One Sided Attribute npwb Chart to Monitor Weibull Mean

This paper proposes a one-sided attribute control chart for monitoring lifetime mean of Weibull distributed processes. A sample of n items is tested and up to a predetermined inspection time t_y and the number Y of items that failed before or at t_y is recorded. Since each item is classified as failed or not failed, the statistical count Y follows a binomial distribution, Y ~ Binomial (n, p_y) where p_y = P(T< t_y), and T ~ Weibull (k, lambda) stands for the duration. 

This approach allows the np_wb chart to be calibrated to meet a in-control average run length target. In this study, the control chart is illustrated for a sample of size n=10, considering an in-control Weibull distribution with parameters k₀=5 and lambda₀=4 to meet ARL₀=370.

The chart provides a simple and practical alternative for Weibull monitoring, particularly when exact lifetime measurements are costly, time-consuming, or require destructive experiments.