Benjamin, R. and Guttman, I. (1986). Statistical inference for P(Y<X), Technometrics, 28(3),

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1 REFERENCES Awad, A.M. and Gharraf, M.K. (1986). Estimation of P( Y X ) in Burr case: A comparative study, Communications in Statistics-Simulation and Computation, 15, Awad, A.M., Azzam, M.M. and Hamadan, M.A. (1981). Some inference results in P( Y X ) in the bivariate exponential model, Communication Statistics- Theory and Methods, 10, Baklizi, A. (2003). Acceptance sampling based on truncated life tests in the Pareto distribution of the second kind, Advances and Applications in Statistics, 3(1), Balakrishnan, N. (1990). Approximate maximum likelihood estimation for a generalized logistic distribution, J. Statist. Plann. & inf., 26, Balakrishnan, N., Leiva, V. and Lopez, J. (2007). Acceptance sampling plans from truncated life tests based on the generalized Birnbaum-Saunders distribution, Communications in Statistics-Simulation and Computation, 36, Benjamin, R. and Guttman, I. (1986). Statistical inference for P(Y<X), Technometrics, 28(3), Betul Kan and Berna Yaziki. (2006). The Individual Control Charts for Burr distributed data, Proceedings of the ninth WSEAS International Conference on Applied Mathematics, Istanbul, Turkey, Bhattacharya, G.K. (1985). The asymptotic of maximum likelihood and related estimators based on Type II censored data, Journal of the American Statistical Association (JASA), 80 (390), Bhattacharya, G.K. and Johnson, R.A. (1974). Estimation of reliability in multicomponent stress-strength model, JASA, 69, Chan, L., K. and Cui, H., J. (2003). Skewness correction for x and R-charts for skewed distributions, Naval Research Logistics, 50, Church, J.D. and Harris, B. (1970). The estimation of reliability from stressstrength relationships, Technometrics, 12, i

2 Cohen, A.C. and Whitten, B. (1980). Modified moment and maximum likelihood estimators for the parameters of the three parameter gamma distribution, Communications in Statistics-Simulation and Computation, 11, Constantine, K. and Karson, M. (1986). The estimation of P(Y<X) in gamma case Communications in Statistics-Simulation and Computation, 15, David, H.A. (1981). Order Statistics, John Wiley and Sons, New York. Downtown, F. (1973). The estimation of P( X Y ) in the normal case, Technometrics, 15, Dutta, K. and Srivastav, G.L. (1989). Warm standbys in stress-strength model, IAPQR Transactions, 14, Edgeman, R. L. (1989). Inverse Gaussian control charts, Australian Journal of Statistics, 31(1), Efron, B. (1982). The Jackknife, the Bootstrap and other Re-sampling Plans, CBMS-NSF Regional Conference Series in Applied Mathematics, 38, SIAM, Philadelphia, PA. Epstein, B. (1954). Truncated life tests in the exponential case, Annals of Mathematical Statistics, 25, Epstein, B. and Sobel, M. (1954). Some theorems relevant to life testing from an exponential distribution, Annals of Mathematical Statistics, 24, Enis, P. and Geisser, S. (1971). Estimation of the probability thaty X, JASA, 66, Goel, A.L. and okumoto, K. (1979). A time dependent error detection rate model for software reliability and other performance measures, IEEE Transaction on Reliability, 28(3), Gokale, S.S. and Trivedi, K.S. (1998). Log-logistic software reliability growth model, Proceedings of 3 rd IEEE - International High Assurance Systems Engineering Symposism, ii

