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Statistical process control optimization with variable sampling interval and nonlinear expected loss
1.  Department of Applied Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O.B. 78, Karmiel 2161002, Israel, Israel 
2.  Department of Industrial Engineering and Management, Ort Braude College of Engineering, 51 Snunit Str., P.O.B. 78, Karmiel 2161002, Israel 
References:
[1] 
R. W. Amin and R. Hemasinha, The switching behavior of X charts with variable sampling intervals, Communication in Statistics  Theory and Methods, 22 (1993), 20812102. doi: 10.1080/03610929308831136. 
[2] 
R. W. Amin and R. W. Miller, A robustness study of X charts with variable sampling intervals, Journal of Quality Technology, 25 (1993), 3644. 
[3] 
V. Babrauskas, Heat Release Rates, in SFPE Handbook of Fire Protection Engineering, (Ed. P.J. DiNenno), National Fire Protection Association, (2008), 159. 
[4] 
E. Bashkansky and V. Y. Glizer, Novel approach to adaptive statistical process control optimization with variable sampling interval and minimum expected loss, International Journal of Quality Engineering and Technology, 3 (2012), 91107. 
[5] 
M. A. K. Bulelzai and J. L. A. Dubbeldam, Long time evolution of atherosclerotic plaques, Journal of Theoretical Biology, 297 (2012), 110. doi: 10.1016/j.jtbi.2011.11.023. 
[6] 
T. E. Carpenter, J. M. O'Brien, A. Hagerman and B. McCarl, Epidemic and economic impacts of delayed detection of footandmouth disease: A case study of a simulated outbreak in California, Journal of Veterinary Diagnostic Investigation, 23 (2011), 2633. doi: 10.1177/104063871102300104. 
[7] 
A. F. B. Costa, X control chart with variable sample size, Journal of Quality Technology, 26 (1994), 155163. 
[8] 
A. F. B. Costa, X charts with variable sample sizes and sampling intervals, Journal of Quality Technology, 29 (1997), 197204. 
[9] 
A. F. B. Costa, Joint X and R control charts with variable parameters, IIE Transactions, 30 (1998), 505514. 
[10] 
A. F. B. Costa, X charts with variable parameters, Journal of Quality Technology, 31 (1999), 408416. 
[11] 
A. F. B. Costa and M. S. De Magalhães, An adaptive chart for monitoring the process mean and variance, Quality and Reliability Engineering International, 23 (2007), 821831. doi: 10.1002/qre.842. 
[12] 
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Dover Publications, Inc., Mineola, NY, 2007. 
[13] 
J. P. Dussault, J. A. Ferland and B. Lemaire, Convex quadratic programming with one constraint and bounded variables, Mathematical Programming, 36 (1986), 90104. doi: 10.1007/BF02591992. 
[14] 
I. M. Gelfand and S. V. Fomin, Calculus of Variations, PrenticeHall, Englewood Cliffs, NJ, 1963. 
[15] 
A. D. Ioffe and V. M. Tihomirov, Theory of Extremal Problems, NorthHolland Pub. Co., Amsterdam, Netherlands, 1979. 
[16] 
S. Kim and D. M. Frangopol, Optimum inspection planning for minimizing fatigue damage detection delay of ship hull structures, International Journal of Fatigue, 33 (2011), 448459. doi: 10.1016/j.ijfatigue.2010.09.018. 
[17] 
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGrawHill Book Company, Inc., New York, NY, 1968. 
[18] 
D. C. Montgomery, Introduction to Statistical Quality Control, John Wiley and Sons Inc., New York, NY, 2005. 
[19] 
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience, New York, NY, 1962. 
[20] 
S. S. Prabhu, D. C. Montgomery and G. C. Runger, A combined adaptive sample size and sampling interval X control scheme, Journal of Quality Technology, 26 (1994), 164176. 
[21] 
M. R. Reynolds, Evaluating properties of variable sampling interval control charts, Sequentional Analysis, 14 (1995), 5997. doi: 10.1080/07474949508836320. 
[22] 
M. R. Reynolds, R. W. Amin, J. C. Arnold and J. Nachlas, X charts with variable sampling intervals, Technometrics, 30 (1988), 181192. doi: 10.2307/1270164. 
[23] 
S. Ross, A First Course in Probability, 9 ed., Prentice Hall, Upper Saddle River, NJ, 2009. 
[24] 
P. Sebastião and C. G. Soares, Modeling the fate of oil spills at sea, Spill Science and Technology Bulletin, 2 (1995), 121131. doi: 10.1016/S13532561(96)000096. 
