Performance of attribute control charts for monitoring the shape parameter of modified power function distribution in the presence of measurement error

Abstract

In this paper, we develop attribute control charts (CCs) using two life data distributions named as Transmuted Power function distribution (TPFD) and Survival Weighted Power function distribution (SWPFD) under a time truncated life test (TTLT). The evaluation of the presented charts is based on the average run length and presented these evaluations in form of tables. The comparative study has been done for the suggested CCs in detail based on the criteria of average run length. We take up a real-life situation assuming that the lifespan of the items under study follows the TPFD and SWPFD to assess the competence of the proposed idea. A simulation study is given to support our idea that the CCs based on SWPFD performs better as compare to control chart based on TPFD for monitoring of non-conforming items.

Classical estimator based modified control charts for phase‐II monitoring in real life

“…In literature, we see some control charts constructed based on assumption of normality such as by Page, 1 Roberts, 2 Shamma and Shamma, 3 Haq, 4 Abbas et al, 5 Zwetsloot et al, 6 Sanusi et al, 7 Ajadi and Riaz, 8 Haq and Munir, 9 Li et al, 10 Nguyen et al, 11 Hossain et al, 12 Abu-Shawiesh and Saeed. 13 Some literature on control charts when the assumption of normality is not fulfilled such as Noorossana et al, 14 Lin et al, 15 Hossain et al, 16 Erto et al, 17 Karagoz, 18 Liang et al, 19 Ahmed et al, 20 Khan et al, 21 Saeed and Abu-Shawiesh, 22 and Zaka et al [23][24][25] proposed the control charts for the shape parameter of reflected power, power and weighted power function distributions under classical estimators, Jabeen and Zaka 26 discussed the modified EWMA control charts for the shape parameter of weighted power function distribution, Zaka et al 27 proposed the attribute control charts of the modified power function distribution and Zaka et al 28 discussed the modified EEWMA control charts for monitoring the shape parameter of reflected power function distribution.…”

“…Some literature on control charts when the assumption of normality is not fulfilled such as Noorossana et al, 14 Lin et al, 15 Hossain et al, 16 Erto et al, 17 Karagoz, 18 Liang et al, 19 Ahmed et al, 20 Khan et al, 21 Saeed and Abu‐Shawiesh, 22 and Zaka et al 23–25 . proposed the control charts for the shape parameter of reflected power, power and weighted power function distributions under classical estimators, Jabeen and Zaka 26 discussed the modified EWMA control charts for the shape parameter of weighted power function distribution, Zaka et al 27 . proposed the attribute control charts of the modified power function distribution and Zaka et al 28 .…”

Calibration and frequency estimation in sensors for electrical parameter measurement using regression and metaheuristic based models

“…Rough set theory‐based statistical feature extraction methods are also analysed in (Kaluri et al, 2021) using a deep neural network for optimum prediction of battery life. Similarly, the control charts proposed in (Zaka et al, 2022) are based on some realistic assumptions whilst predicting the lifespan of different products. Table 1 summarizes other literature that has worked on this particular problem and the remedial measures.…”

Modified calibrated control charts for monitoring the population mean under stratified sampling

“…The studies to control process parameters for different situations are given by Jabeen et al 10 , 11 . The shape parameter of the skewed distributions is studied by Zaka et al 23 …”

“…Noor-ul-Amin et al 17 have done their work on hybrid exponentially weighted moving average (HEWMA) control chart by using the auxiliary information. The studies to control process parameters for different situations are given by Jabeen et al 10 , 11 The shape parameter of the skewed distributions is studied by Zaka et al 23 . Jabeen and Zaka 24 provided some modifications to existing control chart to study the process shape parameter for weighted power function distribution.…”