Roberto da Costa Quinino

Integrating on-line process control and imperfect corrective maintenance: An economical design

Existing studies of on-line process control are concerned with economic aspects, and the parameters of the processes are optimized with respect to the average cost per item produced. However, an equally important dimension is the adoption of an efficient maintenance policy. In most cases, only the frequency of the corrective adjustment is evaluated because it is assumed that the equipment becomes “as good as new” after corrective maintenance. For this condition to be met, a sophisticated and detailed corrective adjustment system needs to be employed. The aim of this paper is to propose an integrated economic model incorporating the following two dimensions: on-line process control and a corrective maintenance program. Both performances are objects of an average cost per item minimization. Adjustments are based on the location of the measurement of a quality characteristic of interest in a three decision zone. Numerical examples are illustrated in the proposal.

Diagnostic errors and repetitive sequential classifications in on-line process control by attributes

The procedure of on-line process control by attributes, known as Taguchis on-line process control, consists of inspecting the mth item (a single item) at every m produced items and deciding, at each inspection, whether the fraction of conforming items was reduced or not. If the inspected item is non-conforming, the production is stopped for adjustment. As the inspection system can be subject to diagnosis errors, one develops a probabilistic model that classifies repeatedly the examined item until a conforming or b non-conforming classification is observed. The first event that occurs (a conforming classifications or b non-conforming classifications) determines the final classification of the examined item. Proprieties of an ergodic Markov chain were used to get the expression of average cost of the system of control, which can be optimized by three parameters: the sampling interval of the inspections (m); the number of repeated conforming classifications (a); and the number of repeated non-conforming classifications (b). The optimum design is compared with two alternative approaches: the first one consists of a simple preventive policy. The production system is adjusted at every n produced items (no inspection is performed). The second classifies the examined item repeatedly r (fixed) times and considers it conforming if most classification results are conforming. Results indicate that the current proposal performs better than the procedure that fixes the number of repeated classifications and classifies the examined item as conforming if most classifications were conforming. On the other hand, the preventive policy can be averagely the most economical alternative rather than those ones that require inspection depending on the degree of errors and costs. A numerical example illustrates the proposed procedure.

An algorithm for insertion of idle time in the single-machine scheduling problem with convex cost functions

This paper addresses the problem of optimally inserting idle time into a single-machine schedule when the sequence is fixed and the cost of each job is a convex function of its completion time. We propose a pseudo-polynomial time algorithm to find a solution within some tolerance of optimality in the solution space, i.e., each completion time will belong to a small time interval z within which the optimal solution lies. Letting H be the planning horizon and |J| the number of jobs, the proposed algorithm is superior to the current best algorithm in terms of time-complexity when |J| < H/z.

Repetitive tests as an economic alternative procedure to control attributes with diagnosis errors

Abstract Optimal procedure for repeated and independent classifications of products with diagnosis errors are obtained in order to minimize the mean total inspection cost. Due to the complexity of the objective function, upper limits of search for the optimal values are proposed. The procedures are implemented in a program using the software Matlab and illustrated by an example.

Bayesian estimation of traffic intensity based on queue length in a multi-server M/M/s queue

ABSTRACT In this article, we focus on multi-server queueing systems in which inter-arrival and service times are exponentially distributed (Markovian). We use a Bayesian technique, the sampling/importance resampling method (SIR), to estimate the parameters of these queueing systems, making possible the determination of performance measures that are essential to the evaluation of important practical applications such as computer and telecommunication networks, manufacturing and service systems, health care, and other similar real-life problems. Extensive numerical results are presented to demonstrate the accuracy and efficiency of the technique, as well as some of its limitations.

