Cause-selecting Control Chart Research Articles

Integration of maintenance policy and statistical process monitoring for a cascade process with multiple assignable causes and random failures

This study develops an integrated model of statistical process monitoring and maintenance policy (MP) for a two-stage cascade process, involving two machines in series where the output of one stage affects the next stage. Instead of a single assignable cause (AC) affecting the quality characteristic, this production process experiences multiple ACs to more precisely simulate real conditions. Traditional and Hotelling’s T2 charts cannot detect the specific stage in which a shift occurs; therefore, this study employs a Cause-selecting control chart. The possibility of equipment failure and system stoppage are considered, with the process failure mechanism following a Weibull distribution. Depending on the conditions affecting the process or equipment, four MPs are considered to acheive the system’s initial condition, resulting in sixteen defined scenarios. The goal is to determine decision variables by minimizing a cost function subject to some statistical measures. This economic-statistical design can improve statistical and/or economic measures. However, it creates a more complex problem. Due to this complexity, a particle swarm optimization algorithm is used for optimization. The proposed model is implemented for a system that produces cotton yarn, with fiber length and skein strength are as the outputs of the first and second stages, respectively. Comparisons with two models validate the proposed model’s performance in cost reduction. A sensitivity analysis is performed for further investigations. The results indicate significant cost savings of the proposed model.

An integrated model of statistical process control and maintenance planning for a two-stage dependent process under general deterioration

Consider a two-stage dependent process in which each stage has a unique quality characteristic. Based on a regression formula, the quality characteristic of the second stage is dependent on that of the first stage. There may be two assignable causes in the process. Each cause can lead to a change in the mean of the process. The process failure mechanism for each stage follows a general continuous distribution function, and two control charts are simultaneously used to monitor the process. Specifically, the first stage is monitored using a Shwehart control chart, and the second stage is monitored using a cause-selecting control chart. An integrated model is developed for maintenance planning (MP) and statistical process control (SPC). To analyse the performance of the integrated model, a stand-alone model for SPC is developed. A comparison of the two models, i.e., the integrated model and the stand-alone model, is conducted. Finally, using a fractional factorial design, a depth analysis is performed about the integrated model. [Received: 10 February 2018; Revised: 21 April 2018; Revised: 4 June 2018; Revised: 12 September 2018; Revised: 7 October 2018; Accepted: 9 October 2018]

Fuzzy Cause Selecting Control Charts for Phase II Monitoring of a Two Stage Process

In this paper, it is assumed that there is a two-stage process in which the quality characteristic of the second stage is represented by fuzzy number which is monitored to detect shifts in the process. Also due to the existence of cascade property in a two-stage process, the quality characteristic of the second stage is affected by the quality characteristic in the first stage. Using fuzzy random variable which includes two kinds of uncertainty randomness and fuzziness simultaneously is considered. We proposed fuzzy Shewhart cause-selecting control chart and fuzzy exponentially weighted moving average (EWMA) cause-selecting control chart to detect different magnitudes of shift in the process parameters in phase II analysis. The performance of the proposed methods is evaluated by simulation in terms of average run length (ARL) criterion. Finally, a numerical example is given to show the application of the proposed methods step by step.

Monitoring the censored lognormal reliability data in a three-stage process using AFT model

Improving the product reliability is the main concern in both manufacturing and service processes which is obtained by monitoring the reliability-related quality characteristics. Nowadays, products or services are the result of processes with dependent stages referred to as multistage processes. In these processes, the quality characteristic in each stage is affected by the quality characteristic in the previous stages known as cascade property. Two regression-adjusted control schemes are applied to monitor the output quality variables of interest. Moreover, censoring is among the main limitations while monitoring the reliability-related quality characteristics, causing not to record the real values of some observations. Hence, the right censored observations are used to extend monitoring schemes under both the fixed- and variable-competing risks. In this paper, the accelerated failure time (AFT) is used to relate the reliability-related quality characteristic with lognormal distribution to the incoming variables. Then, two cause-selecting control charts are developed to monitor outgoing quality variables when censoring happens in each reliability-related stage. The performance of the control charts is evaluated and compared through extensive simulation studies under the censored and non-censored scenarios.

