Evaluating lifetime performance for the Pareto model with censored and imprecise information

Abstract

A lifetime capability index L tp has been proposed to measure the business lifetime performance, wherein output lifetime measurements are assumed to be precise from the Pareto model with censored information. In the present study, we study a more realistic situation where the lifetime output data are imprecise. The approach developed by Buckley [Fuzzy system, Soft Comput. 9 (2005), pp. 757-760; Fuzzy statistics: Regression and prediction, Soft Comput. 9 (2005), pp. 769-775] incorporated with some extensions (a set of confidence intervals, one on top of the other), is used to construct the triangular-shaped fuzzy number for the fuzzy estimate of the L tp . With the sampling distribution of the unbiased estimator of the L tp , two useful fuzzy inference criteria, its critical value and fuzzy p-value are obtained to assess the lifetime performance. The presented methodology can handle the lifetime performance assessment on the condition that sample lifetime data are involved with imprecise information, classifying the lifetime performance with the three-decision rule. With different preset requirements and a certain degree of imprecise data, we also develop a four quadrants decision-making plot where managers can easily simultaneously visualize several important features of lifetime performance for making a decision. An example of business lifetime data is given to illustrate the applicability of the proposed method.

Fuzzy Evaluation Model for Lifetime Performance Using Type-I Censoring Data

“…=− for t > 0. Building upon this assumption, some studies have proposed a relative lifetime performance index to offer the industry a more intuitive and user-friendly tool in practice [14][15][16]. According to Chiou [17] and Chen and Yu [16], the relative electronic component lifetime is denoted with X = T/L, where L represents the period of warranty.…”

Manufacturing process performance evaluation for fuzzy data based on loss-based capability index

“…Conversely, Parchami and Mashinchi (2007), Chang et al (2007), Cheng et al (2007), Hsu and Shu (2008), and Kaya and Kahraman (2010) constructed fuzzy-number PCIs based on the most common situation that observations and specification limits are all real numbers, where Kahraman and Kaya (2009b, c) used their main results to control water level of a dam for irrigation as well as air pollutants in Istanbul, Turkey, respectively. Moreover, Hsu et al (2011) used them with some extensions to evaluate lifetime performance for the Pareto model with censored and imprecise information. But without either fuzzy observations or fuzzy limits, a traditional condition for the PCIs field, complicatedly generating fuzzy-number PCIs might neither adequate nor necessary.…”