International Journal of Mathematics Trends and Technology
Volume 65 | Issue 7 | Year 2019 | Article Id. IJMTT-V65I7P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I7P518
This paper is on the study of continuous acceptance sampling plans for Truncated Lindley distribution and optimization of CUSUM Schemes by using Gauss- Chebyshev integration method. In most of the life test experiments, the Truncated failure models are used to determine an optimal Truncated point. In the present study, we assume that the life of the units produced is distributed according to Truncated Lindley distribution. In a situation where there is a constraint on the lower part and upper part of the lifetime of units, Truncated failure models can be employed to study lifetime behavior of the items. Thus we study the lifetime of the units by using Truncated Lindley failure model. The objective of this paper is to optimize CASP – CUSUM Schemes through Truncated Lindley distribution. Solving integral equations by the Method of Gauss – Chebyshev integration we determine the probability of acceptance at various hypothetical values of the parameters. Finally based on the obtained results we determine the maximum values of Average Run Length and Probability of Acceptance.
[1] Akhtar, P. Md. and Sarma, K.L.A.P. (2004). “Optimization of CASP-CUSUM Schemes based on Truncated Gamma Distribution”. Bulletin of Pure and applied sciences, Vol-23E (No.2), pp215-223.
[2] Beattie, B.W. (1962). “A Continuous Acceptance Sampling procedure based upon a Cumulative Sums Chart for a number of defective”. Applied Statistics, Vol. 11(No.2), pp137- 147.
[3] Murphy, E.M., D.N.Nagpur (1972), “A Gompertz fit that fits: application to Canadian fertility patterns”, Demography, 9, pp35-50.
[4] Hawkins, D.M. (1992). “A Fast Accurate Approximation for Average Lengths of CUSUM Control Charts". Journal of Quality Technology, Vol. 24(No.1), pp37-43.
[5] Jain, M.K., Iyengar, S.R.K. and Jain, R.K. “Numerical Methods of Scientific and Engineering Computations”, Willy Eastern Ltd., New Delhi.
[6] Kakoty, S and Chakravaborthy, A.B., (1990), “A Continuous Acceptance Sampling Plan for Truncated Normal distribution based on Cumulative Sums”, Journal of National Institution for Quality and Reliability, Vol.2 (No.1), pp15-18.
[7] Lonnie, C. Vance. (1986). “Average Run Length of CUSUM Charts for Controlling Normal means”. Journal of Quality Technology, Vol.18, pp189-193.
[8] Page, E.S., (1954) “Continuous Inspection Schemes”, Biometrika, Vol. XLI, pp104- 114.
[9] Vardeman, S. And Di-ou Ray. (1985). “Average Run Length for CUSUM schemes Where observations are Exponentially Distributed”, Technometrics, vol. 27 (No.2), pp145- 150.
[10] Narayana Muthy, B. R, Akhtar, P. Md and Venkataramudu, B.(2012) “Optimization of CASP-CUSUM Schemes based on Truncated Log-Logistic Distribution”. Bulletin of PureAnd Applied Sciences, Vol-31E (Math&Stat.): Issue (No.2), pp243-255.
[11] Narayana Muthy, B. R, Akhtar, P. Md and Venkataramudu, B. (2013) “Optimization of CASP -CUSUM Schemes based on Truncated Rayleigh Distribution”. International Journal of Engineering and Development, Volum 6, Issue 2, pp37 -44.
[12] M.E Ghitany,B.Atieh,S.Nadarajah.(2008) “Lindley Distribution and its applications”. Mathematics and computers in simulation 78(2008) 493-506.
[13] B.Sainath, P.Mohammed Akhtar, G.Venkatesulu, and Narayana Muthy, B. R, (2016) “CASPCUSUM Schemes based on Truncated Burr Distribution using Lobatto Integration method, IOSR Journal of Mathematics (IOSR-JM), Vol-12, Issue 2, pp54-63.
[14] G.Venkatesulu, P.Mohammed Akhtar, B.Sainath and Narayana Murthy, B.R. (2017)“Truncated Gompertz Distribution and its Optimization of CASP- CUSUMSchemes”.Journal of Research in Applied Mathematics, Vol3-Issue7, pp19-28.
[15] D. V. Lindley, Fiducial distributions and Bayes'theorem. Journal of theRoyal Society, series B, 20 (1958), 102-107.
[16] M. Sankaran, The discrete Poisson-Lindley distribution. Biometrics, 26(1970), 145-149.
[17] G.Venkatesulu, P.Mohammed Akhtar, B.Sainath and Narayana Murthy, B.R. (2018)“Continuous Acceptance Sampling Plans for Truncated Lomax Distribution Based on CUSUM Schemes ”.International Journal Mathematics Trends and Technology , Vol-55, pp174-184.
S.Dhanunjaya, Dr P. Mohammed Akhtar, Dr. G.Venkatesulu, "Continuous Acceptance Sampling plans for Truncated Lindley Distribution Based on CUSUM Schemes," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 7, pp. 117-129, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I7P518
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