Adaptive EWMA Control Charts with a Time Varying Smoothing Parameter

It is known that time-weighted charts like EWMA or CUSUM are designed to be optimal to detect a specific shift. If they are designed to detect, for instance, a very small shift, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to circumvent this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper has as main goal to propose some adaptive EWMA control charts (AEWMA) based on the assessment of a potential misadjustment, which is translated into a time-varying smoothing parameter. The resulting control charts can be seen as a smooth combination between Shewhart and EWMA control charts that can be efficient for a wide range of shifts. Markov chain procedures are established to analyze and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals.Acknowledgements: financial support from the Spanish Ministry of Education and Science, research project ECO2012-38442

A Time Truncated Moving Average Chart for the Weibull Distribution

A control chart of monitoring the number of failures is proposed with a moving average scheme, when the life of an item follows a Weibull distribution. A specified number of items are put on a time truncated life test and the number of failures is observed. The proposed control chart has been evaluated by the average run lengths (ARLs) under different parameter settings. The control constant and the test time multiplier are to be determined by considering the in-control ARL. It is observed that the proposed control chart is more efficient in detecting a shift in the process as compared with the existing time truncated control chart. ? 2013 IEEE.11Ysciescopu

On Phase II Monitoring of the Probability Distributions of Univariate Continuous Processes

Statistical process control (SPC) charts are widely used in industry for monitoring the stability of certain sequential processes like manufacturing, health care systems etc. Most SPC charts assume that the parametric form of the “in-control” process distribution F1 is available. However, it has been demonstrated in the literature that their performances are unreliable when the pre-specified process distribution is incorrect. Moreover, most SPC charts are designed to detect any shift in mean and/or variance. In real world problems, shifts in higher moments can happen without much change in mean or variance. If we fail to detect those and let the process run, it can eventually become worse and a shift in mean or variance can creep in. Moreover, the special cause that initiated the shift can inflict further damage to the system, and it may become a financial challenge to fix it. This paper provides an efficient and easy-to-use control chart for Phase II monitoring of univariate continuous processes when the parametric form of the “in-control” process distribution is unknown, but Phase I observations that are believed to be i.i.d. realizations from unknown F1 are available. Data-driven practical guidelines are also provided to choose the tuning parameter and the corresponding control limit of the proposed SPC chart. Numerical simulations and a real-life data analysis show that it can be used in many practical applications

A Cumulative Summation Nonparametric Multiple Stream Process Control Chart Based on the Extended Median Test

In statistical process control applications, situations may arise in which several presumably identical processes or “streams” are desired to be simultaneously monitored. Such a monitoring scenario is commonly referred to as a “Multiple Stream Process (MSP).” Charts which have been designed to monitor an MSP typically monitor the means of the streams through collecting samples from each stream and calculating some function of the sample means. The resulting statistic is then iteratively compared to control limits to determine if a single stream or subset of streams may have shifted away from a specified target value. Traditional MSP charting techniques rely on the assumption of normality, which may or may not be met in practice. Thus, a cumulative summation nonparametric MSP control charting technique, based on a modification of the classical extended median test was developed and is referred to as the “Nonparametric Extended Median Test – Cumulative Summation (NEMT-CUSUM) chart.” The development of control limits and estimation of statistical power are given. Through simulation, the NEMT-CUSUM is shown to perform consistently in the presence of normal and non-normal data. Moreover, it is shown to perform more optimally than parametric alternatives in certain circumstances. Results suggest the NEMT-CUSUM may be an attractive alternative to existing parametric MSP monitoring techniques in the case when distributional assumptions about the underlying monitored process cannot reasonably be made