On the constrained economic design of control charts: a literature review

Abstract

The economic design is an appealing approach to settle the design parameters of a control chart. Unfortunately, the economic models to design control charts have been scarcely implemented by quality practitioners due to the simplifying assumptions when representing the multifaceted complexity and constraints present within manufacturing and transactional environments. Although there has been an increasing scepticism about the economic models usefulness in practice, some recent studies proposed in literature face the problem of the control charts economic design from a new point of view: the objective is to achieve a well balanced trade-off between the operational and the statistical aspects. Under this perspective, the economic design problem can be intended in a broader sense as the constrained design of a SPC inspection procedure. This paper presents a discussion of some recent trends in the economic design stream of research and outlines the importance of considering the constraints related to SPC resources availability and modelling the occurrence of random shifts.

A Study About Average Cycle Time in Maintenance of Equipment.

“…Therefore, the selection of corrected value for shift size can be assumed as a difficult decision tackled by the quality practitioner due to the lack of former process knowledge [20], in such case we should have a state in which if the quality characteristic is located between the zone called "warning zone" of (µ + w ß/ ) and (µ + k ß/ ) or between the zone of (µ -w ß/ ) and (µ -k ß/ ), then an action of maintenance of equipment should be taken and to be done, as affirmed by the study [21], the process will start "in-control" at a random time, then a step shifts during research for the assignable cause, but it is allowed to continue in operation, it is considered cycle time as depicted in Figure 2. [6], and it should be mentioned that the major function of control charting is to detect the occurrence of assignable causes so that the necessary corrective action may be taken before a large quantity of nonconforming product is manufactured [22], because the production process by equipment in the firms is assumed as a series of independent cycles over time, and each cycle begins with the production process in the "in-control" state and it will continue until the process changes and its change is detected and identified [23].…”

A Study About Loss of Costs of Maintenance for Equipment by Using Taguchi Method of Quality Control.

“…But as a rule, there are three variables, they should be selected and assist to monitor and calculate loss of costs of maintenance after designing x-control chart, they are subgroup size (s), interval between successive subgroups (h), control limits (k), and warning coefficient or corrective threshold (w) and most studies assumed them as decision variables in any economic design models [23,24].…”

“…In the designated control chart, the aim is to fix a value for the shift δ of in-control process means μ0 to out-of-control condition μ1, and the selecting correct value for shift size can be assumed as a difficult decision tackled by the quality practitioner, due to the lack of former process knowledge [24], therefore, there is a condition that any further maintenance procedure is not required if the overall process is under control state and the quality characteristic is located between zones of (µ ± w ß/√ ), and the assign w is two third of the magnitude of control width k. Figure 1 shows the cost with Taguchi method and traditional cost function.…”

An economically designed Sequential Probability Ratio Test control chart for short-run production

“…All these works are based on the assumption that the production process is continuous and infinite, and the sampling interval and sample size adopted are fixed. More information on such research is available in Celano (2011).…”