A Note On the Use of Fiducial Limits for Control Charts

TL;DR

This paper discusses a technique for calculating exact control limits in control charts using fiducial limits, especially when distribution parameters are unknown, moving beyond traditional graph-based methods.

Contribution

It introduces a method to compute fiducial limits for control charts without relying on graphs or tables, applicable when distribution parameters are unknown.

Findings

Provides a technique for exact control limit calculation

Clarifies the use of fiducial limits in control charting

Enhances control chart accuracy when parameters are unknown

Abstract

Many of the early works in the quality control literature construct control limits through the use of graphs and tables as described in Wortham and Ringer (1972). However, the methods used in this literature are restricted to using only the values that the graphs and tables can provide and to the case where the parameters of the underlying distribution are known. In this note, we briefly describe a technique which can be used to calculate exact control limits without the use of graphs or tables. We also describe what are commonly referred to in the literature as fiducial limits. Fiducial limits are often used as the limits in control charting when the parameters of the underlying distribution are unknown.