Phase II control charts for monitoring dispersion when parameters are estimated

Shewhart control charts are among the most popular control charts used to monitor process dispersion. To base these control charts on the assumption of known in-control process parameters is often unrealistic. In practice, estimates are used to construct the control charts and this has substantial consequences for the in-control and out-of-control chart performance. The effects are especially severe when the number of Phase I subgroups used to estimate the unknown process dispersion is small. Typically, recommendations are to use around 30 subgroups of size 5 each.

?We derive and tabulate new corrected charting constants that should be used to construct the estimated probability limits of the Phase II Shewhart dispersion (e.g., range and standard deviation) control charts for a given number of Phase I subgroups, subgroup size and nominal in-control average run-length (ICARL). These control limits account for the effects of parameter estimation. Two approaches are used to find the new charting constants, a numerical and an analytic approach, which give similar results. It is seen that the corrected probability limits based charts achieve the desired nominal ICARL performance, but the out-of-control average run-length performance deteriorate when both the size of the shift and the number of Phase I subgroups are small. This is the price one must pay while accounting for the effects of parameter estimation so that the in-control performance is as advertised. An illustration using real-life data is provided along with a summary and recommendations.     

Adaptive cumulative sum charts with the adaptive runs rule

Adaptive cumulative sum (ACUSUM) charts, which adjust the reference value dynamically based on estimated shift size, provide good performance in detecting a range of mean shifts. However, when the range is wide, ACUSUM may not perform well for small shifts over the range. An adaptive runs rule, which is motivated by the concept of supplementary runs rule, is proposed, in order to make control charts more sensitive to small mean shifts. The adaptive runs rule assigns scores to consecutive runs based on the estimated shift size of the mean. The ACUSUM chart is supplemented with the adaptive runs rule to enhance its sensitivity in detecting small mean shifts. The average run length performance of the ACUSUM chart with the adaptive runs rule is compared with those of cumulative sum and variants of adaptive charts including ACUSUM. The experimental results reveal that the ACUSUM chart with the adaptive runs rule achieves superior detection performance over a wide range of mean shifts.     

Directed control charts for detecting the shape changes from linear profiles to quadratic profiles

In profile monitoring, control charts are constructed to detect any unanticipated departures from the statistical stability of product quality over time, where product quality is characterised by a function. In many situations, due to the characteristics of a system or an operation, certain process signals can be anticipated. Thus, when a kind of departure specifically feared is identified in advance, a directed process monitoring approach can be developed. Motivated by the monitoring of cylindrical surfaces, this paper focuses on quickly detecting the shape changes from a straight line to a second-order polynomial curve. Based on the hypothesis testing on the quadratic term, two directed control charts and a combined scheme are proposed to surveillance the sampled linear shape. The performance of our proposed methods is studied and compared with the alternative charts by numerical simulations. Simulation studies show that the two proposed directed charts are almost the same, and outperform the alternative methods in some cases. Moreover, the combined scheme is robust for all the parameter combinations.     

Detecting multiple special causes from multivariate data with applications to fault detection in manufacturing

Several articles in the recent literature propose linear models of product quality for both single station and multistation manufacturing processes. We show how these models may be used in conjunction with statistical methods to design a procedure for multivariate Statistical Process Control (SPC) that outperforms direct application of multivariate SPC. We show how to design the procedure and evaluate its performance in shift detection for models with and without singularities. The use of the procedure is illustrated using two examples from automobile body assembly.     

Statistically constrained economic design of the multivariate exponentially weighted moving average control chart

This paper shows that economic statistical design can provide for better statistical properties without significantly increasing optimal total costs. Cost comparisons between optimal economic statistical designs and optimal economic designs show no significant cost increases. The average run length (ARL) constraints added by economic statistical design significantly improve the statistical properties of the control chart scheme. False alarm frequency is limited while keeping good shift detection characteristics. In addition, the Multivariate Exponentially Weighted Moving Average (MEWMA) control schemes performed better from the cost standpoint than the benchmark pure statistical design—the Hotelling T² control chart. This improvement held for unconstrained and constrained designs. Finally, cost comparisons at small values of n showed significant advantage for the MEWMA schemes. Copyright © 2001 John Wiley & Sons, Ltd.     

过程能力指数与不合格品率的关系模型

传统Shewhart-p控制图只对单一属性的不合格品率进行监控,在过程发生偏移时有一定的滞后性。为提高不合格品率控制图的精度,提出一种多元指数加权移动平均不合格品率 (multivariate exponentially weighted moving average p, MEWMA-p)控制图。该控制图将多个属性的不合格品率应用于多元指数加权移动平均控制图,可同时对多个属性进行监控,并且对于小范围的偏移更加敏感。对比分析同等偏移程度下指数加权移动平均不合格品率 (exponentially weighted moving average p, EWMA-p) 控制图与MEWMA-p控制图的平均运行长度 (average run length, ARL) 结果,并通过模拟仿真说明该方法的有效性。

     

Improving the performance of the multivariate exponentially weighted moving average control chart

Multivariate statistical process control (SPC) procedures are useful in cases where several process variables are monitored simultaneously. A significant disadvantage of these techniques is that the time required to detect a process shift increases with the number of variables being monitored. We show how the shift detection capability of one popular multivariate SPC scheme, the multivariate analogue of the exponentially weighted moving average control chart, can be significantly improved by transforming the original process variables to a lower‐dimensional subspace through the use of a U‐transformation. Copyright © 1999 John Wiley & Sons, Ltd.     

监控不合格品率的MEWMA-p控制图设计

传统Shewhart-p控制图只对单一属性的不合格品率进行监控,在过程发生偏移时有一定的滞后性。为提高不合格品率控制图的精度,提出一种多元指数加权移动平均不合格品率(multivariate exponentially weighted moving average p, MEWMA-p)控制图。该控制图将多个属性的不合格品率应用于多元指数加权移动平均控制图,可同时对多个属性进行监控,并且对于小范围的偏移更加敏感。对比分析同等偏移程度下指数加权移动平均不合格品率(exponentially weighted moving average p, EWMA-p)控制图与MEWMA-p控制图的平均运行长度(average run length,ARL)结果,并通过模拟仿真说明该方法的有效性。