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Quality control charts have proven to be very effective in detecting out-of-control states. When a signal is detected a search begins to identify and eliminate the source(s) of the signal. A critical issue that keeps the mind of the process engineer busy at this point is determining the time when the process first changed. Knowing when the process first changed can assist process engineers to focus efforts effectively on eliminating the source(s) of the signal. The time when a change in the process takes place is referred to as the change point. This paper provides an estimator for a period of time in which a step change in the process non-conformity proportion in highyield processes occurs. In such processes, the number of items until the occurrence of the first non-conforming item can be modeled by a geometric distribution. The performance of the proposed model is investigated through several numerical examples. The results indicate that the proposed estimator provides a reasonable estimate for the period when the step change occurred at the process non-conformity level.

The aim of this study is to examine the effect of the addition of aluminum fumarate (AlFu) nanoparticles on the properties of poly(ether sulfone) (PES) membranes, where the AlFu nanoparticles were synthesized as the nanofillers with the metal−organic framework and their structure was characterized by Fourier transform infrared (FTIR) spectroscopy, X-ray powder diffraction (XRD), and field emission scanning electron microscopy (FESEM) analyses. Subsequently, PES/AlFu mixed-matrix membranes (MMMs) were fabricated in different weight percentages of nanofiller through the phase inversion method and the membrane characterization was accomplished by FTIR, XRD, FESEM, transmission electron microscopy, atomic force microscopy, energy-dispersive X-ray spectroscopy, and elemental mapping analyses. The effect of the addition of nanoparticles on the membrane properties was investigated by measuring the membrane hydrophilicity, pure water flux, solute rejection, and fouling resistance using a dead-end cell under constant pressure and bovine serum albumin as a foulant. The molecular weight cutoff (MWCO) of MMMs was measured by the rejection of poly(ethylene glycol) in various molecular weights, and the membrane surface roughness, porosity, and mean pore radius were calculated. The results showed that AlFu nanoparticles increased the hydrophilicity and porosity of the neat PES membranes and consequently increased the water permeability such that MMM including 0.75 wt % of AlFu possessed the maximum porosity (62.2%), mean pore radius (10.2 nm), and MWCO (154 kDa). Furthermore, this membrane exhibits a superlative flux recovery and minimal total resistance in the antifouling properties examinations.

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