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Very often, in industry, discounted cash flow techniques are applied for analyzing and selecting investment alternatives under consideration. These techniques are usually based on the data under certainty or risk. In reality, however, the decision makers are often facing the situation of vague cash flows and discount rates, or even uncertain durations, when evaluating and selecting potential investments. Fuzzy set theory has the capability of capturing vague data and allows mathematical operations. This article proposes a fuzzy equivalent uniform annual worth (fuzzy EUAW) method to assist practitioners in evaluating investment alternatives utilizing the theory of fuzzy sets. Triangular fuzzy numbers (TFNs) are used throughout the analysis to represent the uncertain cash flows and discount rates. Further, fuzzy capital recovery factors and fuzzy sinking fund factor are derived. Using these two factors, the fuzzy equivalent annual worth of each investment alternative can be found. By ranking these fuzzy numbers with the integral value, the optimal investment alternative is selected. A numerical example is provided to illustrate the results of the alternative selection. [ABSTRACT FROM AUTHOR]

The geometric-Poisson exponentially weighted moving average (EWMA) chart has been shown to be more effective than the Poisson EWMA chart in monitoring the number of defects in the production processes. In these applications, it is assumed that the process parameters are known or have been accurately estimated. However, in practice, the process parameters are rarely known and must be estimated from reference sample to construct the geometric-Poisson EWMA chart. The performance of the given chart, due to variability in the parameter estimation, might differ from known parameters' case. This article explored the effect of estimated parameters on the conditional and marginal performance of the geometric-Poisson EWMA chart. The run length characteristics are calculated using a Markov chain approach and the effect of estimation on the performance of the given chart is shown to be significant. Recommendations about the proposer choice of sample size, smoothing constant, and dispersion parameter are made. Results of this study highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase-I sample. [ABSTRACT FROM AUTHOR]