CASP – CUSUM Schemes Based on Truncated Nadarajah-Haghighi Distribution

P. Adisekhara Reddy; Dr P. Mohammed Akhtar; S. Dhanunjaya; Dr. G. Venkatesulu

doi:https://doi.org/10.14445/22315373/IJMTT-V67I9P520

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 9 | Year 2021 | Article Id. IJMTT-V67I9P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I9P520

CASP – CUSUM Schemes Based on Truncated Nadarajah-Haghighi Distribution

P. Adisekhara Reddy, Dr P. Mohammed Akhtar, S. Dhanunjaya, Dr. G. Venkatesulu

Abstract

Acceptance sampling plans are introduced mainly to accept or reject the lots of finished products. There are several techniques available to control the quality. Some of the techniques are popularly used where testing involves destruction, for instance, in the manufacturing of crackers, bullets, batteries, bulbs and so on, it is impossible to go for 100% inspection. In this paper we optimized CASP-CUSUM Schemes based on the assumption that the continuous variable under consideration follows a Truncated Nadarajah-Haghighi Distribution. The Nadarajah-Haghighi Distribution is continuous distribution generally used in Life-time Analysis of products, particularly in estimating reliability by considering its distribution. Optimization of CASP-CUSUM Schemes is suggested based on numerical result obtained by changing the values of the parameters of the Nadarajah-Haghighi Distribution, finally based on the obtained results we determine the maximum values of Average Run Length and Probability of Acceptance

Keywords

CASP – CUSUM Schemes, Truncated Nadarajah-Haghighi Distribution, Optimal Truncated Point, Upper and lower Truncated Point, Average Run Length.

References

[1] Akhtar, P. Md. and Sarma, K.L.A.P, Optimization of CASP-CUSUM Schemes based on Truncated Distribution, Bulletin of Pure and applied sciences, 23E(2) (2004) 215-223.
[2] Battie, B.W, A Continuous Acceptance Sampling procedure based upon a Cumulative Sums Chart for a number of defective, Applied Statistics, 11(2)(1962) 137- 147.
[3] Hawkins D.M, A Fast Accurate Approximation for Average Lengths of CUSUM Control Charts, Journal of Quality Technology, 24(1) 37-43.
[4] Jain M.K, Iyengar, S.R.K. and Jain R.K, Numerical Methods of Scientific and Engineering Computations, willy Eastern Ltd., New Delhi.
[5] Kakoty S and Chakravaborthy A.B, A Continuous Acceptance Sampling Plan for Truncated Normal distribution based Cumulative Sums, Journal of National Institution for Quality and Reliability, 2 (1) (1990) 15-18.
[6] Lonnie C. Vance. Average Run Length of CUSUM Charts for Controlling Normal means. Journal of Quality Technology, 18, 189-193.
[7] Page, E.S, Continuous Inspection Schemes, Biometrika, XLI (1954) 104-114.
[8] Vardeman S. and Di-ou Ray, Average Run Length for CUSUM schemes where observations are exponentially distributed, Techno metrics, 27 (2) (1985) 145- 150.
[9] Narayana Murthy B. R, Akhtar, P. Md and Venkataramudu. B, Optimization of CASP-CUSUM Schemes based on Truncated Log-Logistic Distribution, Bulletin of Pure and Applied Sciences (Math&Stat.), 31E(2) (2012) 243-255.
[10] B. Sainath, P. Mohammed Akhtar, G. Venkatesulu, and Narayana Murthy B. R, CASP CUSUM Schemes based on Truncated Burr Distribution using Lobatto Integration method, IOSR Journal of Mathematics (IOSR-JM), 12(2) (2016) 54-63.
[11] G. Venkatesulu, P. Mohammed Akhtar, B. Sainath and Narayana Murthy B.R, Truncated Gompertz Distribution and its Optimization of CASP- CUSUM Schemes, Journal of Research in Applied Mathematics, 3(7) (2017) 19-28.
[12] G. Venkatesulu, P. Mohammed Akhtar, B. Sainath and Narayana Murthy B.R, Continuous Acceptance Sampling Plans for Truncated Lomax Distribution Based on CUSUM Schemes, International Journal Mathematics Trends and Technology, 55 (2018) 174-184.
[13] N. Balakrishnan and A. Asghar Zadeh, Inference for the Scaled Nadarajah-Haghighi Distribution Based on Progressively Type-II Censored Samples, Communications in Statistics - Theory and Methods, 34(1) (2005) 73-87.
[14] Ajit Chaturvedi, Taruna Kumari, Robust Bayesian Analysis of Generalized Nadarajah-Haghighi distribution, Statistics Optimization and Information Computing Stat., Optimum Inf. Computer., 5(2017) 158–178.
[15] N. Balakrishnan (1985). Order statistics from the Nadarajah-Haghighi distribution, Journal of Statistical Computation and Simulation, 20(4) 287-309.
[16] S. Dhanunjaya and P. Mohammed Akhtar, Continuous Acceptance Sampling plans for Truncated Lindley Distribution Based on CUSUM Schemes, International Journal of Mathematics Trends and Technology (IJMTT), 65(7) (2019) 117-129.
[17] Saralees Nadarajah and Firooze Haghighi, An extension of the exponential distribution, A Journal of Theoretical and Applied Statistics, 45(6) (2011) 543–558.
[18] Ms. Sana M. Faizan, Bayesian Estimation for Nadarajah-Haghighi Distribution Based on Upper Record Values, Pakistan journal of statistics and operations research, XV(1) (2019) 217-230.
[19] Mingjie Wu and Wenhao Gui, Estimation and Prediction for Nadarajah-Haghighi Distribution under Progressive Type-II Censoring, Journal of Symmetry, 13 (999) (2021) 1-2.
[20] Dodge H. F and Roming H. G, Sampling Inspection Tables-Single and Double Sampling, John Wiley &Sons New York, Inc ,2nd Edition (1959).

Citation :

P. Adisekhara Reddy, Dr P. Mohammed Akhtar, S. Dhanunjaya, Dr. G. Venkatesulu, "CASP – CUSUM Schemes Based on Truncated Nadarajah-Haghighi Distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 9, pp. 171-182, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I9P520