The economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on…
The economic design of control charts has been researched for over four decades since Duncan proposed the concept in 1956. Few studies, however, have focused attention on the economic design of a moving average (MA) control chart. An MA control chart is more effective than the Shewhart chart in detecting small process shifts. This paper provides an economic model for determining the optimal parameters of an MA control chart with multiple assignable causes and two failures in the production process. These parameters consist of the sample size, the spread of the control limit and the sampling interval. A numerical example is shown and the sensititivy analysis shows that the magnitude of shift, rate of occurrence of assignable causes and increasing cost when the process is out of control have a more significant effect on the loss cost, meaning that one should more carefully estimate these values when conducting an economic analysis.
Control charts are important tools of statistical quality control. In 1956, Duncan first proposed the economic design of x‐control charts to control normal process means and insure that the economic design control chart actually has a lower cost, compared with a Shewhart control chart. An moving average (MA) control chart is more effective than a Shewhart control chart in detecting small process shifts and is considered by some to be simpler to implement than the CUSUM. An economic design of MA control chart has also been proposed in 2005. The weaknesses to only the economic design are poor statistics because it does not consider type I or type II errors and average time to signal when selecting design parameters for control chart. This paper provides a construction of an economic‐statistical model to determine the optimal parameters of an MA control chart to improve economic design. A numerical example is employed to demonstrate the model’s working and its sensitivity analysis is also provided.
The problem of optimal software reliability design is considered. Allocation models are usually used to compute the target reliability for each module of a software…
The problem of optimal software reliability design is considered. Allocation models are usually used to compute the target reliability for each module of a software system to maximize the overall system reliability. This objective can also be achieved by employing redundancy, e.g. N‐version programming technique (NVP). A method bridging the allocation model and redundancy approach is derived. The proposed model simultaneously determines both the optimal amount of redundancy and target reliability for each module to achieve the best reliability while the total cost stays within the budget.
The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an…
The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an economic–statistical design of the X̅ control charts under the Burr shock model and multiple assignable causes were considered and compared with three types of prior distribution for the mean shift parameter.
The design of the modified X̅ chart is based on the two new concepts of adjusted average time to signal and average number of false alarms for X̅ control chart under Burr XII shock model with multiple assignable causes.
The cost model was examined through a numerical example, with the same cost and time parameters, so the optimal of design parameters were obtained under uniform and non-uniform sampling schemes. Furthermore, a sensitivity analysis was conducted in a way that the variability of loss cost and design parameters was evaluated supporting the changes of cost, time and Burr XII distribution parameters.
The economic–statistical model scheme of X̅ chart was developed for the Burr XII distributed with multiple assignable causes. The correlated data are among the assumptions to be examined. Moreover, the optimal schemes for the economic-statistic chart can be expanded for correlated observation and continuous process.
The economic–statistical design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects; one of the proper alternatives may be the Burr XII distribution which is quite flexible. Yet, in Burr distribution context, only one assignable cause model was considered where more realistic approach may be to consider multiple assignable causes.
This study presents an advanced theoretical model for cost model that improved the shock model that presented in the literature. The study obviously indicates important evidence to justify the implementation of cost models in a real-life industry.