Optimizing and evaluating performance quality control of the production process of disposable essentials using approach vague goal programming

ABSTRACT To have effective production planning, it is necessary to control the quality of processes. This paper aims at improving the performance of the disposable essentials process using statistical quality control and goal programming in a vague environment. Therefore, in this study, the conditions are examined in a vague environment that is a distance-based environment. The disposable essentials process in Kach Company was studied. Statistical control tools were used to characterize the existing process for four-factor responses including the average of disposable glasses’ weights, heights, crater diameters, and volumes. Goal programming was then utilized to find the combination of optimal factors setting in a vague environment; also, the fuzzy regression model is used to predict the responses of the four described factors. Optimization results show that the process capability index values for disposable glasses were improved.

should always provide these supplies to Kaleh Company with the highest possible output. As a result, the importance of quality in this organization has been one of the main goals.
Statistical quality control is an important approach that helps by using statistical tools to illustrate the process. Chevrolet control charts are one of the most important quality control methods used to illustrate deviations with reason. Fuzzy diagrams with the ability to formulate expert experiences and use vague and imprecise data increase the ability to control quality to improve the quality of products and services. In this research, fuzzy theory is used to empower the statistical control charts. Because of the limitation of measurement tools and uncertainty in the measurement system, such as operators, confusions, environmental conditions, etc. operators cannot provide a precise number for these characteristics, and they inevitably record them in an approximate manner. The processing ability is based on fuzzy measurements and analysis control charts. The fuzzy fashion method and the proposed method of fuzzy rules are used to create fuzzy control graphs [1]. A fuzzy method is provided for vague data in monitoring the mean and variance of fuzzy charts by [2]. One method for calculating fuzzy standard deviations is to obtain a graph for cases provided by ̅ , as well as explained by the theoretical structure of fuzzy control ̅ which is known as local parameters [3]. Several approaches have been proposed to optimize process performance with multiple responses [4]. Therefore, multiple formularizations of goal programming (GP) models were shown for deciding the fuzzy GP (FGP) problems obtaining into account the decision maker's (DM's) priority [5]. An effective FGP technique is the weighted additive model, which considers all shapes of membership functions, with the objective to minimize the weighted deviations from the imprecise fuzzy values for all quality responses and process factors [6]. FGP has been utilized for optimizing process performance in many business applications [7]. A vague set, as well as an Intuitionistic fuzzy set, is a further generalization of a fuzzy set. We describe the Optimization of queuing theory based on vague environment [8]. In this research study, an empirical study of the fuzzy regression model was conducted to better estimate and predict. We explained fuzzy regression model for the evaluation of the functional relation between related and independent variables in the fuzzy environment, practical to diverse problems, such as prediction engineering [9]. The first engineering usage of GP was explained, due to the design and commissioning of spacecraft in the aerospace Optimizing and Evaluating Performance Quality Control of the Production Process of Disposable Essentials Using Approach Vague Goal Programming Hadi Gholizadeh, Ali Tajdin sciences via [10].
In reality, determining the combination of optimal factor settings for disposable glasses' manufacturing processes to improve multiple quality responses is a real challenge. This paper, therefore, aims at optimizing the performance of direct production process for multiple quality characteristics using statistical techniques (statistical quality control, fuzzy regression model) and weighted additive model in GP in a vague environment.
The continuation of this study is as follows. In Section II, the various concepts of the vague set theory are discussed. In Section III, vague process capability analysis and fuzzy regression models are introduced. The vague GP is introduced, and the process capability is expressed in Section IV. We conclude the subject in Section V.  (1)

Definition 4: [8].
Let be a vague set of . Then, we define -cuts and -cuts of as the crisp sets of given by : We denote the class of all vague numbers by A(ℛ).

A. Control Charts
A control chart is one of the primary monitoring techniques of Statistical Process Control (SPC). Control charts plot the points where statistics (such as an average, range, ratio, etc.) measure qualitative and quantitative characteristics of samples that have been obtained at different times of the process. The chart has a central line is in the mean values (CL) as well as the upper and lower levels of control (sometimes called the "natural part of the process"), which represents the threshold "unlikely" of the resulting process and they are drawn in three standard errors from the central line (UCL and LCL, respectively). At initial factor, settings have been explained by the ̅charts for averages disposable glasses' weight, height, crater diameter, and volume [11].

