Designing variable control charts under failure censoring reliability tests with replacement

Abstract

There exist many processes where the quality characteristic does not follow a normal distribution, and the conditions for the application of central limit theorem are not satisfied; for example, because collecting data in a subgroup is impossible or the distribution is highly skewed. Thus, researchers have developed the control charts according to the specific distribution that models the quality characteristic. In this paper, some control charts are designed to monitor an exponentially distributed lifetime. The life testing is conducted according to the failure censoring while during the test; once observing a failure item, it is replaced by a new one so that the total number of items inspected during the test remains constant. Under the condition of the test, it is discussed that the elapsed time until observing the r’th failure has Erlang distribution. According to the relation of Erlang and chi-square distributions, the chart limits are computed to satisfy a specified value of type I error. Examples are presented and the curves of average run length are derived for the one-sided and two-sided control charts. Also, a comparative study is conducted to show the performance and superiority of the proposed control charts.

Memory‐type control charts for censored reliability data

“…Li and Xiao 12 discussed the role of censoring time in life tests when monitoring lifetime data with the likelihood-based control charts. Rasay 13 and Rasay and Arshad 14 discussed charts for type-I censored data with a replacement policy. Similarly, Mohammadipour et al 15 discussed process monitoring strategy using type-II censored reliability data assuming EWMA chart.…”

Monitoring Lifetime Data for a Failure Censoring Reliability Test with Replacement Using Shewhart Type and Exponentially Weighted Moving Average Control Charts

“…Accordingly, EWMA charts are sometimes called memory-based control charts. Some t-charts are developed by 12 to monitor the lifetime data under failure censoring. Under the assumption of Weibull distribution for the lifetime data, in reference 13 , a conditional expected value (CEV) control chart is proposed.…”

Designing Exponentially Weighted Moving Average Control Charts under Failure Censoring Reliability Tests

“…In the research by Faraz et al [16], the shape and scale parameters of the Weibull distribution were assumed to be unknown, and then the control charts of 𝑆 2 and Z̅ were proposed to monitor the shifts in the shape and scale parameter of the Weibull distribution. One-sided and two-sided t-control charts were presented by Rasay and Arshad [17] using a failure censoring test to monitor lifetime when it followed exponential distribution. Table 1 summarizes the most relevant studies in this area.…”