3 Gonzalez, I. and Viles, I. (2000). Semi-Economic design of Mean control charts assuming Gamma distribution, Economic Quality Control, 15, Goode, H.P. and Kao, J.H.K. (1961). Sampling plans based on the Weibull distribution, Proceedings of Seventh National Symposium on Reliability and Quality Control, Philadelphia, Govidarajulu, Z. (1967). Two sided confidence limits for P( X Y ) based on normal samples of X and Y, Sankhya B, 29, Govindarajulu, Z. (1966). Distribution-free confidence limits for P(Y<X), Ann. Inst. Statist. Math., 20, Gupta, S.S. (1962). Life test sampling plans for normal and lognormal distribution. Technometrics, 4, Gupta, R.C. and Brown, N. (2001). Reliability studies of the skew-normal distribution and its application to strength-stress models, Communication Statistics-Theory and Methods, 30, Gupta, S.S and Groll, P.A. (1961). Gamma distribution in acceptance sampling based on life tests, J. Amer. Statist. Assoc., 56, Gupta, R.D. and Gupta, R.C. (1990). Estimation of multivariate normal case, Statistics, 21, ' ' P( a X by) in the Gupta, R.C., Ghitany, M.E. and Al-Mutairib, D.K. (2010). Estimation of reliability from Marshall Olkin extended Lomax distributions, Journal of Statistical Computation and Simulation, 80(8), Gupta, R.C., Ramakrishnan, S. and Zhou, X. (1999). Point and interval estimation of P(X >Y): the normal case with common coefficient of variation, Ann. Inst. Statist. Math., 51, Gupta, R.D. and Kundu, D. (2001). Exponentiated exponential family; an alternative to gamma and Weibull, Biometrical Journal, 33, Handi, S.W. and Johnson, A. (1992). Testing reliability in a stress-strength model when X and Y are normally distributed, Technometrics, 34, iii

4 Huang, C.Y., Sy-Yen Kuo. and Michael, R. Lyu. (2007). An assessment of testing effort dependent software reliability growth models, IEEE Transactions on Reliability, 56 (2), Kakati, M.C. and Srivastav, G.L. (1986). Accelerated life testing under stressstrength model, IAPQR Transactions, 11, Kantam, R.R.L. and Dharma Rao, V. (1993). Half logistic distribution: An improvement over ML estimator, Proceedings of II Annual Conference of Society for Development of Statistics, Kantam, R.R.L. and Rosaiah, K. (1998). Half logistic distribution in acceptance sampling based on life tests, IAPQR Transactions, 23(2), Kantam, R.R.L., Rosaiah, K. and Anjaneyulu, M.S.R. (2000). Estimation of Reliability in multicomponent stress-strength model - half logistic distribution, IAPQR Transactions, 25(2), Kantam, R.R.L., Rosaiah, K. and Srinivasa Rao, G. (2001). Acceptance Sampling based on life tests: log-logistic model, Journal of Applied Statistics, 28(1), Kantam, R.R.L. and Srinivasa Rao, G. (1993). Reliability estimation in Rayleigh distribution with censoring - Some approximations to ML method, Proceedings of II Annual Conference of Society for Development of Statistics, Kantam, R.R.L. and Srinivasa Rao, G. (2002). Log-logistic distribution: modified maximum likelihood estimation, Gujarat Statistical Review, 29(1&2), Kantam, R.R.L. and Srinivasa Rao, G. (2004). A note on point estimation of system reliability exemplified for the log-logistic distribution, Economic Quality Control, 19, 2, Kantam, R.R.L. and Sriram, B. (2001). Variable control charts based on Gamma distribution, IAPQR Transactions, 26(2), iv

5 Kantam, R.R.L., and Sriram, B. (2003). Maximum likelihood estimation from censored samples - Some modifications in length biased version of exponential model, Statistical methods, 5(1), Kantam, R.R.L., Vasudeva Rao, A. and Srinivasa Rao, G. (2006a). Control Charts for log-logistic distribution, Economic Quality Control, 21(1), Kantam, R.R.L., Srinivasa Rao, G. and Sriram, B. (2006b). An economic reliability test plan: log-logistic distribution, Journal of Applied Statistics (U.K.), 33(3), Kantam, R.R.L., Srinivasa Rao, G. and Sriram, B. (2007). On stress-strength reliability model in log-logistic distribution, International Journal of Agricultural Statistical Sciences, 3(1), 1-6. Kantam, R.R.L and Subba Rao, R. (2009). Pareto distribution: A software reliability growth model, International Journal of Performability Engineering, 5(3), Kendall, M.G. and Stuart, A. (1979). The Advanced Theory of Statistics, 2, Charles Griffin and Company Limited, London. Kundu, D. and Gupta, R.D. (2005). Estimation of P(Y<X) for the generalized exponential distribution, Metrika, 61 (3), Kundu, D. and Gupta, R.D. (2006). Estimation of P(Y<X) for Weibull distribution, IEEE Transactions on Reliability, 55 (2), Kundu, D. and Raqab, M.Z. (2009). Estimation of R=P(Y<X) for three-parameter Weibull distribution, Statistics and Probability Letters, 79, Lawless, J.F. (1982). Statistical Models and Methods for Lifetime Data, New York: John Wiley & Sons. Lee. K.R., Kapadia, C.H. and Dwigh, B.B. (1980). On estimating the scale parameter of the Rayleigh distribution from doubly censored samples, Statist. Hefte. 21, v

