Design of an attribute np control chart for process monitoring based on repetitive group sampling under truncated life tests

In this paper, an attribute control chart under repetitive group sampling is designed for monitoring the production process where the lifetime of the product is considered as quality of the product. We assume that the lifetime follows the Pareto distribution of second kind with known shape parameter. The performance of the proposed chart is evaluated by average run length. The control limits coefficients as well as the repetitive group sampling parameter such as sample size are determined such that the in-control average run length is as close as to the specified average run length. Out-of-control average run length is also reported for different shift constants with corresponding optimal parameters. In addition, performance of proposed control chart is compared with the performance of existing chart. An economical designing of proposed control chart is also discussed.     

Time truncated attribute control chart for the Weibull distribution using multiple dependent state sampling

In this article, an attribute control chart is proposed for time truncated tests using the Weibull distribution. The design of proposed control chart is presented using the multiple dependent state (MDS) sampling. The control chart coefficients are determined for various specified average run length. The efficiency of the proposed control chart is elaborated with the help of a simulation data and a real data. The proposed control chart perform better than the existing control chart in terms of average run length.     

A control chart for multivariate Poisson distribution using repetitive sampling

Control charts using repetitive group sampling have attracted a great deal of attention during the last few years. In the present article, we attempt to develop a control chart for the multivariate Poisson distribution using the repetitive group sampling scheme. In the proposed control chart, the monitoring statistic from the multivariate Poisson distribution has been used for the quick detection of the deteriorated process to avoid losses. The control coefficients have been estimated using the specified in-control average run lengths. The procedure of the proposed control chart has been explained by using the real-world example and a simulated data set. It has been observed that the proposed control chart is an efficient development for the quick detection of the nonrandom change in the manufacturing process.     

A new S2 control chart using repetitive sampling

A new S² control chart is presented for monitoring the process variance by utilizing a repetitive sampling scheme. The double control limits called inner and outer control limits are proposed, whose coefficients are determined by considering the average run length (ARL) and the average sample number when the process is in control. The proposed control chart is compared with the existing Shewhart S² control chart in terms of the ARLs. The result shows that the proposed control chart is more efficient than the existing control chart in detecting the process shift.     

New V control chart for the Maxwell distribution

Control charts have been popularly used as a user-friendly yet technically sophisticated tool to monitor whether a process is in statistical control or not. These charts are basically constructed under the normality assumption. But in many practical situations in real life this normality assumption may be violated. One such non-normal situation is to monitor the process variability from a skewed parent distribution where we propose the use of a Maxwell control chart. We introduce a pivotal quantity for the scale parameter of the Maxwell distribution which follows a gamma distribution. Probability limits and L-sigma limits are studied along with performance measure based on average run length and power curve. To avoid the complexity of future calculations for practitioners, factors for constructing control chart for monitoring the Maxwell parameter are given for different sample sizes and for different false alarm rate. We also provide simulated data to illustrate the Maxwell control chart. Finally, a real life example has been given to show the importance of such a control chart.     

A new double sampling control chart for monitoring process mean using auxiliary information

Statistical quality control charts have been widely accepted as a potentially powerful process monitoring tool because of their excellent speed in tracking shifts in the underlying process parameter(s). In recent studies, auxiliary-information-based (AIB) control charts have shown superior run length performances than those constructed without using it. In this paper, a new double sampling (DS) control chart is constructed whose plotting-statistics requires information on the study variable and on any correlated auxiliary variable for efficiently monitoring the process mean, namely AIB DS chart. The AIB DS chart also encompasses the classical DS chart. We discuss in detail the construction, optimal design, run length profiles, and the performance evaluations of the proposed chart. It turns out that the AIB DS chart performs uniformly better than the DS chart when detecting different kinds of shifts in the process mean. It is also more sensitive than the classical synthetic and AIB synthetic charts when detecting a particular shift in the process mean. Moreover, with some realistic beliefs, the proposed chart outperforms the exponentially weighted moving average chart. An illustrative example is also presented to explain the working and implementation of the proposed chart.     

A new synthetic control chart for monitoring process mean using auxiliary information

ABSTRACT

Quality control charts have been widely recognized as a potentially powerful statistical process monitoring tool in statistical process control because of their superior ability in detecting shifts in the process parameters. Recently, auxiliary-information-based control charts have been proposed and shown to have excellent speed in detecting process shifts than those based without it. In this paper, we design a new synthetic control chart that is based on a statistic that utilizes information from both the study and auxiliary variables. The proposed synthetic chart encompasses the classical synthetic chart. The construction, optimal design, run length profiles, and the performance evaluation of the new chart are discussed in detail. It turns out that the proposed synthetic chart performs uniformly better than the classical synthetic chart when detecting different kinds of shifts in the process mean under both zero-state and steady-state run length performances. Moreover, with reasonable assumptions, the proposed chart also surpasses the exponentially weighted moving average control chart. An application with a simulated data set is also presented to explain the implementation of the proposed control chart.     

Designing of a control chart using belief statistic for exponential distribution

A new control chart is proposed by using the belief statistic for the exponential distribution. The structure of the proposed control chart is given to measure the average run length for the shifted process. The comparison of the proposed chart is given with the existing charts in terms of the average run lengths, which shows the outperformance of the proposed chart. The performance of the proposed control chart is also discussed with the help of simulated data.     

Performance of the zone control chart

Average run lengths of the zone control chart are presented, The performance of this chart is compared with that of several Shewhart charts with and without runs rules, It is shown that the standard zone control chart has performance similar to some even simpler charts and a much higher false alarm rate than the Shewhart chart with all of the common runs rules. It is also shown that a slightly modified zone control chart outperforms the Shewhart chart with the common runs rules.     

