Conforming Run Length Chart Research Articles

A Synthetic Control Chart for Detecting Fraction Nonconforming Increases

In this paper we propose a new control chart, the synthetic control chart, for the detection of increases in the fraction nonconforming (p). The operation, design, and performance of this control chart are described. The synthetic chart is a combination of the np chart and the conforming run length chart. It provides the user with some freedom in adjusting the control chart parameters so that the out-of-control average time to signal can be minimized. Numerical tests have indicated that the synthetic chart has a higher power for detecting process shifts in the fraction nonconforming than both the np chart and the conforming run length chart. The improvement is significant for all cases, resulting in a 50% or greater reduction of the out-of-control average time to signal. The application of the synthetic chart may therefore substantially enhance the effectiveness of statistical process control for attributes.

A Synthetic Control Chart for Detecting Small Shifts in the Process Mean

This paper presents a synthetic control chart that is an integration of the Shewhart X̄ chart and the conforming run length chart. Like the Shewhart X̄ chart, the synthetic chart is used to detect the process mean shift, δ. We found from intensive performance tests that the synthetic control chart consistently produces smaller out-of-control average run lengths (ARL's) than the Shewhart X̄ chart (with or without supplementary runs rules) for any size of δ when the false alarm rate is held at a specified value. Compared to the Shewhart X̄ chart, when δ is moderate (between 0.5σ and 1.5σ), the synthetic control chart can reduce the out-of-control ARL by nearly half. The synthetic control chart also outperforms the exponentially weighted moving average (EWMA) chart and the joint X̄-EWMA charts when δ is greater than 0.8σ.

Evaluation of ATS for CRL control chart

The CRL (Conforming Run Length) control chart has attracted increasing interest in the last few years. Many researchers have claimed that the CRL chart is superior to the traditional attribute control charts (e.g. the np chart or p chart) in many aspects. In this paper, accurate formulae have been derived for calculating the out-of-control ATS (Average Time to Signal) of the CRL chart. These formulae take into account the random-shift model of p (fraction nonconforming), in which the p value may shift at any point during a conforming run length. Comparative studies reveal that the conventional approximate method for evaluating the ATS of the CRL chart may produce notable error. The new formulae provide the QA (Quality Assurance) engineers with a tool to accurately assess the performance of the CRL chart, and will therefore promote further application of the CRL chart.