Monitoring reliability for a gamma distribution with a double progressive mean control chart

Abstract

Abstract Control charting technique for time between events (TBE) is very important in high‐yield processes for monitoring reliability. For a regularly maintained system, the interfailure times can be modeled by a gamma distribution. This article proposes a new control chart based on the double progressive mean statistic for monitoring the time between k (≥1) failures of a maintained gamma distributed system (referred as DPM‐TBE chart). The performance of the proposed scheme is measured in terms of the average run‐length (ARL) for the case when the scale parameter is known as well as when it is unknown and is estimated from an in‐control (IC) reference sample. A comparison study with other TBE charts shows that the DPM‐TBE chart is more effective. In addition, the proposed chart is shown to be very robust for large shifts when the true distribution of time between failures is a Weibull or a lognormal. Finally, an illustrative example is given to demonstrate the implementation of the proposed chart.

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