Algorithm of Multi-Causes Process Quality Diagnosis Using Binary Tree and Intermediate Quality

Process quality control is the core in product’s quality management. To solve the problem of multi-causes process quality diagnosis in manufacturing, an algorithm based on binary tree of quality cause set and intermediate quality is proposed. Firstly, the set of quality cause is divided progressively to form a complete binary tree, and then every node of subsets is chose as non-control cause set to construct the cause-selecting control chart of the intermediate qualities in its parent node. In diagnosis, control charts with same parent are compared to narrow the scope of abnormal quality causes until they are confirmed. Practice proves that the proposed algorithm can make the procedure of quality cause judgment independent to the adjustment, thus the comparison times of control charts could be greatly reduced and the efficiency of diagnosis is highly promoted.

Algorithm of Multi-cause Process Quality Diagnosis Based on Dichotomy

Aiming at the problem of multi-cause process quality diagnosis in manufacturing, an algorithm based on dichotomy is proposed. Quality cause set is divided by degrees to build its complete binary tree, and then every node in the complete binary tree is selected as non-control cause set to construct cause-selecting control chart of the intermediate quality index in its parent node. In quality diagnosis, control charts with same parent are compared to determine the scope of the abnormal quality causes until they are affirmed. Theoretical analysis and practice prove that the diagnosis algorithm based on dichotomy could make the procedure of quality diagnosis independent to the adjustment procedure, and the steps of control charts comparison can be reduced greatly, so the efficiency of diagnosis is highly improved.

Method and Application of Multistage Machining Quality Control Based on Minimum Overall Mean Quality Loss

To improve the quality control effect and decrease the manufacturing cost in the product’s multistage machining processes, based on the quality loss of single stage machining process, an overall mean quality loss model of multistage machining processes is established by the integration of Duncan cost model, Taguchi quality loss model, mean shift index and average time to signal (ATS). By using this quality loss model, the overall mean quality loss optimal function of multistage machining processes is constructed and the control parameters of this function are optimally solved. Besides, The Shewhart control chart and Cause-selecting control chart can be optimally designed with the control parameters of this optimal function. Finally, on the basis of an application, the multistage machining quality control based on minimum overall mean quality loss is verified to improve the control chart’s performance under the condition of the minimum overall mean quality loss.

Cause-selecting control charts based on Huber’s M-estimator

Cause-selecting chart (CSC) is effective in monitoring and diagnosing multistage processes. It discriminates between the overall and specific qualities by establishing the relationship between input and output measurements. In practice, the model relating the input and output variables must be estimated. To this end, historical data are used, which often contain outliers. The presence of outliers has a deleterious effect on the control charting procedure. To alleviate the encountered problem, a robust monitoring approach based on Huber’s M-estimator is proposed. Subsequently, the performance of the robust and non-robust CSCs is investigated using the average run length criterion while conducting a simulation study. The results reveal that the Huber-based CSC is superior to the traditional CSC due to its prompt detection of out-of-control conditions.

Transforms for cause-selecting control chart for a bivariate high-sigma process

When two production processes are interdependent, cause-selecting control charts are used to detect the variations in the succeeding process on account of the preceding process. In current literature, these charts are discussed for three-sigma process quality monitoring. In high-sigma processes that operate above three-sigma, the defect counts are in the order of parts per million. The traditional charts are obsolete for monitoring such processes. Count of conforming items between two non-conforming items is being used as data for the high-sigma process control charts. The underlying distribution is geometric distribution. Transforms are being used to convert the data to normality. In this work, a new transform is proposed for residual-type, cause-selecting control charts for a bivariate high-sigma process.