Variable Interval Sampling in Economical Designs for Online Process Control of Attributes with Misclassification Errors

Online process control consists of inspecting a single item at every mth items produced, where m is an integer greater than two. Based on the results of the inspection, one decides if the process is in-control (the fraction of conforming item is p1—state I) or out-of-control (the fraction of conforming item is p2—state II). If the inspected item is non-conforming, the process is designated as out-of-control and production is stopped for possible adjustment; otherwise, production goes on. In this paper, a contribution to online process control is presented, where the inspection system is considered to be subject to classification errors. After every adjustment, the sampling interval is L units (L⩾m), and in the case of non-adjustment, the sampling interval is m units. The expression for the average cost per produced item is calculated, and optimum parameters (the sampling intervals L and m) are obtained by a direct search. The procedure is illustrated by a numerical example.

Monitoring the Process Mean Based on Attribute Inspection When a Small Sample is Available

This paper proposes a new control chart, denoted by to evaluate the stability of a process mean when a small sample is available. This chart is based on attribute inspection rather than the physical measurements (taken with an instrument, such as a caliper or precision balance) of the quality characteristics of interest of the sampled items. The main goal is to recover measurements on a continuous scale by generating random measurements using the frequencies observed for the sample as inputs. The average sample obtained using these recovery measures () is calculated and used to draw the standard chart. The average sample can be shown to be a mixture of normal distributions. The values of the lower control limit (LCL) and the upper control limit (UCL) are chosen to minimize the average run length (ARL).This paper proposes a new control chart, denoted by to evaluate the stability of a process mean when a small sample is available. This chart is based on attribute inspection rather than the physical measurements (taken with an instrument, such as a caliper or precision balance) of the quality characteristics of interest of the sampled items. The main goal is to recover measurements on a continuous scale by generating random measurements using the frequencies observed for the sample as inputs. The average sample obtained using these recovery measures () is calculated and used to draw the standard chart. The average sample can be shown to be a mixture of normal distributions. The values of the lower control limit (LCL) and the upper control limit (UCL) are chosen to minimize the average run length (ARL).

Self-oriented control charts for efficient monitoring of mean vectors.

Abstract This work presents a procedure for monitoring the centre of multivariate processes by optimising the noncentrality parameter with respect to the maximum separability between the in- and out-of-control states. Similarly to the Principal Component Analysis, this procedure is a linear transformation but using a different criterion which maximises the trace of two scatter matrices. The proposed linear statistic is self-oriented in the sense that no prior information is given, then it is monitored by two types of control charts aiming to identify small and intermediate shifts. As the control charts performances depend only on the noncentrality parameter, comparisons are made with traditional quadratic approaches, such as the Multivariate Cumulative Sum (MCUSUM), the Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling’s T 2 control chart. The results show that the proposed statistic is a solution for the problem of finding directions to be monitored without the need of selecting eigenvectors, maximising efficiency with respect to the average run length.

A Single Statistic for Monitoring the Covariance Matrix of Bivariate Processes

ABSTRACT In this article, we present a new control chart for monitoring the covariance matrix in a bivariate process. In this method, n observations of the two variables were considered as if they came from a single variable (as a sample of 2n observations), and a sample variance was calculated. This statistic was used to build a new control chart specifically as a VMIX chart. The performance of the new control chart was compared with its main competitors: the generalized sampled variance chart, the likelihood ratio test, Nagaos test, probability integral transformation (v t ), and the recently proposed VMAX chart. Among these statistics, only the VMAX chart was competitive with the VMIX chart. For shifts in both variances, the VMIX chart outperformed VMAX; however, VMAX showed better performance for large shifts (higher than 10%) in one variance.

Bayesian judgment of a dichotomous inspection system when the true state of an evaluated item is unknown

In the quality control of attributes, the evaluation of conforming items is an important task. An inspection system, in a general sense, is not free of errors. Two types are possible: an item is classified as non-conforming when it is conforming, or an item is classified as conforming when it is truly non-conforming. In this paper, a Bayesian method is proposed to judge the efficiency of a new inspection system based on repeated classifications performed on the evaluated items when their true state is not known.