EWMA and adaptive EWMA variable sampling intervals charts for simultaneous monitoring of Weibull parameters

ABSTRACT

In this article, we first propose an exponentially weighted moving average (EWMA) chart for monitoring both the shape and scale parameters of the Weibull distribution. The proposed chart was developed by incorporating two individual EWMA charts, one for monitoring the shape parameter and the other for monitoring both the shape and scale parameters. Particularly, it is shown that these two individual EWMA charts are mutually independent. Simulation studies are presented to compare the performance of the proposed EWMA chart and the existing Shewhart schemes with the EWMA setup. Further, to reduce the time for detecting an out-of-control (OC) process, an EWMA chart with variable sampling intervals (VSIs) and an adaptive EWMA chart with VSI for monitoring both the shape and scale parameters were also developed based on the proposed EWMA chart. The EWMA chart with VSI and the adaptive EWMA chart with VSI were studied and their performances were evaluated. An example to illustrate the applicability and implementation of the proposed charts is also provided.

KEYWORDS:

• Weibull distribution
• shape and scale parameters
• EWMA
• variable sampling intervals
• average time to signal
• adaptive chart

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Ministry of Science and Technology of Taiwan Grant MOST 106-2118-M-007-001-MY2.