Volume 38, Issue 2

This study develops a higher-order Markov model (HOM) for an inventory system with remanufacturing, substitution, and lost sales. Defective and disposed items are other factors that are considered in addition to probabilistic demand for both manufacturing and remanufacturing items. One year is the warranty period for items manufactured, and items sold return from customers to the manufacturer in increasing cumulative percentages over the months of the year. To the best our knowledge, a higher-order Markov model has rarely been used in a hybrid inventory system. The challenge is how to determine the steady state of the system with the probable demand for manufacturing and remanufacturing. We propose a new search algorithm to select the best control strategy from several strategies, and then compare it with the two-phase local search algorithm. Each state deals with (12) a probabilistic demand (policy), so the system steady state is set to (22632) policies in total for each production plan. The results showed profit maximization using the new search algorithm compared with the two-phase local search algorithm. Also, an increase in defective and returned items over time, and therefore an increase in remanufactured items. But it does not satisfy all the demand, so manufacturing increases over time due to substitution. Substitution strategy leads to increase the expected average profit.

Artificial neural networks (NNs) have been extensively studied for their application to quality control (QC) to monitor the conformity of processes to quality specifications. However, the requirement of at least five QC measurements increases the associated costs. This study explores the potential of using NNs on samples of QC measurements of very small size. To achieve this, three one-dimensional (1-D) convolutional NNs (CNNs) were designed, trained, and tested on datasets of n -tuples of simulated, standardized, normally distributed QC measurements, where 2 ≤ n ≤ 4 {2\leq n\leq 4} . The performance of the designed CNNs was compared to that of statistical QC functions applied to samples of equal sizes, maintaining equal probabilities for false rejection. The results demonstrated that for n -tuples of QC measurements distributed as 𝒩 ⁢ ( 0 , s 2 ) \mathscr{N}(0,s^{2}) , where 1.2 < s ≤ 9.0 1.2<s\leq 9.0 , the designed CNNs outperformed their statistical QC functions counterparts. Therefore, the use of 1-D CNNs applied to samples of two to four QC measurements can effectively enhance the detection of nonconformity of a process to quality specifications. This approach has the potential to significantly reduce the costs of QC measurements and improve the overall efficiency of the QC process.

In this paper, a c-control chart using a triple sampling scheme (TS-c) is studied. The chart design, procedure, and a bi-objective optimization model are given to optimize the TS-c-chart. The Average Run Length for in-control and out-of-control ( ARL 1 \mathrm{ARL}_{1} ), and Average Sample Number metrics are calculated. A Comparison among TS-c, Fixed parameters c (FP-c), VSS-c, EWMA-c, and Double Sampling c (DS-c) control charts are carried out in terms of ARL 1 \mathrm{ARL}_{1} . The proposed TS-c-chart has lower ARL 1 \mathrm{ARL}_{1} values for detecting small and moderate shifts in the mean number of non-conformities in control compared with FP-c, VSS-c, EWMA-c, and DS-c.

Many quality characteristics in manufacturing industry are of one sided specifications. The well-known process capability indices C P ⁢ U C_{PU} and C P ⁢ L C_{PL} are often used to measure the performance of such type of production process. It is usually assumed that process observations are independent and measurement system is free of errors. But actually in many industry it has been proven that auto-correlation is an inherent nature of the production process, especially for chemical processes. Moreover, even with the use of highly sophisticated advanced measuring instruments some amount of measurement error is always present in the observed data. Hence gauge measurement error also needs to be considered. In this paper we discuss some inferential properties of one-sided process capability indices for a stationary Gaussian process in the presence of measurement errors. As a particular case of a stationary Gaussian process, we discuss the case of a stationary AR ⁡ ( 1 ) \operatorname{AR}(1) process where measurement error follows an independent Gaussian distribution.

Classical Hotelling’s T 2 T^{2} control chart is frequently used for monitoring a multivariate process. The existence of outlying observations in the Phase I data used to determine the control limit can have a significant impact on the accuracy of such control charts, as is well known. Based on the robust reweighted orthogonalized comedian estimates, a robust multivariate quality control chart for individual observations is proposed in this study. Control limit of the proposed robust control chart is estimated by modelling the simulated quantiles for any sample size. A Simulation study has been conducted to examine the performance of the proposed method and compare it with the performances of the classical Hotelling T 2 T^{2} control chart, a robust control chart based on shrinkage reweighted estimator and two robust control charts based on the reweighted minimum covariance determinant estimator. The results demonstrate the effectiveness of the proposed method, even under high-dimensional settings or when the contamination in the Phase I data is high, with both independent and correlated variables. Performance of the proposed method is also illustrated by implementing in a real-world example

We given an elementary proof that in a Markov chain with absorbing states, and positive probability of absorption at some time t > 0 {t>0} , time to absorption follows a mixture distribution of hypo-exponential random variables. We use this fact to show that early approximations of such a distribution yield the length of the shortest path from an initial state to an absorbing state. Thus different Markov chains with the same distance of shortest paths can yield identical first order approximations. Our work is motivated by the classical Armitage and Doll model of carcinogenesis.