Krane, Scott A.* (1963, ASQC and the American Statistical Association) CEIR, Inc., Dugway, Utah
* - Prepared while the author was at the Statistical Laboratory, Iowa State University, Ames, and originally presented at the 119th Annual Meeting of the American Statistical Association, Washington, DC, December 27-30, 1959.The nature of the process of retirement of groups of industrial properties is so complex that it is difficult to postulate adequate mathematical models such as those employed in life-testing, etc. Assuming that there exists a survivor function, M(t), representing the proportion of a group remaining in service at time t, such function is given by exp [-y(t)], where y(t) is the time integral of the retirement rte, r(t) = -d(logM(t))/dt. Rather than to hazard a guess as to the parametric form of any of these functions, it is the intent of this paper to approximate the integral, y(t), by a polynomial, whereupon M(t) may be graduated by the descending exponential function. For large samples it is found that the covariance structure for the polynomial regression of y(t) on t may be obtained from the multinomial distribution when the data are grouped. Thus the method of weighted least squares may be employed in fitting y(t). "Censored" data in no way vitiate the method.