Effects of Measurement Error on Controlling Two Dependent Process Steps

Imprecise measurements may seriously affect the efficiency of process control and production cost. For two dependent processes, the in-coming quality variable in the first process may influence the out-going quality variable in the second process. To effectively monitor and distinguish the state of the two dependent process steps with imprecise measurements, the EWMA control chart and cause-selecting control chart are constructed by taking account of the measurement errors. The EWMA control chart for imprecise measurements is constructed to monitor small shifts in the process mean on the first step, and the cause-selecting control chart for imprecise measurements, is constructed to monitor small shifts in the process mean in the second step. The effects of imprecise measurements on the performance of the two proposed control charts are examined for the case, where the mean of each process may be changed by the occurrence of a special cause. The performance of the proposed control charts is measured by the average run length. A sensitivity analysis indicates that a larger variation of imprecise measurements leads to a larger average run length for the out-of-control process and a larger average loss.

Adaptive sampling interval cause-selecting control charts

This article considers the statistical adaptive process control for two dependent process steps. We construct an adaptive sampling interval Z X control chart to monitor the quality variable produced by the first process step, and use the adaptive sampling interval Z e control chart to monitor the specific quality variable produced by the second process step. By using the proposed adaptive sampling interval control charts, we can quickly detect and distinguish which process step is out of control. The performance of the proposed adaptive sampling interval control charts is measured by the adjusted average time to signal (AATS), which was derived by a Markov chain approach, for an out-of-control process. An empirical automobile braking system example shows the application and the performance of the proposed adaptive sampling control charts in detecting shifts in process means. Some numerical results obtained demonstrated that the performance of the proposed adaptive sampling cause-selecting control charts outperforms the fixed sampling interval cause-selecting control charts.

Optimal control policy for dependent process steps with over-adjusted means and variances

Over-adjustment to processes may result in shifts in process mean and variance, ultimately affecting the quality of products. An economic adjustment model is developed for the joint design of X-S2 control charts and ē-Se2 cause-selecting control charts to control both means and variances of two dependent process steps using the Markov chain approach. The objective is to determine the optimal control policy of the proposed control charts, which effectively detect and distinguish the shifts of means and variances on the dependent process steps and minimize the total quality control cost. Application of the proposed control charts is illustrated through a numerical example.

An approach to controlling two dependent process steps with autocorrelated observations

The observations from the process output are always assumed independent when using a control chart to monitor a process. However, for many processes the process observations are autocorrelated. This autocorrelation can have a significant effect on the performance of the control chart. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process step and the mean of a quality characteristic Y on the second process step, in which the observations X can be modeled as an AR(1) model and observations Y can be modeled as a transfer function of X since the state of the second process step is dependent on the state of the first process step. To effectively distinguish and maintain the state of the two dependent process steps, the Shewhart control chart of residual and the cause-selecting control chart are proposed. The proposed control charts’ performance is measured by the rate of alarm on the proposed charts. From numerical analysis, it shows that the performance of the proposed control charts is much better than the misused Hotelling T2 control chart and the individual Shewhart X and Y control charts.

Effects of imprecise measurement on the two dependent processes control for the autocorrelated observations

The observations from the process output are always assumed to be independent when using a control chart to monitor a process. However, for many processes the observations are autocorrelated and including the measurement error due to the measurement instrument. This autocorrelation and measurement error can have a significant effect on the performance of the process control. This paper considers the problem of monitoring the mean of a quality characteristic X on the first process, and the mean of a quality characteristic Y on the second process, in which the observations X can be modeled as an ARMA model and observations Y can be modeled as an transfer function of X since the state of the second process is dependent on the state of the first process. To distinguish and maintain the state of the two dependent processes with measurement errors, the Shewhart control chart of residuals and the cause-selecting control chart, based on residuals, are proposed. The performance of the proposed control charts is evaluated by the rate of true or false alarms. By numerical analysis, it shows that the performance of the proposed control charts is significantly influenced by the variation of measurement errors. The application of the proposed control charts is illustrated by a numerical example .