6 Lio, Y.L., Tsai, T.R., and Wu, S.J. (2010). Acceptance sampling plans from truncated life tests based on the Birnbaum-Saunders distribution for percentiles, Communications in Statistics-Simulation and Computation 39, Marshall, A.W. and Olkin, I. (2007). Life Distributions-Structure of Nonparametric, Semiparametric, and Parametric Families, NewYork, Springer. Mazen and Zaindin. (2010). Parameter estimation of the modified Weibull model based on grouped and censored data, International Journal of Basic and Applied Sciences, 10(2), McCool, J. I. (1991). Inference on P( Y X ) in the Weibull case, Communications in Statistics-Simulation and Computation, 20, Mehrotra, K.G. and Nanda, P. (1974). Unbiased estimation of parameters by order statistics in the case of censored samples, Biometrika, 61, Mokhlis, N.A. (2005). Reliability of a stress-strength model with Burr type III distributions, Communication Statistics-Theory and Methods, 34, Mukherjee, S.P. and Maiti, S.S. (1997). A percentile estimator of the inverse Rayleigh parameter, IAPQR Transactions, 21, Mukherjee, S.P. and Saran, L.K. (1984). Bivariate inverse Rayleigh distributions in reliability studies, Journal of Indian Statistical Association, 22, Musa, J.D. (2004). Software Reliability Engineering, Tata McGraw-Hill, New Delhi. Nandi, S.B. and Aich, A.B. (1994). A note on estimation of p( X Y ) for some distributions useful in life-testing, IAPQR Transactions, 19(1), Ott, E.R. (1967). Analysis of means - A graphical procedure, Industrial Quality Control, 24, vi

7 Pandey, M. and Borhan Uddin, Md. (1985). Estimation of reliability in multicomponent stress-strength model following Burr distribution, Proceedings of the First Asian congress on Quality and Reliability, New Delhi, India, Pandey, M. and Upadhyay, S.K. (1986). Baye s estimation of reliability in stressstrength model of weibull distribution with equal scale parameters, Microelectronics and Reliability, 26, Persson, T. and Rootzen, H. (1977). Simple highly efficient estimators for a Type - I censored normal sample, Biometrika, 64, Pham, H. (2000). Software Reliability, Springer-Verlag. Pham, H. (2005). A generalized logistic software reliability growth model, Opsearch, 42(4), Pham, T. and Almhana, J. (1995), The generalized gamma distribution, its hazard rate and stress-strength model, IEEE Transactions on reliability, 44(3), Polovko, A.M. (1968). Fundamentals of Reliability Theory. Academic Press, New York. Porat, Z., Haim, M. and Markiewicz, Y. (1994). Estimation for a reliability model of form P(X>Y) or P(X<Y), IEEE Transactions on reliability, 43(3), Proschan, F. (1963). Theoretical explanation of observed decreasing failure rate, Technometrics, 5, Rao, C.R. (1973). Linear Statistical Inference and its Applications, Wiley Eastern Limited, India. Raqab, M.Z. and Kundu, D. (2005). Comparison of different estimators of P( Y X ) for a scaled Burr type X distribution, Communications in Statistics-Simulation and Computation, 34 (2), vii

8 Raqab, M.Z., Madi, M.T. and Kundu, D. (2008). Estimation of P( Y X ) for the 3- parameter generalized exponential distribution, Communication Statistics- Theory and Methods, 37 (18), Rosaiah, K. and Kantam, R.R.L. (2005). Acceptance Sampling Based on the inverse Rayleigh distribution, Economic Quality Control, 20(2), Rosaiah, K., Kantam, R.R.L. and Santhosh Kumar, Ch. (2005). ML and Modified ML estimation in exponentiated log-logistic distribution, Proceedings of National seminar on recent development in Statistics, Acharya Nagarjuna Univ., Rosaiah, K., Kantam, R.R.L. and Narasimham, V.L. (1993a). ML and modified ML estimation in gamma distribution with a known prior relation among the parameters, Pakistan Journal of Statistics, 9(3) B, Rosaiah, K., Kantam, R.R.L. and Narasimham, V.L. (1993b). On modified maximum likelihood estimation of gamma parameters, Journal of Statistical Research,(Bangladesh), 27(1&2), Rosaiah, K., Kantam, R.R.L. and Jayaprakash, B. (1997). Reliability Estimation in half logistic model, Gujarat Statistical Review, 24(2), Rosaiah, K., Kantam, R.R.L. and Santosh Kumar, Ch. (2005). Reliability Test Plans for exponentiated log-logistic distribution, Economic Quality Control, 21(2), Rosaiah, K., Kantam, R.R.L., Prasad, S.V.S.V.S.V. and Pratapa Reddy, J. (2008). Reliability estimation in type - II generalized log-logistic distribution, International Journal of Agricultural and Statistical Sciences, 4(2), Sathe, Y.S. and Shah, S.P. (1981). On estimation P( Y X ) for the exponential distribution, Communication Statistics-Theory and Methods, 10, Siddiqui, M.M. (1962). Some problems connected with Rayleigh distribution, Journal of Research of the National Bureau of Standards, 66D, viii

