APA

Aslam, M., Balamurali, S., Jun, C.-H. y Hussain, B. (2015). Design of SkSP-R Variables Sampling Plans. Revista Colombiana de Estadística, 38(2), 413–429. https://doi.org/10.15446/rce.v38n2.51669

ACM

[1]
Aslam, M., Balamurali, S., Jun, C.-H. y Hussain, B. 2015. Design of SkSP-R Variables Sampling Plans. Revista Colombiana de Estadística. 38, 2 (jul. 2015), 413–429. DOI:https://doi.org/10.15446/rce.v38n2.51669.

ACS

(1)
Aslam, M.; Balamurali, S.; Jun, C.-H.; Hussain, B. Design of SkSP-R Variables Sampling Plans. Rev. colomb. estad. 2015, 38, 413-429.

ABNT

ASLAM, M.; BALAMURALI, S.; JUN, C.-H.; HUSSAIN, B. Design of SkSP-R Variables Sampling Plans. Revista Colombiana de Estadística, [S. l.], v. 38, n. 2, p. 413–429, 2015. DOI: 10.15446/rce.v38n2.51669. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/51669. Acesso em: 22 ene. 2025.

Chicago

Aslam, Muhammad, Saminathan Balamurali, Chi-Hyuck Jun, y Batool Hussain. 2015. «Design of SkSP-R Variables Sampling Plans». Revista Colombiana De Estadística 38 (2):413-29. https://doi.org/10.15446/rce.v38n2.51669.

Harvard

Aslam, M., Balamurali, S., Jun, C.-H. y Hussain, B. (2015) «Design of SkSP-R Variables Sampling Plans», Revista Colombiana de Estadística, 38(2), pp. 413–429. doi: 10.15446/rce.v38n2.51669.

IEEE

[1]
M. Aslam, S. Balamurali, C.-H. Jun, y B. Hussain, «Design of SkSP-R Variables Sampling Plans», Rev. colomb. estad., vol. 38, n.º 2, pp. 413–429, jul. 2015.

MLA

Aslam, M., S. Balamurali, C.-H. Jun, y B. Hussain. «Design of SkSP-R Variables Sampling Plans». Revista Colombiana de Estadística, vol. 38, n.º 2, julio de 2015, pp. 413-29, doi:10.15446/rce.v38n2.51669.

Turabian

Aslam, Muhammad, Saminathan Balamurali, Chi-Hyuck Jun, y Batool Hussain. «Design of SkSP-R Variables Sampling Plans». Revista Colombiana de Estadística 38, no. 2 (julio 1, 2015): 413–429. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/51669.

Vancouver

1.
Aslam M, Balamurali S, Jun C-H, Hussain B. Design of SkSP-R Variables Sampling Plans. Rev. colomb. estad. [Internet]. 1 de julio de 2015 [citado 22 de enero de 2025];38(2):413-29. Disponible en: https://revistas.unal.edu.co/index.php/estad/article/view/51669

Descargar cita

CrossRef Cited-by

CrossRef citations8

1. J. S. Usher, M. Aslam, C. T. Hardin, C.-H. Jun. (2017). Repetitive Availability Demonstration Testing Procedure. Journal of Testing and Evaluation, 45(3), p.1016. https://doi.org/10.1520/JTE20150415.

2. P. Jeyadurga, S. Balamurali. (2022). Optimal designing of multiple deferred (dependent) state repetitive group sampling plan for variables inspection. Communications in Statistics - Theory and Methods, 51(13), p.4417. https://doi.org/10.1080/03610926.2020.1814815.

3. Muhammad Aslam, Mir Masoom Ali. (2019). Testing and Inspection Using Acceptance Sampling Plans. , p.173. https://doi.org/10.1007/978-981-13-9306-8_6.

4. N. Murugeswari, P. Jeyadurga, S. Balamurali. (2024). Evaluation and optimal designing of a two-level skip-lot sampling plan for resubmitted lots. Communications in Statistics - Theory and Methods, 53(6), p.2043. https://doi.org/10.1080/03610926.2022.2117986.

5. N. Murugeswari, P. Jeyadurga, S. Sridevi, S. Balamurali. (2023). Developing and Optimal Designing of a Two-Level Skip-Lot Sampling Reinspection Plan. American Journal of Mathematical and Management Sciences, 42(3), p.216. https://doi.org/10.1080/01966324.2023.2226337.

6. Li Xue, Zhen He, Kauko Leiviskä. (2021). Economic Design of EWMA Control Charts with Variable Sampling Intervals for Monitoring the Mean and Standard Deviation under Preventive Maintenance and Taguchi’s Loss Functions. Mathematical Problems in Engineering, 2021, p.1. https://doi.org/10.1155/2021/6686426.

7. S. Sridevi, S. Balamurali. (2025). Evaluation and design of a new system of tightened single-level skip-lot sampling plan. Communications in Statistics - Simulation and Computation, 54(2), p.449. https://doi.org/10.1080/03610918.2023.2257007.

8. Chien-Wei Wu, Amy H. I. Lee, Yi-San Huang. (2021). A variable-type skip-lot sampling plan for products with a unilateral specification limit. International Journal of Production Research, 59(14), p.4140. https://doi.org/10.1080/00207543.2020.1757778.

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