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The purpose of this paper is to develop an economic statistical design based on the concepts of adjusted average time to signal (AATS) and ANF for X ¯ control chart under a Weibull shock model with multiple assignable causes.

The design used in this study is based on a multiple assignable causes cost model. The new proposed cost model is compared with the same cost and time parameters and optimal design parameters under uniform and non-uniform sampling schemes.

Numerical results indicate that the cost model with non-uniform sampling cost has a lower cost than that with uniform sampling. By using sensitivity analysis, the effect of changing fixed and variable parameters of time, cost and Weibull distribution parameters on the optimum values of design parameters and loss cost is examined and discussed.

This research adds to the body of knowledge relating to the quality control of process monitoring systems. This paper may be of particular interest to practitioners of quality systems in factories where multiple assignable causes affect the production process.

The cost functions for uniform and non-uniform sampling schemes are presented based on multiple assignable causes with AATS and ANF concepts for the first time.

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.

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.

Proposes a renewal theory approach to derive the cost model for two dependent processes. Thus, constructs the economic individual X chart and cause‐selecting chart to monitor the two processes. They may be used to maintain the process with minimum cost and effectively distinguish which component of the processes is out of control. The optimal design parameters of these control charts can be determined by minimizing the cost model using a simple grid search method. Gives an example to illustrate the design procedure and application of the economic individual X chart and cause‐selecting chart.

Discusses the economic designs of np charts for a single assignable cause. Develops a simple algorithm to get the optimum designs of np charts. Twenty numerical examples show that the algorithm is very efficient and accurate indeed.

In the economic design of •‐control charts the two extreme approaches used are that the design parameters are: (i) fixed once determined, and (ii) change from sample to sample. Administrative convenience favours the first approach in practice, although research work indicates, for instance, that constant sampling intervals are not necessarily optimal. This article provides an economic but partially dynamic model where the sampling intervals are of random lengths but other parameters are kept fixed once determined. Random sampling intervals are practical especially in labour‐intensive economies and job‐shop situations where assignable causes are introduced by external factors such as operator skill, fatigue, carelessness and other physical environments. In such work environments, operators have been found to take undue advantage of constant sampling intervals. The model developed here incorporates statistical, economic and administrative considerations in addition to other practical work situations. Some guidelines for implementing the model in the production environment are provided.

In 1973, Goel and Wu presented an algorithm for the economic design of cusum charts to control the mean of a process with a normally distributed quality characteristic. They employed the two‐dimensional pattern search technique to determine the optimal values of the sample size, the sampling interval and the decision limit. Proposes a search algorithm required to use the one‐dimensional pattern search technique to get the optimal values of design parameters instead of the two‐dimensional pattern search technique. So, our search algorithm is not only accurate and efficient but also simpler to solve than that of Goel and Wu.

Presents two production models for maintaining current control of an industrial process under the surveillance of an np‐control chart. The first model assumes that the process is not allowed to continue in operation during the search for the assignable cause. The second assumes that the process is allowed to continue in operation during the search for the assignable cause. Develops two simple algorithms, which are implementable in real time on a personal computer, to get the optimum designs of np‐charts. Twenty‐six numerical examples show that the algorithms are very accurate and efficient.

A manufacturing process quality model for investigating the operation of a manufacturing unit has been developed incorporating the failure mechanism of instantaneous assignable cause, mean drift and standard deviation drift. Describes an illustrative example, showing how the new model can be used in conjunction with simulation to optimize the control of a manufacturing process from a cost‐quality perspective.

The purpose of this paper is to develop a double-objective economic statistical design (ESD) of (X ‾) control chart under Weibull failure properties with the Linex asymmetric loss function. The authors have expressed the probability of type II error (β) as the statistical objective and the expected cost as the economic objective.

The design used in this study is based on a double-objective economic statistical design of (X ‾) control chart with Weibull shock model via applying Banerjee and Rahim's model for non-uniform and uniform schemes with Linex asymmetric loss function. The results in the least average cost and β in uniform and non-uniform schemes by Linex loss function, compared with the same schemes without loss function.

Numerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the X ‾ control chart in practice. When the authors use non-uniform schemes instead of uniform schemes, the average cost per unit time decreases by an average and when the authors apply loss function, the average cost per unit time increases by an average. Also, this quantity for double-objective schemes with loss function compared to without loss function schemes in cases uniform and non-uniform increases. The reason for this result is that the model underestimated the costs before using the loss function.

This research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.

The cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.