ROBUSTNESS OF SHAPE PARAMETER FOR ERLANG AND WEIBULL BAYESIAN ACCEPTANCE SAMPLING PLANS

Document Type : Article

Authors

Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan

Abstract

This article assesses the robustness of shape parameter for Bayesian acceptance sampling plans assuming Erlang and Weibull distributions. In particular, the prior information on the parameter is combined assuming different loss functions to derive different sampling plans. The cost model for the group sampling plans is studied by satisfying the constraints of producer's and consumer's risks for the Weibull sampling. The single sampling plan is compared with the group sampling plan and the results suggest that the group sampling plan performs better than the single sampling in terms of cost. It is noticed that the shape parameters of Erlang and Weibull distributions are not robust as claimed in the literature.

Keywords


References
1. Montgomery, D. C., “Statistical quality control: a modern introduction”. John Wiley (2009).
2. 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. 643–656 (2007).
3. Dodge, H. F. and Romig, H. G., “Sampling inspection tables: single and double sampling”.
Wiley Series in Probability and Statistics - Applied Probability and Statistics Section Series,
Wiley (1959).
4. Moskowitz, H. and Tang, K., “Bayesian variables acceptance-sampling plans: quadratic loss
function and step-loss function”, Technometrics, 34(3), pp. 340–347 (1992).
5. Tang, K., Plante, R., and Moskowitz, H., “Multiattribute Bayesian acceptance sampling
plans under nondestructive inspection”, Management Science, 32(6), pp. 739–750 (1986).
6. Chun, Y. H. and Sumichrast, R. T., “Bayesian inspection model with the negative binomial
prior in the presence of inspection errors”, European Journal of Operational Research, 182(3),
pp. 1188–1202 (2007).
7. Kwon, Y. I., “A bayesian life test sampling plan for products with Weibull lifetime distribution
sold under warranty”, Reliability Engineering & System Safety, 53(1), pp. 61–66
(1996).
8. Fallahnezhad, M. S. and Aslam, M., “A new economical design of acceptance sampling models
using Bayesian inference”, Accreditation and Quality Assurance, 18(3), pp. 187–195 (2013).
9. Fallahnezhad, M. S. and Babadi, A. Y., “A new acceptance sampling plan using Bayesian
approach in the presence of inspection errors”, Transactions of the Institute of Measurement
and Control, 37(9), pp. 1060–1073 (2015).
10. Fallahnezhad, M. S. and Saredorahi, F., “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).
11. Gonzalez, C. and Palomo, G., “Bayesian acceptance sampling plans following economic criteria:
an application to paper pulp manufacturing”, Journal of Applied Statistics, 30(3),
pp. 319–333 (2003).
12. Lira, I., “A Bayesian approach to the consumer’s and producer’s risks in measurement”,
Metrologia, 36(5), p. 397 (1999).
13. Adibfar, S., Fallahnezhad, M. S., and Jafari, R., “Optimal acceptance sampling policy considering
Bayesian risks”, Communications in Statistics-Theory and Methods, 46(11), pp. 5228–
5237 (2017).
14. Baklizi, A. and El Masri, A. El. Q., “Acceptance sampling based on truncated life tests in the
Birnbaum Saunders model”, Risk Analysis: An International Journal, 24(6), pp. 1453–1457
(2004).
15. Rosaiah, K., Kantam, R. R. L., and Kumar, S., “Reliability test plans for exponentiated
log-logistic distribution”, Economic Quality Control, 21(2), pp. 279–289 (2006).
16. Tsai, Tzong-Ru. and Wu, Shuo-Jye., “Acceptance sampling based on truncated life tests for
generalized Rayleigh distribution”, Journal of Applied Statistics, 33(6), pp. 595–600 (2006).
17. Lio, Y. L. and Tsai, Shuo-Jye., Tzong-Ru.and Wu, “Acceptance sampling plans from truncated
life tests based on the Burr type XII percentiles”, Journal of the Chinese institute of
Industrial Engineers, 27(4), pp. 270–280 (2010).
18. Aslam, M., Kundu, D., and Ahmad, M., “Time truncated acceptance sampling plans for generalized
exponential distribution”, Journal of Applied Statistics, 37(4), pp. 555–566 (2010).
BAYESIAN ERLANG 11
19. Jun, Chi-Hyuck., Balamurali, S., and Lee, Sang-Ho., “Variables sampling plans for Weibull
distributed lifetimes under sudden death testing”, IEEE Transactions on Reliability, 55(1),
pp. 53–58 (2006).
