Capability Indices for Rayleigh Process
الموضوعات :Davoud Dariae 1 , Bahram Sadeghpour Gildeh 2
1 - Department Of Mathematics, Ferdowsi University of Mashhad, Mashhad,Iran
2 - Department Of Mathematics,Ferdowsi University Of Mashhad, Mashhad,Iran
الکلمات المفتاحية: Process capability indices, Rayleigh distribution, Manufacturing Processes, Clements’s Method,
ملخص المقالة :
Monitoring, control and improvement of quality are important for companies. Process capability indices (PCIs) are tools widely used by the industries to determine the quality of their products and the performance of their manufacturing processes. Classic versions of these indices were constructed for processes whose quality characteristics have a normal distribution. But, many of these characteristics do not follow this distribution. In such a case, the classic PCIs must be modified to take into account the non-normality, because the effect of this non-normality can lead to misinterpretation of the process capability and ill-advised business decisions. A non-normal model is the Rayleigh distribution which is very useful. This paper proposes a Clements’s method to estimate the PCIs for Rayleigh processes. Finally, an example to evaluate its performance is presented.
M. Aslam, C.W. Wu, M. Azam, and C.-H. Jun, Variable sampling inspection for resubmitted lots based on process capability index
) for normally distributed items , Appl. Math. Model. 37 (2013),
667–675.
J.A. Clements, Process capability calculations for non-normal distributions, Qual. Prog. 22 (1989), 95–100.
D.D. Dyer, C.W. Whisenand, Best linear unbiased estimator of the parameter of the Rayleigh distribution—Part I: small sample theory for censored order statistics, IEEE Transactions on Reliability 22 (1973) 27–34.
D.D. Dyer, C.W. Whisenand, Best linear unbiased estimator of the parameter of the Rayleigh distribution—Part II: optimum theory for selected order statistics, IEEE Transactions on Reliability 22 (1973)
229–231.
W. Gilchrist, Modeling capability, J. Oper. Res. Soc. 44 (1993), 909–
923.
N. Johnson, S. Kotz, and W.L. Pearn, Flexible process capability indices, Pak. J. Stat. 10 (1994), 23–31.
V.E. Kane, Process capability indices, J. Qual. Technol. 18 (1986),
41–52.
W.C. Lee, J.W. Wu, M.L. Hong, L.S. Lin, R.L. Chan, Assessing the lifetime performance index of Rayleigh products based on the Bayesian estimation under progressive type II right censored samples, J. of Comput and Appl Math. 235 (2011) 1676–1688 .
V. Leiva, C. Marchant, H. Saulo, M. Aslam, F. Rojas, Capability indices for Birnbaum Saunders processes applied to electronic and food industries, J.Appl. Stat. (2014)Vol. 41, No. 9, 1881–1902 .
D. Montgomery, Introduction to Statistical Quality Control, Wiley, New York, 2004.
W.L. Pearn and K.S. Chen, Estimating process capability indices for non-normal Pearson populations, Qual. Reliab. Eng. Int. 11 (1995),
386–388.
A.M. Polovko, Fundamentals of Reliability Theory, Academic Press, New York, 1968.
J.W.S. Rayleigh, On the resultant of a large number of vibrations of the same pitch and of arbitray phase, Philosophical Magazine, Series 5
10 (1880) 73–78.
J.W.S. Rayleigh, Philosophical Magazine, Series 6 37 (1919) 321–
347.