Monitoring reliability for a three-parameter Weibull distribution

Operational reliability analysis applied to a gas turbine based on three parameter Weibull distribution

“…In deterministic approaches developed in several studies [1,[12][13][14], the reliability is the system resistance to sustained loads is assumed to be known and time-invariant, regardless of the type of system. In fact, this capacity may differ depending on the type of equipment, and for various reasons; changes in system properties, dimensional tolerances and other factors that affect the conduct of a component or a system composed of several components, error in the manufacturing process [15][16][17].…”

“…According to the Sturges rule given in[12], to grouping in the order of magnitude of the amount of data…”

New statistical inference for the Weibull distribution

“…For instance, estimations of unknown parameters, using methods such as the method of moment, the likelihood approach, least square methods, nonlinear regression estimators, robust estimation methods, and Bayesian methods, have been applied to Weibull distribution (Bain & Engelhardt, 1980;Duffy, Starlinger, & Powers, 1993;Lockhart & Stephens, 1994;Kuo & Yang, 1996;Ryan, 2003;Verma & Kapur, 2006;Sürücü & Sazak, 2009). In hypotheses tests, Lockhart and Stephens (1994) introduced the empirical distribution function methods to test whether the considered sample follows the threeparameter Weibull distribution.…”

Circle Chart for the Monitoring of Maxima in Periodic Processes

“…There are several recent works on control charts for skewed distributions, for example, the Weibull and extreme value distributions (see, e.g., Xie et al ., Nichols and Padgett, Sürücü and Sazak, Khoo and Xie, Yang et al ., Pascual and Li, Achcar et al ., etc.). However, control charts for periodic data from extreme value distribution are rather limited.…”