20. Aslam, M. and Jun, Chi-Hyuck., “A group acceptance sampling plans for truncated life tests
based on the inverse Rayleigh and Log-logistic distributions.”, Pakistan Journal of Statistics,
25(2), pp. 333–340 (2009).
21. Aslam, M. and Jun, Chi-Hyuck., “A group acceptance sampling plan for truncated life test
having Weibull distribution”, Journal of Applied Statistics, 36(9), pp. 1021–1027 (2009).
22. Aslam, M., Jun, Chi-Hyuck., 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).
23. Rao, G. S., “A group acceptance sampling plans for lifetimes following a generalized exponential
distribution”, Economic Quality Control, 24(1), pp. 75–85 (2009).
24. Aslam, M., Jun, Chi-Hyuck., Lee, H., Ahmad, M., and Rasool, M., “Improved group sampling
plans based on time-truncated life tests”, Chilean Journal of Statistics, 2(1), pp. 85–97
(2011).
25. Aslam, M., Pervaiz, M. K., and Jun, Chi-Hyuck., “An improved group sampling plan based on
time-truncated life tests”, Communications for Statistical Applications and Methods, 17(3),
pp. 319–326 (2010).
26. Aslam, M., Azam, M., Balamurali, S., and Jun, Chi-Hyuck, “An economic design of a group
sampling plan for a Weibull distribution using a Bayesian approach”, Journal of Testing and
Evaluation, 43(6), pp. 1497–1503 (2014).
27. Sina, S. and Fallahnezhad, M. S., “Variable sampling plan for resubmitted lots based on
process capability index and Bayesian approach”, International Journal of Advanced Manufacturing
Technologies, 88, pp. 2547–2555 (2017).
28. Li, X., Chen, W., Sun, F., Liao, H., Kang, R., and Li, R., “Bayesian accelerated acceptance
sampling plans for a lognormal lifetime distribution under type-i censoring”, Reliability Engineering
& System Safety, 171, pp. 78 – 86 (2018).
29. 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).
30. Al-Omari, A. I., “The transmuted generalized inverse Weibull distribution in acceptance
sampling plans based on life tests”, Transactions of the Institute of Measurement and Control,
40(16), pp. 4432–4443 (2018).
31. d, M. S. F. and Seifi, S., “Designing optimal double-sampling plan based on process capability
index”, Communications in Statistics - Theory and Methods, 46(13), pp. 6624–6634 (2017).
32. Hu, M. and Gui, W., “Acceptance sampling plans based on truncated life tests for Burr type
X distribution”, Journal of Statistics and Management Systems, 21(3), pp. 323–336 (2018).
33. Balamurali, S., Jeyadurga, P., and Usha, M., “Designing of multiple deferred state sampling
plan for generalized inverted exponential distribution”, Sequential Analysis, 36(1), pp. 76–86
(2017).
34. Balamurali, S., Jeyadurga, P., and Usha, M., “Optimal designing of a multiple deferred state
sampling plan for Weibull distributed life time assuring mean life”, American Journal of
Mathematical and Management Sciences, 36(2), pp. 150–161 (2017).
35. Hsu, Jia-Tzer, “Economic design of single sample acceptance sampling plans”, Journal of
Hungkuang University, 97, pp. 108–122 (2009).
36. Schmidt, J. W., Case, K. E., and Bennett, G. K., “The choice of variables sampling plans
using cost effective criteria”, AIIE Transactions, 6(3), pp. 178–184 (1974).
12 BAYESIAN ERLANG
37. Schmidt, J. W., Bennett, G. K., and Case, K.E., “A three action cost model for acceptance
sampling by variables”, Journal of Quality Technology, 12(1), pp. 10–18 (1980).
38. Tagaras, G., “Economic acceptance sampling by variables with quadratic quality costs”, IIE
Transactions, 26(6), pp. 29–36 (1994).
39. Aslam, M., Mughal, A. R., Hanif, M., and Ahmad, M., “Economic reliability group acceptance
sampling based on truncated life tests using Pareto distribution of the second kind”,
Communications for Statistical Applications and Methods, 17(5), pp. 725–731 (2010).
40. Fallahnezhad, M. S. and Fakhrzad, M. B., “Determining an economically optimal (n,
c) design via using loss functions”,, pp. 197–201 (2012).
41. Aslam, M., “A variable acceptance sampling plan under neutrosophic statistical interval
method”, Symmetry, 11(1), p. 365–370 (2019).
42. Aslam, M., “A new attribute sampling plan using neutrosophic statistical interval method”,
Complex & Intelligent Systems, 5, pp. 365–370 (2019).
43. Aslam, M., “Testing average wind speed using sampling plan for Weibull distribution under
indeterminacy”, Scientific Reports, 11, p. 7532 (2021).