Progressive Variance Control Charts for Monitoring Process Dispersion

Self Cite

Process control measures are mostly applied in production and manufacturing industries. The most important tool used in these disciplines is control chart. In manufacturing and production processes, when the quality characteristic of interest cannot be directly measured, it becomes essential to apply attribute control charts. To monitor fraction nonconforming of the output, quality practitioners mostly prefer p‐chart. In this article, a new progressive mean (PM) control chart is being proposed for monitoring drift in proportion of nonconforming products. The design evaluations of the proposed chart are made and compared through different properties of run length distribution, such as average run length (ARL), standard deviation of run length (SDRL), and some percentile points. The performance of the proposed chart is assessed under zero‐state and steady‐state scenarios. The proposed PM chart is compared with p‐chart, moving average (MA) chart, optimal CUSUM chart, modified exponentially weighted moving average (EWMA) chart, and runs rules p‐charts for monitoring fraction nonconforming. The proposed chart spots efficiently sustained disturbances in the process as compared with their existing counterparts. Two illustrative examples are also provided; one from real‐life application of nonconforming bearing and seal assemblies data and the other from simulated data for the implementation of PM chart.

Section: Introductionmentioning

confidence: 99%

On designing an efficient control chart to monitor fraction nonconforming

Abbas

Nazir

Akhtar

et al. 2019

Self Cite

“…Recently a new idea (cf N Abbas et al and RF Zafar) has been proposed in SPC for the monitoring of quantitative data that makes use of the progressive mean (PM) statistic for monitoring process location and dispersion. They showed an improved performance of PM based charts compared to the Shewhart, EWMA, and CUSUM charts.…”

Section: Introductionmentioning

confidence: 99%

“…The initial work on Poisson EWMA chart was done in a previous study, 13 but its method involves rounding the EWMA statistic to the nearest integer value and hence resulting in a loss of information. CH White et al 14 19 ) has been proposed in SPC for the monitoring of quantitative data that makes use of the progressive mean (PM) statistic for monitoring process location and dispersion. They showed an improved performance of PM based charts compared to the Shewhart, EWMA, and CUSUM charts.…”

Section: Introductionmentioning

confidence: 99%

Poisson progressive mean control chart

Abbasi

2017

In real life applications, many process‐monitoring problems in statistical process control are based on attribute data resulting from quality characteristics that cannot be measured on numerical or quantitative scales. For the monitoring of such data, a new attribute control chart has been proposed in this study, namely, the Poisson progressive Mean (PPM) control chart. The performance of the PPM chart is compared with the existing charts used for the monitoring of Poisson processes such as the Shewhart c‐chart, Poisson Exponentially Weighted Moving Average chart, Poisson double Exponentially Weighted Moving Average chart and the Poisson Cumulative Sum charts. The average run length comparison indicated the superior performance of the PPM chart in terms of shift detection ability. This study will help quality practitioners to choose an efficient attribute control chart.

“…Kumar and Baranwal 29 studied the design of the t r chart based on the quantiles of the run-length distribution for both the known and unknown exponential parameter case. Zafar et al 38 used the progressive structure to monitor the variance of a process. For details about control charts based on Weibull distribution, the reader is referred to the works of Zhang and Chen, 30 Khoo and Xie, 31 Pascual, 32 Akhundjanov and Pascual, 33 Shafae et al, 34 and Wang et al 35 Many other modifications of EWMA and CUSUM charts, as well as another memory-type control charts have been studied by researchers in order to detect more quickly process shifts.…”

mentioning

confidence: 99%

“…Abbasi et al 37 proposed a nonparametric chart using the PM statistic, and it has been shown that this chart outperforms the nonparametric EWMA (NPEWMA) and nonparametric CUSUM (NPCUSUM) charts. Zafar et al 38 used the progressive structure to monitor the variance of a process. Abbas 39 showed that the PM statistic is a special case of the EWMA statistic where the smoothing parameter updated after every sample.…”

mentioning

confidence: 99%

A progressive mean control chart for monitoring time between events

Alevizakos

Koukouvinos

2019

Control charts based on time between events (TBE) are widely used in highquality manufacturing processes where the events occur rarely. For monitoring such data, a new two-sided TBE control chart called progressive mean control chart (regarded as PM-TBE chart) is proposed in the present study. Through a simulation study and using the average run-length (ARL) measure, it is shown that the proposed chart outperforms the t r , ARL-unbiased gamma, GWMA-TBE, and DEWMA-TBE charts in detecting very small to moderate downward shifts, as well as in some cases small upward shifts. Moreover, the PM-TBE chart is very robust for moderate to large shifts when the true distribution of the TBE observations is a Weibull or a lognormal. Finally, examples are given to display the application of the proposed chart. KEYWORDSaverage run length, Erlang distribution, progressive mean, robustness, time between events | INTRODUCTIONControl charts based on time between events (TBE) are frequently used in high-quality processes where the rate of occurrences is low. The traditional Shewhart control charts for attributes, such as c chart, u chart, p chart, and np chart, are used to monitor the number or the proportion of nonconformities or defective products, 1 whereas TBE control charts are used to monitor the inter-arrival times between the occurrences of events, which are assumed to be exponentially distributed. 2 Many researchers have focused on the study of TBE control charts. Lucas 3 studied the cumulative sum (CUSUM) chart for exponentially distributed observations, while Vardeman and Ray 4 used integral equations to calculate the average run-length (ARL) of the exponential CUSUM chart. Gan 5 investigated the optimal design of the exponential CUSUM chart, and Gan and Choi 6 presented a program for calculating the ARL of the above control chart. Gan 2 proposed the exponentially weighted moving average (EWMA) control chart for exponential data computing its ARL using differential equations, and he found it slightly less sensitive than the exponential CUSUM chart. Chan et al 7 proposed a Shewhart-type chart, called cumulative quantity control chart (CQC chart) for monitoring exponential TBE data. Jones and Champ 8 studied the phase I of Shewhart-type TBE control charts. Xie et al 9 proposed a Shewhart-type control chart, namely, t r chart, based on the Erlang distribution, to monitor the time between r (r ≥ 1) failures. Borror et al 10 studied the robustness of the exponential CUSUM chart assuming that the TBE observations follow a Weibull or a lognormal distribution, and they showed that it is very robust for both small and large shifts of parameters. Liu et al 11 compared various one-and two-sided exponential TBE control charts. Liu et al 12,13 proposed CUSUM and EWMA schemes, respectively, for monitoring exponential data after transforming it to an approximate normal distribution using the double square root transformation. Zhang et al 14 proposed a TBE control chart based on gamma distribution using the Let Y t ∼ iid ExpðθÞ, t=1,2,… r...