Browsing by Author "Cassady, Charles Richard"
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- The frequency distribution of availabilityCassady, Charles Richard (Virginia Tech, 1993-12-07)The use of availability measures is very informative when analyzing the performance of repairable components. The derivation and evaluation of such measures is usually focused on describing the status of the component over time. It is not generally acknowledged that the resulting availability measure is in fact an expected value with respect to frequency. In a population of n independent, identical components, the number functioning at any point in time is a random variable. The distribution of this random variable is determined and described here. The intuitive view that this frequency distribution is binomial is verified. This is accomplished using direct analysis and Monte Carlo simulation. Two general cases are considered: (1) components with exponential life and repair time distributions, and (2) components with Weibull life distributions and exponential repair time distributions. The analysis leads to more accurate models of component behavior in terms of frequency including an exact confidence bound on the number of components functioning at any point in time. In addition, the time evolution of the frequency distribution is described and the relationships between the frequency distribution and the life and repair time distribution parameters are explored. Finally, the implications for availability decision analyses are shown. The overall result is a new perspective on availability which should prove to be very useful.
- Statistical quality control techniques using multilevel discrete product quality measuresCassady, Charles Richard (Virginia Tech, 1996-07-02)Statistical quality control is the application of statistical methods to problems for which it is of interest to evaluate, establish, or verify the quality of a product. The two basic areas of statistical quality control that have received both the greatest attention in the literature and the widest acceptance in industry are acceptance sampling and statistical process control. In the majority of such techniques, a single characteristic of an item is used to describe its quality. In such cases, one of two basic types of product quality measures is typically used: attributes product quality measures and variables product quality measures. Variables product quality measures evaluate an item’s quality by measuring its quality characteristic on a continuous scale. Attributes product quality measures assign a 0 to an item if its characteristic is conforming to some specification, and 1 if its characteristic is nonconforming. Although attributes and variables product quality measures have many appropriate applications, there are many situations m which product quality is best described by classifying a single characteristic of the item using three or more discrete levels. A multilevel discrete product quality measure is a function that assigns a numerical value to such an item corresponding to the level in which it is classified. Several acceptance sampling plans and control charts that incorporate the use of multilevel discrete product quality measures are defined here. In addition to the multilevel discrete product quality measure, each of the defined methods utilizes a quality value function. A quality value function assigns a numerical value to an item based on the classification it receives from the multilevel discrete product quality measure. Each of the defined multilevel acceptance sampling plans and multilevel control charts is evaluated with respect to its probabilistic behavior. In addition, the problem of parameter selection and quality value function specification is addressed for each of the defined techniques. The cases considered are the 3-level case, the 4-level case, and the general j-level case.