B. Vague Control Charts
This paper develops vague as a control chart which is    Fig. 2 The ̅ s charts for average disposable glasses at initial factory settings III. VAGUE PROCESS CAPABILITY ANALYSIS Capability analysis is used to assess whether a process is statistically capable to meet a set of customer desired product specifications. In practice, the process standard deviation, , is unknown and is frequently estimated by:

Xbar-S Chart of Volume
where is a constant related to the sample size, The estimator, , can be expressed mathematically by:

A. Fuzzy Regression Models
In fuzzy linear regression (FLR) analysis, uncertainty is obtained by a fuzzy relationship between the input and the output. In this paper, the approach in [12] is used, and accordingly, the regression models were calculated according to the expressed factors.
Three main process factors are identified affecting the disposable glasses' quality, including: : Speed away on the sheet from extruder hinges to the model forming machine.
: The amount of wind pressure on the sheet produced from the extruder hall in the model forming machine.
: Thickness sheet fluctuations produced from the extruder hall in the model forming machine. Table I shows the initial settings for the company that in the continuation will be used, and in Table II, the selected experimental design is shown. 16 samples are selected; each of size 4 is taken for the weight, fragility, crater diameter and volume, respectively. Each experiment is repeated three times. The final average values are calculated for the four responses and recorded in Table III. Let , , and denote the measured averages of weight, height, crater diameter and volume, respectively. To optimize process performance, the weighted additive model GP in a vague environment was utilized. The optimization procedure is described as follows: We formulate the mathematical relationship between each quality response and process factors.

1
The obtained optimal process conditions were found to be: The expected values for the Weight (g), Height (mm), Crater diameter (mm), and Volume (cc) are calculated as 18 g, 130 mm, 116 mm and 850 cc, respectively.
The vague control chart for the four factors of weight, height, crater diameter and volume is shown in Fig. 3.

A. Discussion
Organizations are able to make the best decisions in a variety of ways and have the best performance in order to adopt the process' effectiveness and the ability and efficiency of the production process. Considering the calculations and the control charts, we analyzed the sensitivity of the system function by considering the vague conditions of the distancing based uncertainty. The values for the averages of disposable glasses' weight, height, crater diameter, and volume are 1.38, 1.89, 1.80 and 2.28, respectively. The corresponding improvement relations were found to be 69.5%, 45.5%, 36% and 33.3%, respectively. Thus, results will affect in significant recovery in quality and thereby they increase productivity. By increasing the amount of , and , the amount of decreases, as a result, the amount of dispersion increases and the process acts out of the center, which increases the amount of waste and we are at Level2 , at this level, customers are satisfied with the organization, but they are putting a lot of pressure on the organization, such as low-profit margins, high operating costs, and a lot waste. Regarding the average deviation, we find that this deviation are due to machine error and is not related to sampling error and requires 100% inspection. Regarding waste recycling, the cost of rebuilding and rework increases. Therefore, in general, when we increase the amount of , and , the processing ability becomes less and the process will be less accurate, but it will work properly.
The main reason for these problems can be attributed to the accuracy of the device due to its exhaustion or the operator's skill changes (losing skill).

V. CONCLUSION
Given that the fuzzy quality control charts have greater flexibility than classical control charts; their use reduces the time needed to detect abnormalities in the process being investigated. This paper explains improving the performance of the disposable essentials process using statistical quality control and GP in an unclear environment. Therefore, in this study, the conditions are examined in a vague environment that is an environment based on distance. The statistical quality control tools were used for the four factors referred to the disposable glasses production process. Optimization results showed that the process capability index values for disposable glasses' averages of weight, height, crater diameter and volume relative to the classical model were improved accordingly. Such improvements resulted in significant savings in production costs and increase quality. The values for the averages of disposable glasses' weight, height, crater diameter, and volume were improved, respectively. In this way, the results will have a significant effect on improving quality and thus increasing productivity.
The value goal of the membership function is almost equal in both conditions, which shows that the distance between these two membership functions is relatively little and they found a heuristic fuzzy membership function.