Kolmogorov-Smirnov Type Test-Statistics For The Gamma,Erlang-2 And The Inverse Gaussian Distributions When The Parameters Are Unknown.

Critical values are presented for the Kolmogorov-Smirnov type test statistics for the following three cases: (i) the gamma distribution when both the scale and the shape parameters are not known, (ii) the scale parameter of the gamma distribution is not known and (iii) the inverse Gaussian distribution when both the parameters are unknown. This study was motivated by the necessity to fit the gamma, the Erlang-2 and the inverse Gaussian distributions to the interpurchase times of individuals for coffee in marketing research.     

Tables to Facilitate Fitting Tadikamalla and Johnson's LB Distributions

This paper is concerned with estimating the parameters of Tadikamalla-Johnson's L_B distribution using the first four moments. Tables of the parameters of the L_B distribution are given for selected values of skewness (0.0(0.05) 1.0(0.1)2.0) and corresponding available values of kurtosis at intervals of 0.2. The construction and use of these tables is explained with a numerical example.     

A comparison of several approximations to the lead time demand distribution

Several distributions have been used for approximating the lead time demand distribution in inventory systems. We compare five distributions, the normal, the logistic, the lognormal, the gamma and the Weibull for obtaining the expected number of back orders, the reorder levels to have a given protection and the optimal order quantity, reorder levels in continuous review models of (Q, r) type. The normal and the logistic distributions are inadequate to represent the situations where the coefficient of variation (the ratio of the standard deviation to the mean) of the lead time demand distribution is large. The lognormal, the gamma and the Weibull distributions are versatile and adequate; however the lognormal seems to be a viable candidate because of its computational simplicity.     

Customization: Impact on Product and Process Performance

Manufacturing capability has often been viewed to be a major obstacle in achieving higher levels of customization. Companies follow various strategies ranging from equipment selection to order process management to cope with the challenges of increased customization. We examined how the customization process affects product performance and conformance in the context of a design‐to‐order (DTO) manufacturer of industrial components. Our competing risk hazard function model incorporates two thresholds, which we define as mismatch and manufacturing thresholds. Product performance was adversely affected when the degree of customization exceeded the mismatch threshold. Likewise, product conformance eroded when the degree of customization exceeded the manufacturing threshold. Relative sizes of the two thresholds have management implications for the subsequent investments to improve customization capabilities. Our research developed a rigorous framework to address two key questions relevant to the implementation of product customization: (1) what degrees of customization to offer, and (2) how to customize the product design process.     

One-sided tolerance limits for unbalanced one-way anova andomc effects model

In this article, we investigate techniques for constructing tolerance limits such that the probability is γ that at least _p proportion of the population would exceed that limit. We consider the unbalanced case and study the behavior of the limit as a function of n_i 's (where n_i is the number of observations in the ith batch), as well as that of the variance ratio. To construct the tolerance limits we use the approximation given in Thomas and Hultquist (1978). We also discuss the procedure for constructing the tolerance limits when the variance ratio is unknown. An example is given to illustrate the results.     

Tables to facilitate fitting lu distributions

This paper is concerned with estimating the parameters of Tadikamalla-Johnson's L_Udistributions based on the method of moments. Tables of the parameters of the L_U distribution are given for selected values of skewness (0.0(0.05) 1.0(0.1)2.0) and for twenty values of kurtosis at intervals of 0.2. The construction and use of these tables is explained with a numerical example.     

The lognormal approximation to the lead time demand in inventory control

This paper is intended to show that the lognormal distribution can be used to approximate the lead time demand in inventory control problems. The computations involved with this approximation are shown to be simpler compared to the gamma distribution approximation. Some pertinent properties of the lognormal distribution are summarized. Numerical examples are given in two cases of distributed demands and lead times and in each case the lognormal approximation results are compared with the exact and/or other approximations.     

The Use of Stochastic Simulation in Knowledge-Based Systems

Knowledge-based systems support the decision-making process with the help of domain specific knowledge bases. The knowledge bases almost always have uncertainty associated with them. A variety of approaches have been proposed in the artificial intelligence (AI) literature for the construction of and reasoning with uncertain knowledge bases. Building on this stream of research, we focus on how stochastic simulation can be used to construct and reason with knowledge bases that have uncertainties. An advantage of the simulation methodology is that it may not have to make many of the assumptions made by other approaches. It also allows the designer of the knowledge-based system to control the methodology based on accuracy and time requirements. The simulation approach to knowledge base construction is a modified version of the concept induction procedure used in AI. However, it incorporates, as does simulation modeling, statistical tests to identify the best rule that describes the relationship among the variables. We show that when simulation is used to reason with uncertain knowledge bases, under certain conditions, the number of simulation trials needed to achieve a given level of accuracy is independent of the characteristics, such as the size, of the knowledge base. Empirical results obtained from an experiment confirm our theoretical results and provide evidence that simulation methodology is practical for real life knowledge-based systems.