Dependent processes control for overadjusted process means

Overadjustment to processes may result in shifts in process mean, ultimately affecting the quality of products. An economic model is developed for the joint economic design of individual X and cause-selecting control charts to control both means of the dependent processes. The objective is to determine the design parameters of the proposed control charts that minimize the total quality control cost. A Markov chain approach is proposed to derive the economic- adjustment model. Application of the model is demonstrated through a numerical example.

Optimal Processes Control for a Failure Mechanism

This article considers the economic statistical process control for two dependent processes with a failure mechanism which obeys Weibull shock model and has an increasing failure rate. We construct individual economic statistical X control chart to monitor the quality variable produced by the first process, and use the cause-selecting control chart to monitor the specific quality produced by the second process with minimal cost and required statistical properties. By using the proposed control charts, we can effectively and economically distinguish which process is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and optimization method is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts. Sensitivity analysis that illustrates the effects of the cost and process parameters on the optimal design parameters and the minimal expected cost per unit time for the proposed control charts is also presented.

PROCESSES CONTROL FOR TWO FAILURE MECHANISMS

ABSTRACT This paper considers the economic statistical process control for two dependent processes with two failure mechanisms which obey Weibull shock models and have increasing failure rates. We construct individual economic statistical X control chart to monitor the in-coming quality produced by the first process, and use the cause-selecting control chart to monitor the specific quality produced by the second process with minimal cost and required statistical properties. By using the proposed control charts, we can effectively and economically distinguish which process is out of control. The renewal theorem approach is extended to construct the cost model for our proposed control charts, and optimization method is used to determine the optimal design parameters of the proposed control charts. Finally, we give an example to show how to construct and apply the proposed control charts.

STATISTICAL PROCESS CONTROL FOR TWO GRADE PRODUCTS UNDER TWO DEPENDENT PROCESSES

ABSTRACT In this paper, we propose an efficient approach to distinguish which process step is out of control and examine which kind of special cause occurs the shift of process means for two-grade products produced from two dependent processes. Two EWMA control charts are proposed to detect if the first kind of special causes, which affect one of the two-grade products, occur; and a combined EWMA control chart is designed to examine if another kind of special causes, which affect both the two-grade products, occur in the previous process. Two EWMA-type cause-selecting control charts are proposed to examine if the first kind of special causes, which affect the interested quality characteristic for each grade products, occur in the previous process. A combined cause-selecting control chart is designed to detect if another kind of special causes, which affect both the interested quality characteristics for two-grade products, occur in the current process. A simulated data analysis shows our proposed control charts are superior to Shewhart control charts and Hotelling T2 control charts in distinguishing which process is out of control and detecting which kind of special causes occur for two-grade products.

Improving the Sensitivity of the T2 Statistic in Multivariate Process Control

The T2 statistic associated with an observation from a multivariate process is a function of the residuals taken from a set of linear regressions existing among the various process variables. These residuals are contained in the conditional T2 terms of the orthogonal decomposition of the statistic. It is shown in this paper that a large residual in one of these fitted models can be due to incorrect model specification. By improving model specification at the time that the historical data set is constructed, it may be possible to increase the sensitivity of the T2 statistic to signal detection. The resulting regression residuals also can be used to improve the sensitivity of the T2 statistic to small but consistent process shifts. This is accomplished using plots that are similar to cause-selecting control charts.

Economic Process Management and Its Application on Bank Industry

A renewal equation approach is proposed to derive the multiple special-cause cost model for a system with two dependent subprocesses. The economic individual X control chart and simple cause-selecting control chart are thus constructed to monitor the two subprocesses. They may be used to maintain the whole process with minimum cost and effectively distinguish which component of the subprocesses is out of control. The economic design parameters of these two control charts can be determined by minimizing the cost model using a simple grid search method. An example of its application on controlling service quality in the bank industry is given to illustrate the design procedure and its application. It shows that these control charts may be used to control not only manufacturing dependent subprocesses but also service organisations with dependent subprocesses.