Neil B. Marks

Estimation of Weibull parameters from common percentiles

Estimation of Weibull distribution shape and scale parameters is accomplished through use of symmetrically located percentiles from a sample. The process requires algebraic solution of two equations derived from the cumulative distribution function. Three alternatives examined are compared for precision and variability with maximum likelihood (MLE) and least squares (LS) estimators. The best percentile estimator (using the 10th and 90th) is inferior to MLE in variability and to one least squares estimator in accuracy and variability to a small degree. However, application of a correction factor related to sample size improves the percentile estimator substantially, making it more accurate than LS.

EWMA control charts for autoregressive processes

Many processes must be monitored by using observations that are correlated. An approach called algorithmic statistical process control can be employed in such situations. This involves fitting an autoregressive/moving average time series model to the data. Forecasts obtained from the model are used for active control, while the forecast errors are monitored by using a control chart. In this paper we consider using an exponentially weighted moving average (EWMA) chart for monitoring the residuals from an autoregressive model. We present a computational method for finding the out-of-control average run length (ARL) for such a control chart when the process mean shifts. As an application, we suggest a procedure and provide an example for finding the control limits of an EWMA chart for monitoring residuals from an autoregressive model that will provide an acceptable out-of-control ARL. A computer program for the needed calculations is provided via the World Wide Web.

Kolmogorov–Smirnov Test Statistic and Critical Values for the Erlang-3 and Erlang-4 Distributions

Abstract Following a procedure applied to the Erlang-2 distribution in a recent paper, an adjusted Kolmogorov–Smirnov statistic and critical values are developed for the Erlang-3 and -4 cases using data from Monte Carlo simulations. The test statistic produced features of compactness and ease of implementation. It is quite accurate for sample sizes as low as ten.

Modification of the kolmogorov-smirnov test for the erlang-2 distribution

An adjusted Kolmogorov-Smirnov statistic and critical values are developed for the Erlang-2 probability distribution using data from Monte Carlo simulations. The process used is similar to that of Stephens in the 1970s. The test statistic produced features of compactness and ease of implementation. It is quite accurate for sample sizes as low as ten.

Simulating alternative production policies with sequence-dependent costs

This article studies various sequencing and inventory rules in a manufacturing environment with nonlinear technological coefficients and stochastic demand. Multiple products require setup on a single machine and setup time and setup cost decrease with repeated setups. Furthermore, setup operations for different products have common components and an item can benefit from the setup operation of another item. The single-level, multi-item lot size model is used to model the production environment. The learning curve is used to represent this decrease in setup time with repeated setups. The learning transmission between items affects the scheduling of the products and the resulting model considers simultaneous decisions about lot sizing and sequencing in a nonlinear formulation. The problem is formulated and various production policies are simulated. Two sequencing rules and four inventory rules are examined. A simulation experiment of 6400 runs is used to compare the schedules produced by simple policies and those produced by more involved ones. A statistical analysis of the simulation results indicates that the simple rules perform equally well and in some cases better than the computationally harder rules.

A combined‐methodologies approach to problem solving in management science courses

In this paper it is suggested that an effective way to teach the introductory management science/operations research course is to tie together techniques in solving some fairly complex, realistic problems. A multistage process of analysis called the combined‐methodologies approach (CMA) is proposed. A queueing design problem is given as an example. Its solution requires the use of simulation, regression analysis, and goal programming. The particular techniques applied under CMA are specific to the situation under study. The authors believe the approach will increase student interest and address some criticisms of MS/OR instruction in universities.

Introduction of criticality indices into PERT instruction

A case is made for topical inclusion of criticality indices in classroom instruction on PERT networks. A probabilistic method for calculating the indices in a small network is presented, followed by a discussion of the implications and advantages of the pedagogy.