Showing papers by "Palaniappan Vellaisamy published in 2001"

On the nature of the binomial distribution

Abstract: We examine how the binomial distribution B(n, p) arises as the distribution S n = Σ n i=1 X i of an arbitrary sequence of Bernoulli variables. It is shown that B(n, p) arises in infinitely many ways as the distribution of dependent and non-identical Bernoulli variables, and arises uniquely as that of independent Bernoulli variables. A number of illustrative examples are given. The cases B(2, p) and B(3, p) are completely analyzed to bring out some of the intrinsic properties of the binomial distribution. The conditions under which S n follows B(n, p), given that S n-1 is not necessarily a binomial variable, are investigated. Several natural characterizations of B(n, p), including one which relates the binomial distributions and the Poisson process, are also given. These results and characterizations lead to a better understanding of the nature of the binomial distribution and enhance the utility.

Sequential and systematic sampling plans for the Markov-dependent production process

Abstract: Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov-dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and, in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called “systematic sampling plans.” The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 451–467, 2001