[25] 
G. Taguchi, S. Chowdhury and Y. Wu, Taguchi's Quality Engineering Handbook, John Wiley and Sons Inc., Hoboken, NJ, 2007. doi: 10.1002/9780470258354. 
show all references
References:
[1] 
R. W. Amin and R. Hemasinha, The switching behavior of X charts with variable sampling intervals, Communication in Statistics  Theory and Methods, 22 (1993), 20812102. doi: 10.1080/03610929308831136. 
[2] 
R. W. Amin and R. W. Miller, A robustness study of X charts with variable sampling intervals, Journal of Quality Technology, 25 (1993), 3644. 
[3] 
V. Babrauskas, Heat Release Rates, in SFPE Handbook of Fire Protection Engineering, (Ed. P.J. DiNenno), National Fire Protection Association, (2008), 159. 
[4] 
E. Bashkansky and V. Y. Glizer, Novel approach to adaptive statistical process control optimization with variable sampling interval and minimum expected loss, International Journal of Quality Engineering and Technology, 3 (2012), 91107. 
[5] 
M. A. K. Bulelzai and J. L. A. Dubbeldam, Long time evolution of atherosclerotic plaques, Journal of Theoretical Biology, 297 (2012), 110. doi: 10.1016/j.jtbi.2011.11.023. 
[6] 
T. E. Carpenter, J. M. O'Brien, A. Hagerman and B. McCarl, Epidemic and economic impacts of delayed detection of footandmouth disease: A case study of a simulated outbreak in California, Journal of Veterinary Diagnostic Investigation, 23 (2011), 2633. doi: 10.1177/104063871102300104. 
[7] 
A. F. B. Costa, X control chart with variable sample size, Journal of Quality Technology, 26 (1994), 155163. 
[8] 
A. F. B. Costa, X charts with variable sample sizes and sampling intervals, Journal of Quality Technology, 29 (1997), 197204. 
[9] 
A. F. B. Costa, Joint X and R control charts with variable parameters, IIE Transactions, 30 (1998), 505514. 
[10] 
A. F. B. Costa, X charts with variable parameters, Journal of Quality Technology, 31 (1999), 408416. 
[11] 
A. F. B. Costa and M. S. De Magalhães, An adaptive chart for monitoring the process mean and variance, Quality and Reliability Engineering International, 23 (2007), 821831. doi: 10.1002/qre.842. 
[12] 
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Dover Publications, Inc., Mineola, NY, 2007. 
[13] 
J. P. Dussault, J. A. Ferland and B. Lemaire, Convex quadratic programming with one constraint and bounded variables, Mathematical Programming, 36 (1986), 90104. doi: 10.1007/BF02591992. 
[14] 
I. M. Gelfand and S. V. Fomin, Calculus of Variations, PrenticeHall, Englewood Cliffs, NJ, 1963. 
[15] 
A. D. Ioffe and V. M. Tihomirov, Theory of Extremal Problems, NorthHolland Pub. Co., Amsterdam, Netherlands, 1979. 
[16] 
S. Kim and D. M. Frangopol, Optimum inspection planning for minimizing fatigue damage detection delay of ship hull structures, International Journal of Fatigue, 33 (2011), 448459. doi: 10.1016/j.ijfatigue.2010.09.018. 
[17] 
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGrawHill Book Company, Inc., New York, NY, 1968. 
[18] 
D. C. Montgomery, Introduction to Statistical Quality Control, John Wiley and Sons Inc., New York, NY, 2005. 
[19] 
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience, New York, NY, 1962. 
[20] 
S. S. Prabhu, D. C. Montgomery and G. C. Runger, A combined adaptive sample size and sampling interval X control scheme, Journal of Quality Technology, 26 (1994), 164176. 
[21] 
M. R. Reynolds, Evaluating properties of variable sampling interval control charts, Sequentional Analysis, 14 (1995), 5997. doi: 10.1080/07474949508836320. 
[22] 
M. R. Reynolds, R. W. Amin, J. C. Arnold and J. Nachlas, X charts with variable sampling intervals, Technometrics, 30 (1988), 181192. doi: 10.2307/1270164. 
[23] 
S. Ross, A First Course in Probability, 9 ed., Prentice Hall, Upper Saddle River, NJ, 2009. 
[24] 
P. Sebastião and C. G. Soares, Modeling the fate of oil spills at sea, Spill Science and Technology Bulletin, 2 (1995), 121131. doi: 10.1016/S13532561(96)000096. 
[25] 
G. Taguchi, S. Chowdhury and Y. Wu, Taguchi's Quality Engineering Handbook, John Wiley and Sons Inc., Hoboken, NJ, 2007. doi: 10.1002/9780470258354. 
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