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Making the DMAIC Model More Lean and Agile: Measure
Published in Terra Vanzant Stern, Lean and Agile Project Management, 2017
A process is capable if it falls within the specification limits. Graphically, the process capability is accomplished by plotting the process specification limits on a histogram or control chart. If the histogram data falls within the specification limits, then the process is capable. Often manufacturing environments prefer to use Cp. Traditionally, if Cp is measured at 1 or higher, the index is indicating that the process is capable. In manufacturing, the number often needs to be at 1.33, which is the same as 4 sigma. The number 2 in the index represents 6 sigma. The process capability index, or Cpk, measures a process’s ability to create a product within the specification limits.
Leaner and More Agile: Measure
Published in Terra Vanzant Stern, Lean and Agile Project Management, 2020
A process is capable if it falls within the specification limits. Graphically, the process capability is accomplished by plotting the process specification limits on a histogram or control chart. If the histogram data fall within the specification limits, then the process is capable. Often manufacturing environments prefer to use Cp. Traditionally, if Cp is measured at 1 or higher, the index is indicating that the process is capable. In manufacturing, the number often needs to be at 1.33, which is the same as 4 sigma. The number 2 in the index represents 6 sigma. The process capability index, or Cpk, measures a process’s ability to create a product within the specification limits.
Economic quality design under model uncertainty in micro-drilling manufacturing process
Published in International Journal of Production Research, 2022
Yunxia Han, Yiliu Tu, Linhan Ouyang, Jianjun Wang, Yizhong Ma
In this paper, we assume the design variables follow normal distribution and process capability index is 1. An anonymous suggests that we should justify these assumptions. To verify whether the design variables follow the normal distribution, we use normal probability graph and Lilliefors method to examine the normality of design variables. The design variables can be generated by Monte Carlo simulation according to the optimal settings of parameters and tolerances in the micro-drilling process. We apply normplot from the Matlab Statistics Toolbox to draw the normal probability plot of the design variables. Figure 5 shows the normal probability plot of x1, x2, and x3. Intuitively, the probability value of the design variable sample in Figure 5 is a straight line or close to a straight line. Besides, to more accurately determine the distribution type of design variables, we use the function lillietest in Matlab to validate whether the design variables obey a normal distribution. The results show that P values of the test are 0.2550, 0.5000, and 0.1383, respectively, which disclose that the design variables follow a normal distribution. It is consistent with our research hypothesis.
An improved multiple quality characteristic analysis chart for simultaneous monitoring of process mean and variance of steering knuckle pin for green manufacturing
Published in Quality Engineering, 2021
Two process parameters (process mean μ and process standard deviation σ) are commonly used to quantify the performance of manufacturing processes. In process improvement efforts, the process must be in control statistically; i.e., process mean μ must be sufficiently close to process target value T with minimum variation. However, application of the process mean μ and process standard deviation σ only to monitor and control the manufacturing process is not enough. The process must meet the quality levels specified by customers. Process capability index (PCI) is considered a practical measurement tool for the monitoring of specification limits, as well as process mean μ and process standard deviation σ. It provides sufficient and useful information to both the manufacturer and the customer to determine whether the product quality conforms to a specified tolerance range. Moreover, the PCIs have a mathematical relationship with quality yield: a smaller PCI value implies lower process yield and poor product quality (Hsu, Chen, and Yang 2016; Wu, Pearn, and Kotz 2009). As a result, quality manager need only track and improve the value of the PCI to reduce faulty products, waste, rework, and operating and quality costs (Balamurali and Usha 2017). In recent years, many researchers have conducted studies focused on PCIs (see, for example, Weusten and Tummers 2017; Wu et al. 2017; Lee, Wu, and Wang 2018; Otsuka and Nagata 2018, Ganji and Gildeh 2019; Koukouvinos and Lappa 2019). In addition to the papers above, the works of Kotz and Johnson (1993), Kotz and Lovelace (1998), and Pearn and Kotz (2006) provide a complete introduction to the history of PCIs.
A pairwise comparison-based interactive procedure for the process capability approach to multiple-response surface optimization
Published in Engineering Optimization, 2020
The process capability approach first estimates the mean and standard deviation models of a response, which are treated as separate responses. Then, it derives a functionally formed process capability index from the estimated mean and standard deviation models for each response. The overall process capability function is obtained by combining the individual process capability functions. The optimal setting is determined by maximizing the overall process capability function. This approach is comparable to the dual-response surface optimization (DRSO) approach in the sense that it considers the mean and standard deviation of a response simultaneously.