9 Sobel, M. and Tischendrof, J.A. (1959). Acceptance Sampling with new life test objectives, Proceedings of fifth National Symposium on Reliability and Quality Control, Philadelphia, Pennsylvania, Srinivasa Rao, B. (2010). Software Reliability and Quality Control Methods based on Half logistic distribution, unpublished Ph.D thesis awarded by Acharya Nagarjuna University. Srinivasa Rao, G. (2001). Some problems of Statistical inference with applications in log-logistic distribution, Unpublished Ph.D. thesis awarded by Acharya Nagarjuna University. Srinivasa Rao, G. and Kantam, R.R.L. (2010a). Acceptance sampling plans from truncated life tests based on the log-logistic distribution for percentiles, Economic Quality Control, 25(2), Srinivasa Rao, G. and Kantam, R.R.L. (2010b). Estimation of reliability in multicomponent stress strength model: log-logistic distribution, Electronic Journal of Applied Statistical Analysis, 3(2), Srinivasa Rao, G., Ghitany, M.E. and Kantam, R.R.L. (2008). Acceptance sampling plans for Marshall-Olkin extended Lomax distribution. International Journal of Applied Mathematics, 21(2), Srinivasa Rao, G., Ghitany, M.E. and Kantam, R.R.L. (2009a). Marshall-Olkin extended Lomax distribution: an economic reliability test plan, International Journal of Applied Mathematics, 22(1), Srinivasa Rao, G., Ghitany, M.E. and Kantam, R.R.L. (2009b). Reliability Test Plans for Marshall-Olkin extended exponential distribution, Applied Mathematical Sciences, 3(55), Sultan, K. S. (2007). Order statistics from the generalized exponential distribution and applications, Communications in Statistics-Theory and Methods, 36, Surles, J.G. and Padgett, W.J. (1998). Inference for P( Y X ) in the Burr type X model, Journal of Applied Statistical Sciences, 7, ix

10 Surles, J.G. and Padgett, W.J. (2001). Inference for reliability and stress-strength for a scaled Burr type X distribution, Lifetime Data Analysis, 7, Tiku, M. L. (1967). Estimating the mean and standard deviation from a censored normal sample, Biometrika, 54, Tiku, M.L. and Suresh, R.P. (1992). A new method of estimation for location and scale parameters, J. Statist. Plann & Inf., 30, Tiku, M.L., Tan, W.Y. and Balakrishnan, N. (1986). Robust Inference, Marcel Dekker, INC, New York. Tong, H. (1977). On the estimation of P( Y X ) for exponential families, IEEE Transactions on Reliability, 26, Travadi, R.J. and Ratani, R.T. (1990). On estimation of reliability function for inverse Guassian distribution with known coefficient of variation, IAPQR Transactions, 5, Treyer, V. N. (1964). Doklady Acad, Nauk, Belorus, U.S.S.R. Tsai, T.R., and Wu, S.J. (2006). Acceptance sampling based on truncated life tests for generalized Rayleigh distribution, Journal of Applied Statistics 33, Voda, V.Gh. (1972). On the inverse Rayleigh distributed random variable, Rep. Statist. App. Res., JUSE, 19, Wood, A. (1996). Predicting software reliability, IEEE Transactions on Software Engineering, 22, Wu, C.J. and Tsai, T.R. (2005). Acceptance sampling plans for Birnbaum Saunders distribution under truncated life tests, International Journal of Reliability, Quality and Safety Engineering 12, Yamada, S., Ohba, M. and Osaki, S. (1983). S-shaped reliability growth modeling for software error detection, IEEE Transactions on Reliability, 12, x

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