A study of time‐between‐events control chart for the monitoring of regularly maintained systems

Abstract

Owing to usage, environment and aging, the condition of a system deteriorates over time. Regular maintenance is often conducted to restore its condition and to prevent failures from occurring. In this kind of a situation, the process is considered to be stable, thus statistical process control charts can be used to monitor the process. The monitoring can help in making a decision on whether further maintenance is worthwhile or whether the system has deteriorated to a state where regular maintenance is no longer effective. When modeling a deteriorating system, lifetime distributions with increasing failure rate are more appropriate. However, for a regularly maintained system, the failure time distribution can be approximated by the exponential distribution with an average failure rate that depends on the maintenance interval. In this paper, we adopt a modification for a time-between-events control chart, i.e. the exponential chart for monitoring the failure process of a maintained Weibull distributed system. We study the effect of changes on the scale parameter of the Weibull distribution while the shape parameter remains at the same level on the sensitivity of the exponential chart. This paper illustrates an approach of integrating maintenance decision with statistical process monitoring methods.

Design of exponential control charts based on average time to signal using a sequential sampling scheme

“…Besides manufacturing processes, the TBE control chart can be used to monitor any processes with TBE or inter-arrival time random variables, such as time between failures in maintenance (Khoo and Xie 2009), time between medical errors (Doğu 2012) and time between consecutive radiation pulses (Luo, DeVol, and Sharp 2012). The TBE control chart is based on the inter-arrival times of non-conforming items, which are assumed to be independent and identically distributed (i.i.d.)…”

Moving range EWMA control charts for monitoring the Weibull shape parameter

“…Standards-given scenario: The stable-process value of the Weibull shape parameter is β S = 1.5 (see [9]), which implies σ S = 1/β S = 1/1.5 = 0.6. The centre line is CL = 2 log(2) × 0.6 = 0.9242.…”

“…In this section, we implement the EWMA control charts to monitor the Weibull process data of [9], which is provided in Table 4. The data come from a study of a set of simulated failure data (in hours) of a regularly maintained Weibull-distributed system.…”

“…We also discuss the sample size requirements for Phase I of retrospective charts. Lastly, we apply the proposed methods to the simulated failure time data provided by Khoo and Xie [9].…”

Sequential change detection in the presence of unknown parameters

“…We illustrate this phenomena by introducing a novel statistic for detecting changes in sequences of Exponentially distributed random variables. Control charts for the Exponential distribution are of interest to SPC due to their use in monitoring the time between failures generated by high yield processes (Khool and Xie, 2009;Liua et al, 2007;Chan et al, 2000), and our proposal extends this work by not requiring prior knowledge of either the pre-or postchange distributional parameter.…”