TY - GEN
T1 - An Analysis of the Performance of the SPRT Chart with Estimated Parameters Under the Weibull Distribution
AU - Teoh, Jing Wei
AU - Teoh, Wei Lin
AU - El-Ghandour, Laila
AU - Chong, Zhi Lin
AU - Teh, Sin Yin
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
PY - 2024/3/31
Y1 - 2024/3/31
N2 - Most developments of the sequential probability ratio test (SPRT) control chart assume that the underlying process comes from a Normal distribution with known mean and standard deviation. Nevertheless, the true values of the process parameters are usually inaccessible in production settings, and they must be approximated from a set of Phase-I data. In certain areas, the process data can be positively skewed, which in turn affect the performance of control charts designed under the Normal distribution. In this paper, we provide a thorough analysis on the performances of the SPRT chart with estimated process parameters under the influence of Weibull distributed data. The unconditional properties of the expected value and standard deviation of the time to signal are evaluated using Monte Carlo simulation to facilitate comparisons between the Normal and Weibull distributions. Results show that both the in-control and out-of-control performances of the SPRT chart deteriorate when Weibull data are used. However, the optimal design of the SPRT chart with estimated process parameters seems to reverse the effect for large process mean shifts.
AB - Most developments of the sequential probability ratio test (SPRT) control chart assume that the underlying process comes from a Normal distribution with known mean and standard deviation. Nevertheless, the true values of the process parameters are usually inaccessible in production settings, and they must be approximated from a set of Phase-I data. In certain areas, the process data can be positively skewed, which in turn affect the performance of control charts designed under the Normal distribution. In this paper, we provide a thorough analysis on the performances of the SPRT chart with estimated process parameters under the influence of Weibull distributed data. The unconditional properties of the expected value and standard deviation of the time to signal are evaluated using Monte Carlo simulation to facilitate comparisons between the Normal and Weibull distributions. Results show that both the in-control and out-of-control performances of the SPRT chart deteriorate when Weibull data are used. However, the optimal design of the SPRT chart with estimated process parameters seems to reverse the effect for large process mean shifts.
KW - Average time to signal
KW - Process parameter estimation
KW - Sequential probability ratio test
KW - Statistical process control
KW - Weibull distribution
UR - http://www.scopus.com/inward/record.url?scp=85190370355&partnerID=8YFLogxK
U2 - 10.1007/978-981-99-9005-4_22
DO - 10.1007/978-981-99-9005-4_22
M3 - Conference contribution
AN - SCOPUS:85190370355
SN - 9789819990047
T3 - Lecture Notes in Electrical Engineering
SP - 175
EP - 182
BT - Proceedings of the 12th International Conference on Robotics, Vision, Signal Processing and Power Applications
A2 - Ahmad, Nur Syazreen
A2 - Mohamad-Saleh, Junita
A2 - Teh, Jiashen
PB - Springer
T2 - 12th International Conference on Robotics, Vision, Signal Processing, and Power Applications 2023
Y2 - 28 August 2023 through 29 August 2023
ER -