Single-Subgroup Performance Measures and Diagnostic Procedures for X-Bar Control Charts

Although Shewhart control charts have had a tremendous impact on quality improvement, the inability to precisely measure chart performance has limited their role, and subsequently overall effectiveness in the control of manufacturing processes. Measures of performance in terms of operational characteristics (OC) are defined on two distinct levels: (a) single-subgroup level, which examines the probability of a rule violation at any given subgroup (b) multiple-subgroup level, which considers the probability of one or more rule violations throughout process monitoring. Single-subgroup performance measures for X-bar charts that employ four rules are formulated. These measures are exact expressions of operational characteristics, except for the numerical approximation to the integral of the normal distribution. Applications of these models to simulated data demonstrate their accuracy in predicting chart performance. In addition, a diagnostic methodology is described which utilizes the derived performance measures to predict the mean of a shifted distribution. The proposed diagnostic procedure is illustrated in validation and application examples.

Download Full-text

Design of a Control Chart Using Extended EWMA Statistic

Technologies ◽

10.3390/technologies6040108 ◽

2018 ◽

Vol 6 (4) ◽

pp. 108 ◽

Cited By ~ 3

Author(s):

Muhammad Naveed ◽

Muhamma Azam ◽

Nasrullah Khan ◽

Muhammad Aslam

Keyword(s):

Control Chart ◽

Control Charts ◽

Average Run Length ◽

Moving Average ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Application Data ◽

Mean And Variance ◽

The Mean ◽

Working Procedure

In the present paper, we propose a control chart based on extended exponentially weighted moving average (EEWMA) statistic to detect a quick shift in the mean. The mean and variance expression of the proposed EEWMA statistic are derived. The proposed EEWMA statistic is unbiased and simulation results show a smaller variance as compared to the traditional EWMA. The performance of the proposed control chart with the existing chart based on the EWMA statistic is evaluated in terms of average run length (ARL). Various tables were constructed for different values of parameters. The comparison of the EEWMA control chart with the traditional EWMA and Shewhart control charts illustrates that the proposed control chart performs better in terms of quick detection of the shift. The working procedure of the proposed control chart was also illustrated by simulated and application data.

Download Full-text

SHEWHART CHARTS FOR THE DETECTION OF LINEAR TRENDS AND OF SHIFTS IN AN AUTOREGRESSION MODEL

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539300000250 ◽

2000 ◽

Vol 07 (04) ◽

pp. 309-330 ◽

Cited By ~ 2

Author(s):

RAINER GÖB

Keyword(s):

Control Charts ◽

Linear Trend ◽

Average Run Length ◽

Model Parameters ◽

Adjustment Policy ◽

Shewhart Control Charts ◽

Shewhart Control ◽

Autoregression Model ◽

The Mean ◽

Biased Estimates

The paper considers a univariate characteristic of a manufacturing process which is measured at discrete time points. The characteristic exhibits a linear trend under an AR(1) disturbance. If the slope of the linear trend and the autoregression coefficient are known, the process characteristic can be adjusted to vary as white noise around its target. However, the adjustment policy is very sensitive to departures from model assumptions and fails to achieve its objective in case of shifted model parameters, e.g., in case of biased estimates or external assignable causes which change the parameters. A discussion of the behaviour of the adjusted process shows that parameter shifts can have harmful consequences. As a protection against parameter shifts, additional statistical monitoring of the process is indispensable. The paper introduces various Shewhart control charts for the detection of shifts in the mean, the trend parameter, or the autoregression parameter. The performance of the charts is analyzed by the average run length criterion.

Download Full-text

PERFORMANCE OF SENSITIZING RULES ON SHEWHART CONTROL CHARTS WITH AUTOCORRELATED DATA

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539301000438 ◽

2001 ◽

Vol 08 (02) ◽

pp. 159-171 ◽

Cited By ~ 3

Author(s):

SANDY D. BALKIN ◽

DENNIS K. J. LIN

Keyword(s):

Time Series ◽

Control Charts ◽

Moving Average ◽

Correlated Data ◽

Autoregressive Moving Average ◽

Shewhart Control Charts ◽

Shewhart Control ◽

The Mean ◽

Autocorrelated Data ◽

Using Data

Sensitizing Rules are commonly applied to Shewhart Charts to increase their effectiveness in detecting shifts in the mean that may otherwise go unnoticed by the usual "out-of-control" signals. The purpose of this paper is to demonstrate how well these rules actually perform when the data exhibit autocorrelation compared to non-correlated data. Since most control chart data are collected as time series, it is of interest to examine the performance of Shewhart's [Formula: see text] Chart using data generated from typical time series models. In this paper, measurements arising from autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) processes are examined using Shewhart Control Charts in conjunction with several sensitizing rules. The results indicate that the rules work well when there are strong autocorrelative relationships, but are not as effective in recognizing small to moderate levels of correlation. We conclude with the recommendation to practitioners that they use a more definitive measure of autocorrelation such as the Sample Autocorrelation Function correlogram to detect dependency.

Download Full-text