A synthetic control chart for the coefficient of variation

The coefficient of variation (CV) control chart has recently been introduced in the literature. Here, the salient features of this chart and the conforming run length chart are integrated to produce a synthetic coefficient of variation (SynCV) chart. The run length profile of the SynCV chart is numerically compared with the originally proposed chart and the upward EWMA-γ² chart. The SynCV chart outperforms the original CV chart, while the EWMA-γ² outperforms the SynCV chart for small increases in the CV. However, for large increases in the CV, the SynCV chart outperforms the EWMA-γ² chart.     

A HEWMA-CUSUM control chart for the Weibull distribution

The Weibull distribution is one of the most popular distributions for lifetime modeling. However, there has not been much research on control charts for a Weibull distribution. Shewhart control is known to be inefficient to detect a small shift in the process, while exponentially weighted moving average (EWMA) and cumulative sum control chart (CUSUM) charts have the ability to detect small changes in the process. To enhance the performance of a control chart for a Weibull distribution, we introduce a new control chart based on hybrid EWMA and CUSUM statistic, called the HEWMA-CUSUM chart. The performance of the proposed chart is compared with the existing chart in terms of the average run length (ARL). The proposed chart is found to be more sensitive than the existing chart in ARL. A simulation study is provided for illustration purposes. A real data is also applied to the proposed chart for practical use.     

The extended GWMA control chart

This study extends the generally weighted moving average (GWMA) control chart by imitating the double exponentially weighted moving average (DEWMA) technique. The proposed chart is called the double generally weighted moving average (DGWMA) control chart. Simulation is employed to evaluate the average run length characteristics of the GWMA, DEWMA and DGWMA control charts. An extensive comparison of these control charts reveals that the DGWMA control chart with time-varying control limits is more sensitive than the GWMA and the DEWMA control charts for detecting medium shifts in the mean of a process when the shifts are between 0.5 and 1.5 standard deviations. Additionally, the GWMA control chart performs better when the mean shifts are below the 0.5 standard deviation, and the DEWMA control performs better when the mean shifts are above the 1.5 standard deviation. The design of the DGWMA control chart is also discussed.     

The performance of the truncated mixed control chart

Abstract

When the mixed chart proposed by Aslam et al. (2015 Aslam, M., M. Azam, N. Khan, and C.-H. Jun. 2015. A mixed control chart to monitor the process. International Journal of Production Research 53 (15):4684–93. doi:10.1080/00207543.2015.1031354.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is in use, the sample items are classified as defective or not defective and, depending on the number of defectives, the quality characteristic X of the sample items are also measured. In this case, an Xbar chart decides the state of the process. The previous conforming/non-conforming classification truncates the X distribution and, because of that, the mathematical development to obtain the ARLs is complex. Aslam et al. (2015 Aslam, M., M. Azam, N. Khan, and C.-H. Jun. 2015. A mixed control chart to monitor the process. International Journal of Production Research 53 (15):4684–93. doi:10.1080/00207543.2015.1031354.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) didn’t pay attention to the fact that the X distribution is truncated and, due to that, they obtained incorrect ARLs.     

Globally applicable control chart for online monitoring of stability of process mean

The shape features of run chart patterns of the most recent m observations arising from stable and unstable processes are different. Using this fact, a new monitoring statistic is defined whose value for given m depends on the pattern parameters but not on the process parameters. A control chart for this statistic for given m, therefore, will be globally applicable to normal processes. The simulation study reveals that the proposed statistic approximately follows normal distribution. The performances of the globally applicable control chart in terms of average run lengths (ARLs) are evaluated and compared with the X chart. Both in-control ARL and out-of-control ARLs with respect to different abnormal process conditions are found to be larger than the X chart. However, the proposed concept is promising because it can eliminate the burden of designing separate control charts for different quality characteristics or processes in a manufacturing set-up.     

A control chart for monitoring process variation using multiple dependent state sampling

A control chart for monitoring process variation by using multiple dependent state (MDS) sampling is constructed in the present article. The operational formulas for in-control and out-of-control average run lengths (ARLs) are derived. Control constants are established by considering the target in-control ARL at a normal process. The extensive ARL tables are reported for various parameters and shifted values of process parameters. The performance of the proposed control chart has been evaluated with several existing charts in regard of ARLs, which empowered the presented chart and proved far better for timely detection of assignable causes. The application of the proposed concept is illustrated with a real-life industrial example and a simulation-based study to elaborate strength of the proposed chart over the existing concepts.     

A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

A more generalized stirling distribution of the second kind

A more generalized stirling distribution of the second kind (MGSDSK) is introduced in this paper as the distribution of the sum of the independent but not identically distributed left truncated Poisson variables. Properties of MGSDSK are studied. The recursion relation and decomposition of MGSDSK are obtained. The rth moment is also found and a new recurrence relationship for them are given. A new incomplete exponential function is utilized in the derivations. A MVU estimate of the p, d, f. of MGSDSK is obtained.     

Improving the performance of the zone control chart

A general model for the zone control chart is presented. Using this model, it is shown that there are score vectors for zone control charts which result in superior average run length performance in comparison to Shewhart charts with common runs rules.

A fast initial response (FIR) feature for the zone control chart is also proposed. Average run lengths of the zone control chart with this feature are calculated. It is shown that the FIR feature improves zone control chart performance by providing significantly earlier signals when the process is out of control.