Capability Control Charts Research Articles

Process Capability Control Charts for Monitoring Process Accuracy and Precision

Process capability index (PCI) is a convenient and useful tool of process quality evaluation that allows a company to have a complete picture of its manufacturing process in order to prevent defective products while ensuring the product quality is at the required level. The aim of this study was to develop a control chart for process incapability index , which differentiates between information related to accuracy and precision. Index measures process inaccuracy as the degree to which the mean departs from the target value, while index measures imprecision in terms of process variation. The most important advantage of using these control charts of , , and is that practitioners can monitor and evaluate both the quality of the process and the differences in process capability. The and charts were instead of Shewhart’s and chart since the process target values and tolerances can be incorporated in the charts for evaluation as a whole, which makes the charts capable of monitoring process stability and quality simultaneously. The proposed , , and control charts enable practitioners to monitor and evaluate process quality as well as differences in process capability. The control charts are defined using probability limits, and operating characteristic (OC) curves used to detect shifts in process quality. The method proposed in this study can easily and accurately determine the process quality capability and a case is used to illustrate the application of control charts of , , and .

Process capability monitoring and change-point analysis for S-type quality characteristic

ABSTRACT Among various quality assurance activities, process capability indices (PCIs) are recognized as the most effective tools to quantify and evaluate process performance. The one-sided capability index can adequately measure the process capability for processes with a smaller-is-better (S-type) quality characteristic. While focusing on the index , this study constructs a capability control chart to monitor the short-term capability based on the exponentially weighted moving average (EWMA). Simulations have shown that the EWMA capability control chart is adaptive regarding average run length. Further, this study applies change-point analysis to determine whether and when the short-term capability-level changes. Using these two proposed methods, engineers can realize a variety of short-term process capabilities in good time and implement control measures efficiently against a poor long-term process capability.

Exact expression for the expectation of estimated Cpk based on control chart information and the corresponding process capability control charts

ABSTRACTAmong all the process capability indices, is the most popular among the practitioners, when the underlying quality characteristic follow normal distribution. Due to its complicated expression, properties of its plug-in estimator have been of particular interest to several researchers both from classical and Bayesian statistical arena. In the present article, we have proposed plug-in estimators of based on the and chart information under the assumption that each of the samples are drawn independently. We have also derived the expressions for expected values of these estimators and the associated bias. These estimators are found to work similar to the Bayesian-like estimators without depending upon any historical information. The corresponding process capability control charts have also been designed to enable continuous assessment of a process. Finally, a simulated example and two real-life examples have been discussed to supplement the theory developed in this article.

Process capability control chart for non-normal data – evidence of on-going capability assessment

Process capability indices are widely used for various quality assurance activities in many high-tech industries. By a suitable analysis of an index, a production department can trace and improve a poor process to enhance the quality level and satisfy customer requirements. Recently, some practical process capability control charts were developed for illustrating the continuous assessments of normal process capability. These charts contain information regarding the ability of the process to meet or exceed customer requirement over the life of a process. Monitoring the behaviour of the process’s ability to meet customer requirement can provide managers with feedback and evidence of the process’s ability in terms they understand. However, process distribution is often ab normal. Therefore, this study incorporates bootstrap procedure to construct capability control chart for non-normal processes. The simulations show that the empirical coverage probability of this chart is close to the desired coverage probability as the number of subgroup is large enough.

Some process capability indices for unilateral specification limits—Their properties and the process capability control charts

ABSTRACTProcesses with smaller the better and larger the better types of quality characteristics and consequently the unilateral specification limits are very common in manufacturing industries. However, very little theoretical resources are available in literature, compared to the bilateral specification limits, for assessing the capability of such processes. In the present article, we have studied the expressions for the threshold value and relationship with proportion of non conformance for some of the process capability indices (PCIs) for unilateral specification limits. We have also explored the distributional aspects along with the uniformly minimum variance unbiased estimators of those PCIs based on both single-sample information as well as the information obtained from the corresponding and control charts. The process capability control charts for these PCIs have been designed as well for the purpose of the continuous assessment of the capability of a process over the entire production cycle. Finally, a numerical example has been discussed in the context of the theory developed in this article.

Distributions and Process Capability Control Charts for CPU and CPL Using Subgroup Information

Process capability analysis is a very well-known and widely accepted method of assessing the ability of a process to produce items within pre-assigned specification limits. Most of the process capability indices (PCI) available in literature are formulated in terms of the parameters of the concerned quality characteristics. However, since the actual values of these parameters are often unknown, their estimated values are used to evaluate the estimated capability of a process. One such estimation procedure may be to use the estimates of these parameters obtained from the corresponding control charts used to check the stability of the said process. In this article, we used this approach to redefine plug-in (natural) estimators of the two most famous PCI’s for unilateral specification limits viz., CPU and CPL. We formulated the corresponding unbiased estimators and uniformly minimum variance unbiased estimators (UMVUE), wherever possible, and their distributions as well. We also designed the process capability control charts of CPU and CPL based on these UMVUEs. For constructing these control charts, we used the estimators of the parameters of the quality characteristics as obtained from the corresponding and charts. These charts can be used to check the consistency of capability of a process and also to keep a constant vigil on the process. Two numerical examples have been discussed and it has been observed that our proposed process capability control charts are more efficient to detect changes in process capability than those already available in literature.

Effective Control Chart for Monitoring the Stability of Non-normal Process Capability

Quality has been shown as the major criterion in many supplier selection studies. Among various quality assurance activities, process capability indices are widely used to quantify the relationship between the actual process performance and specification limits in many high-tech industries. By a suitable analysis of an index, a production department can trace and improve a poor process to enhance the quality level and satisfy customer requirements. Recently, some practical process capability control charts were developed for illustrating the continuous assessments of process capability. These charts contain information regarding the ability of the process to meet or exceed customer requirement over the life of a process. However, the process distribution is often ab-normal. Therefore, this study integrates the bootstrap procedure to construct a capability control chart for non-normal processes. The simulations show that the empirical coverage probability of our proposed chart is close to the desired coverage probability as the size of subgroup is large enough.

A simple algorithm for calculating values for folded normal distribution

Folded normal distribution originates from the modulus of normal distribution. In the present article, we have formulated the cumulative distribution function (cdf) of a folded normal distribution in terms of standard normal cdf and the parameters of the mother normal distribution. Although cdf values of folded normal distribution were earlier tabulated in the literature, we have shown that those values are valid for very particular situations. We have also provided a simple approach to obtain values of the parameters of the mother normal distribution from those of the folded normal distribution. These results find ample application in practice, for example, in obtaining the so-called upper and lower α-points of folded normal distribution, which, in turn, is useful in testing of the hypothesis relating to folded normal distribution and in designing process capability control chart of some process capability indices. A thorough study has been made to compare the performance of the newly developed theory to the existing ones. Some simulated as well as real-life examples have been discussed to supplement the theory developed in this article. Codes (generated by R software) for the theory developed in this article are also presented for the ease of application.