Acceptance sampling plan using new truncated Weibull-X family based on run lengths of conforming items

Document Type : Article

Authors

Department of Statistics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan

Abstract

In this paper, we develop two acceptance sampling plans where the lifetimes of the product follow Weibull Exponential and Weibull Lomax distributions both belonging to the new truncated Weibull–X family of distributions based on run lengths of the conforming items. The model parameters are estimated by using the maximum likelihood method contrary to the existing plans where authors have been selecting arbitrary values of the parameters. The efficiency of the proposed plan is established by comparing it with the existing plans based on the average number of inspected items. A real example of failure rates of a piece of electronic equipment operating in a specific mode is presented to illustrate the proposed plans for industrial use.

Keywords


References:
1. Balakrishnan, N., Leiva, V., and Lopez, J. "Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution", Communications in Statistics-Simulation and Computation, 36(3), pp. 645-656 (2007).
2. Bourke, P.D. "A continuous sampling plan using CUSUMs", Journal of Applied Statistics, 29(8), pp. 1121-1133 (2002).
3. Bourke, P.D. "A continuous sampling plan using sums of conforming run lengths", Quality and Reliability Engineering International, 19(1), pp. 53-66 (2003).
4. Niaki, S.A. and Fallahnezhad, M.S. "Designing an optimum acceptance sampling plan using Bayesian inferences and a stochastic dynamic programming approach", Scientia Iranica, Transaction E, Industrial Engineering, 16(1), pp. 19-25 (2009).
5. Mirabi, M. and Fallahnezhad, M.S. "Analysing acceptance sampling plans by Markov chains", South African Journal of Industrial Engineering, 23(1), pp. 151-161 (2012).
6. Fallahnezhad, M.S. "A new Markov chain based acceptance sampling policy via the minimum angle method", Iranian Journal of Operations Research, 3(1), pp. 104- 111 (2012).
7. Fallahnezhad, M.S. and Niaki, S. "A new machine replacement policy based on number of defective items and Markov chains", Iranian Journal of Operations Research, 2(2), pp. 17-28 (2011).
8. Balamurali, S., Aslam, M., Ahmad, L., et al. "A mixed double sampling plan based on Cpk", Communications in Statistics-Theory and Methods, 49(8), pp. 1840- 1857 (2020). DOI: 10.1080/03610926.2019.1565836. 
9. Baklizi, A. "Acceptance sampling based on truncated life tests in the Pareto distribution of the second kind", Advances and Applications in Statistics, 3(1), pp. 33- 48 (2003).
10. Aslam, M., Jun, C.-H., and Ahmad, M. "A group sampling plan based on truncated life test for Gamma distributed items", Pakistan Journal of Statistics, 25 (3), pp. 333-340 (2009).
11. Aslam, M., Nezhad, M.S.F., and Azam, M. "Decision procedure for the Weibull distribution based on run lengths of conforming items", Journal of Testing and Evaluation, 41(5), pp. 826-832 (2013).
12. Chowdhury, S. "Acceptance sampling plans based on truncated life test for the generalized Weibull model", IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), pp. 886-889 (2016). DOI: 10.1109/IEEM.2016.7798004.
13. Shahbaz, S.H., Khan, K., and Shahbaz, M.Q. "Acceptance sampling plans for finite and infinite lot size under power lindley distribution", Symmetry, 10, p. 496 (2018).
14. Al-Omari, A., Al-Nasser, A., and Ciavolino, E. "Acceptance sampling plans based on truncated life tests for Rama distribution", International Journal of Quality & Reliability Management, 36(7), pp. 1181-1191 (2019).
15. Mahdy, M. and Ahmed, B. "New distributions in designing of double acceptance sampling plan with application", Pakistan Journal of Statistics and Operation Research, 14(2), pp. 333-346 (2018).
16. Fallahnezhad, M.S. and Saredorahi, F.Z. "A new policy for designing acceptance sampling plan based on Bayesian inference in the presence of inspection errors", Communications in Statistics-Theory and Methods, 47(21), pp. 5307-5318 (2018).
17. Fallahnezhad, M.S. and Seifi, S. "Repetitive group sampling plan based on the process capability index for the lot acceptance problem", Journal of Statistical Computation and Simulation, 87(1), pp. 29-41 (2017).
