Downloaded from https://www.everyspec.com AMCP 706.1"S tion to calculating the corresponding sample (Refs. 3, 4, 5, 22, and 23). Procedures for property and using that directly to estimate the s-normal, lognormal, and Weibull distribu- the population property. It is essentially a tions are quite simple to apply, and are illus- distribution-free method and is not subject trated in the remainder of this paragraph. to errors caused by the distribution not fitting the population out in the tail region In graphical methods, the data from the where there are no data.
Goodness-of-fit sample are rearranged so that they are in tests for this purpose are appropriate if the order from smallest to largest; they are then only property of the distribution that is referred to as order-sta tintics. Occasionally being used is one inside the data. It is quite the ordez is from largest to smallest, but inappropriate if properties of the distribution since it is so rarely done in reliability work, outside the data are used, for example, In all illustrations will be in the usual way. In calculating a mean.
order to plot the data points, a method is needed for choosing the Cdf (or the equ iv- 2-2 GRAPHICAL ESTIMATION OF alent cumulative hazard) at which each point PARAMETERS OF A DISTRIBUTION is to be plotted. There are several methods for doing this; they are explained in par. 2-2.1 The underlying distribution governing the and 2-2.2, There is no clear-cut way that is reliability characteristics should be chosen acceptable to everyone, But some of the carefully, because the validity of the reli- disapreements are needless, for the simple ability predictions and tests depends on this reason that when the sample size is small, the selection.
Although the exponential distribu- inherent uncertainty in plotting position is tion is most common for electronic equip. very large (regardless of the method used); ments, other distributions are used. The and when the sample size is large, all the failure characteristics of electromechanical methods tend to give the same position. and mechanical systems often can be de- Besides, if the finer phases of parameter scribed by distributions such as the s-normal, estimation by graphical methods are impor- lognormal, or Welbull.
Computer programs tant to you, you ought to be using an ana- are available for estimating thi• parameters lytic method for thosc finer phases-graphical for an assumed distribution from a set of methods just don't have the ability to make data, In many practical cases, graphical precise point estimates or to estimate the techniques are simple to apply and produce uncertainty in those point estimates. adequate results for estimating the underlying distribution. They are virtually always a 2.2.1 PLOTTING POSITIONS (CUMULA- useful prn Iminary to analytic estimation.
TIVE DISTRIBUTION FUNCTION) The basic Idea эn developing special graph Two methods of determining plotting posi- paper for use in gpaphical analysis Is to have tion are described. Both require that once the population Cdf or its cumulative hazard testing is stopped for any nonfailed item, It plot as a straight line. A straight line has 2 be stoppud for all remaining items.
Likewise, parameters (slope and intercept); so 2 pare- neither can us& the extra information if test- meters for the distribution can be determined, Ing continues beyond the failure time of the if the distribution can be appropriately trans- last recorded item (this tends to be true for formed, any graphical method and many analytic methods)., Graphical curve fitting techniques have been developed for all of the distributions 1, The sample Cdf is plotted, and the commonly associated with reliability testing uncertainty it looked-up in a simple table.