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Shewhart Control Charts in Phase I
Published in John Lawson, An Introduction to Acceptance Sampling and SPC with R, 2021
Notice that the control limits for the X¯ and R charts described in Section 6.2.3.1 of the online NIST Engineering Statistics Handbook (https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc321.htm)[1], and computed by the qcc function as shown in Figure 4.3, have no relationship with the specification limits described in Chapter 3. Specification limits are determined by a design engineer or another familiar with the customer needs (that may be the next process). The control limits for the control chart are calculated from observed data, and they show the limits of what the process is currently capable of. The Center (or X¯¯ ) and the StDev (or standard deviation) shown in the group of statistics at the bottom of the chart in Figure 4.5 are estimates of the current process average and standard deviation. Specification limits should never be added to the control charts because they will be misleading.
Green Productivity Tools and Techniques
Published in Guttila Yugantha Jayasinghe, Shehani Sharadha Maheepala, Prabuddhi Chathurika Wijekoon, Green Productivity and Cleaner Production, 2020
Guttila Yugantha Jayasinghe, Shehani Sharadha Maheepala, Prabuddhi Chathurika Wijekoon
A control chart is a graphical representation of a variable’s behavior over a period of time. To be considered as acting under normal conditions, the variable should behave within two set limit levels called the upper and lower limit (Tennant et al., 2007). If the variable’s behavior exceeds these limits, this signals an unusual condition and some issues will likely be identified. Control charts are used to identify issues in a process and monitor the effectiveness of an improvement in an organization. Further actions or improvements may be needed to eliminate the identified issues (Tennant et al., 2007). Control charts also facilitate the identification of critical parameters in a process that can lead to system failures. Thus, control charts can be considered the “pulse monitors” of an event that seek to mitigate failures. They can be applied to any parameter that needs to improve its efficiency or prevent problems from occurring.
Quality Management
Published in Susmita Bandyopadhyay, Production and Operations Analysis, 2019
As indicated in the above section, in order to improve quality, process improvement is essential. Process improvement can be accomplished through the application of control charts. A control chart is basically a statistical tool which can differentiate between a variation due to common causes and the variation due to special causes. Special causes are those causes which are not present in the process. The differences can be shown graphically by control charts. The basic objective of a process control chart is to bring process stability, which can be defined as the state of a process which shows certain level of consistency in the future, which was also shown in the past. In other words, a stable process shows consistency over time. The consistency is characterized by control limits based on ±3 of standard deviation. The basic objectives of control chart are shown below. Observe and monitor the process variations over timeDifferentiate between common cause and special cause (as mentioned above)Evaluate changesCommunicate the performance of the process under study
An adaptive exponentially weighted moving average control chart for poisson processes
Published in Quality Engineering, 2021
Aya A. Aly, Nesma A. Saleh, Mahmoud A. Mahmoud
A control chart is a statistical quality control tool that is used to monitor changes in the process parameters like the mean, variance or proportion of non-conformities. A chart statistic is computed from the sample data and plotted between the control limits of the chart, usually an upper control limit (UCL) and a lower control limit (LCL). The process is said to be in-control if the chart statistic is between the control limits and is said to be out-of-control if it is outside one of these limits (Montgomery 2009). Three of the commonly used charts in production and service industry are the Shewhart chart, the Exponentially Weighted Moving Average (EWMA) chart, and the Cumulative Sum (CUSUM) chart. Walter A. Shewhart introduced the Shewhart chart in the 1920s which is known to be efficient in detecting large shift sizes. Roberts (1959) introduced the EWMA chart and Page (1954) introduced the CUSUM chart; which are known to be efficient in detecting small and moderate shift sizes. Since all sizes of parameters' shifts – small, moderate, or large – have their effect on the process quality, attempts in literature were conducted to introduce control charts that monitor simultaneously different shift sizes. Double charting techniques – such as combined Shewhart and EWMA charts or combined Shewhart and CUSUM charts – were proposed. Also, adaptable charts were introduced such that the sampling parameters or design parameters are adapted during the run of the process to detect instantly the process change regardless of its size.
Monitoring schedule time using exponentially modified Gaussian distribution
Published in Quality Technology & Quantitative Management, 2020
Jehan Ara, Sajid Ali, Ismail Shah
A control chart is one of many statistical tools that can be used to aid in continuous process improvement as it monitors a process over time. Attribute and variable control charts are the two types of control charts, where the former are used to monitor the fraction of nonconformities of a process while later for variable data monitoring. The most commonly used attribute control charts like p and np, c and u are used when the number of defects follows the Bernoulli, the binomial or the Poisson distribution, respectively. Despite their wide-spread usage, the attributes charts have some drawbacks to monitor high yield data (Xie & Goh, 1997). In particular, the normal approximation is poor for high yield process where the defect rate is a part per million or even per billion. Although the normal approximation holds near the center of the distribution, the accuracy is very poor at the tails. Further, a downward shift in the process cannot be detected due to the negative lower control limit. The detection of a downward shift is very important as it shows process improvement. Similarly, for a low defect rate the upper control limit of the p and c charts are and < 1, respectively. As the number of defects is positive, each defect would be an out-of-control alarm. In short, the in- or out-of-control decision is a function of sample size, despite the magnitude of the defect rate.
A comparative study on Poisson control charts
Published in Quality Technology & Quantitative Management, 2020
Vasileios Alevizakos, Christos Koukouvinos
Statistical process control (SPC) is a useful tool of the statistical quality control (SQC) which employs statistical methods to monitor and control the quality of industrial processes. Control charts are a very powerful tool of the SPC and are used to monitor the parameters of a process. Shewhart control charts are the most popular control charts, as they are very user-friendly. There are two main types of control charts: (i) the control charts for measurement data and (ii) the control charts for attribute data, such as the number of nonconformities or the number of defective products in a production unit. The most well-known Shewhart control charts for attribute data are the -chart and the -chart for binomial-distributed data and the -chart and the -chart for Poisson distributed data (Montgomery, 2013). Unfortunately, the Shewhart -chart is very insensitive to detect small process shifts (say, ) and under certain circumstances, it cannot detect a downward process shift.