18. Fallahnezhad, M.S. and Yazdi, A.A. "An optimization model for economic design of sampling plans based on conforming run length considering outgoing quality", Communications in Statistics-Theory and Methods, 46(5), pp. 2202-2211 (2017).
19. Rasay, H., Pourgharibshahi, M., and Fallahnezhad, M.S. "Sequential sampling plan in the truncated life test for Weibull distribution", Journal of Testing and Evaluation, 46(2), pp. 693-703 (2018).
20. Fallahnezhad, M.S. and Saredorahi, F.Z. "Designing an economically optimal repetitive group-sampling plan based on loss functions", Communications in Statistics-Simulation and Computation, 47(3), pp. 783-799 (2018).
21. Al-Omari, A.I. and Al-Hadhrami, S.A. "Acceptance sampling plans based on truncated life tests for extended exponential distribution", Kuwait Journal of Science, 45(2), pp. 89-99 (2018).
22. Al-Omari, A.I. "Acceptance sampling plans based on truncated life tests for Sushila distribution", Journal of Mathematical and Fundamental Sciences, 50(1), pp. 72-83 (2018).
23. Aslam, M., Jeyadurga, P., Balamurali, S., et al. "Timetruncated group plan under a Weibull distribution based on neutrosophic statistics", Mathematics, 7(10) p. 905 (2019).
24. Singh, N. and Buttar, G.S. "Sequential sampling plan based on truncated life test for generalized exponential distribution", International Journal on Emerging Technologies, 10(4), pp. 119-124 (2019).
25. Al-Nasser, A.D. and Obeidat, M. "Acceptance sampling plans from truncated life test based on Tsallis q-exponential distribution", Journal of Applied Statistics, 47(4), pp. 685-697 (2020).
26. Divecha, J. and Raykundaliya, D.P. "Three economical life test acceptance sampling plans", Communications in Statistics-Simulation and Computation, 51(6), pp. 3305-3323 (2022). DOI: 10.1080/03610918.2020.1711948.
27. Luko, S.N. "A review of the Weibull distribution and selected engineering applications", Journal of Commercial Vehicles, 108(2), pp. 398-412 (1999).
28. Mandouh, R. "Lomax-modified Weibull distribution: A new generalization", Journal of Advances in Mathematics and Computer Science, 27(1), pp. 1-7, (2018). https://doi.org/10.9734/JAMCS/2018/38975.
29. Hanook, S., Shahbaz, M.Q., Mohsin, M., et al. "A note on beta Inverse-Weibull distribution", Communications in Statistics-Theory and Methods, 42(2), pp. 320-335 (2013).
30. Cordeiro, G.M. and de Castro, M. "A new family of generalized distributions", Journal of Statistical Computation and Simulation, 81(7), pp. 883-898 (2011).
31. Ahsanullah, M., Shahbaz, S., Shahbaz, M.Q., et al. "Concomitants of upper record statistics for bivariate Pseudo-Weibull distribution", App. & Applied Math, 5(10), pp. 1379-1388 (2010).
32. Alzaatreh, A., Lee, C., and Famoye, F. "A new method for generating families of continuous distributions", Metron, 71(1), pp. 63-79 (2013).
33. Aljarrah, M.A., Lee, C., and Famoye, F. "On generating TX family of distributions using quantile functions", Journal of Statistical Distributions and Applications, 1(2), pp. 1-17 (2014). https://doi.org/10.1186/2195-5832-1-2.
34. Rather, N. and Rather, T. "New generalizations of exponential distribution with applications", Journal of Probability and Statistics, Article ID 2106748, pp. 1-9 (2017). http://doi.org/10.1155/2017/2106748.
35. Mahdavi, A. and Oliveira Silva, G. "A method to expand family of continuous distributions based on truncated distributions", Journal of Statistical Research of Iran, 13(2), pp. 231-247 (2017).
36. Bowling, S.R., Khasawneh, M.T., Kaewkuekool, S., et al. "A Markovian approach to determining optimum process target levels for a multi-stage serial production system", European Journal of Operational Research, 159, pp. 636-650 (2004).
37. Juran, J. and Gryna, F., Quality Planing and Analysis, McGraw-Hill, New York (1980).
38. Schneider, H., Lin, B.-S., and O'Cinneide, C. "Comparison of nonparameteric estimators for the renewal function", Applied Statistics, 39(1), pp. 55-61 (1990).
Volume 30, Issue 1
Transactions on Industrial Engineering (E)
January and February 2023
Pages 273-284
  • Receive Date: 30 December 2019
  • Revise Date: 15 November 2020
  • Accept Date: 28 December 2020