What is Process Capability (Normal Distribution)?
Process capability, in the context of a normal distribution, is a statistical measure that quantifies the ability of a process to consistently produce output within specified limits. It assesses how well a process meets the desired requirements or specifications.
The process capability is typically evaluated using two key parameters: the process mean and the process standard deviation. The process mean represents the center of the distribution, while the process standard deviation indicates the spread or variability of the data.
When to use Process Capability (Normal Distribution)?
Here are some scenarios where process capability analysis is commonly employed:
- Quality control: Process capability analysis is widely used in manufacturing industries to evaluate the capability of a production process to meet customer requirements. It helps identify whether the process is capable of producing products within the specified tolerances.
- Process improvement: Process capability analysis can be employed to identify areas for improvement in a process. By understanding the current capability of a process, organizations can target improvements to reduce variability and enhance the process's ability to meet customer needs.
- New product development: When introducing a new product or process, process capability analysis can provide insights into the process's performance and help determine if it meets the required specifications. It allows organizations to identify potential issues early on and make necessary adjustments before full-scale production.
- Supplier evaluation: Process capability analysis can be utilized to evaluate the capability of suppliers in meeting specified requirements. By assessing the capability of their processes, organizations can make informed decisions when selecting or evaluating suppliers.
- Six Sigma projects: Process capability analysis is an integral part of Six Sigma methodology. It helps measure the initial process capability, establish baseline performance, and assess the effectiveness of process improvement efforts.
Guidelines for correct usage of Process Capability (Normal Distribution)
- Ensure the data is continuous, representing measurements along a continuous scale.
- If working with attribute data, consider using Binomial Capability Analysis or Poisson Capability Analysis.
- Collect a sufficient amount of data (at least 100 total data points) to obtain reliable estimates of process capability.
- Collect data in rational subgroups that are representative of the process, with similar inputs and conditions.
- Ensure that the process is stable and in control before assessing its capability.
- Verify that the data follows a normal distribution for accurate capability estimates.
- If the data is non-normal, consider transforming it using options like Box-Cox or Johnson transformation.
- Use Individual Distribution Identification to determine data normality and the effectiveness of transformation.
- If data remains non-normal after transformation, consider Nonnormal Capability Analysis as an alternative.
Alternatives: When not to use Process Capability (Normal Distribution)
- If you do not know whether your process data are in control or whether they can be evaluated using a normal distribution, use Normal Capability Six pack to assess these assumptions before you use this analysis.
- If your data are non-normal and you want to evaluate process capability by fitting a non-normal distribution, rather than by transforming your data, use Non normal Capability Analysis.
- If you have attribute data, such as counts of defectives or defects, use Binomial Capability Analysis or Poisson Capability Analysis.
Example of Process Capability (Normal Distribution)?
In order to assess the process capability, quality engineers at an engine manufacturer utilize a forging process to produce piston rings. They collect 25 subgroups of five piston rings and measure their diameters. The specification limits for piston ring diameter are set at 74.0 mm ± 0.05 mm. The engineers opt for normal capability analysis to evaluate how the diameters of the piston rings compare to the specified limits. She has performed this in following steps:
- She worked all day and gathered the necessary data.
- Now, she analyzes the data with the help of https://qtools.zometric.com/
- Inside the tool, she feeds the data. Also, she puts lsl as 73.95, usl as 74.05, target as 74 and K as 6.
- After using the above mentioned tool, she fetches the output as follows:
How to do Process Capability (Normal Distribution)
The guide is as follows:
- Login in to QTools account with the help of https://qtools.zometric.com/
- On the home page, you can see Process Capability (Normal Distribution) under Process Capability.
- Click on Process Capability (Normal Distribution) and reach the dashboard.
- Next, update the data manually or can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
- Next, you need to fill the desired details such as lsl, usl, target, K, etc.
- Finally, click on calculate at the bottom of the page and you will get desired results.
On the dashboard of Process Capability (Normal Distribution), the window is separated into two parts.
On the left part, Data Pane is present. In the Data Pane, each row makes one subgroup. Data can be fed manually or the one can completely copy (Ctrl+C) the data from excel sheet and paste (Ctrl+V) it here.
On the right part, there are many options present as follows:
- Lsl: LSL in process capability refers to the Lower Specification Limit. It is the lower boundary or threshold set for a specific process parameter or characteristic. In process capability analysis, LSL is used to determine whether a process is capable of producing outputs within the desired range or specifications.
- Usl: USL in process capability refers to the Upper Specification Limit. It represents the upper boundary or threshold set for a specific process parameter or characteristic. During process capability analysis, the USL is used to assess whether a process is capable of producing outputs within the desired range or specifications.
- Target: In process capability, the target refers to the desired or ideal value for a specific process parameter or characteristic. It represents the value that the process is intended to achieve or center around. The target is often based on design specifications or customer requirements.
- Historical Mean: The historical mean in process capability refers to the average or central tendency of a process parameter or characteristic based on past or historical data. It represents the typical or expected value that the process has demonstrated over a period of time.
- Historical Standard Deviation: The historical standard deviation in process capability refers to the measure of the dispersion or variability of a process parameter or characteristic based on past or historical data. It quantifies how much the data points deviate from the historical mean or central tendency.
- K: In process capability, K refers to the process capability index known as the "Process Capability Index for Non-Centered Distribution" or simply the K-index. It is used to evaluate the capability of a process in relation to the specification limits.
- Within Stdev estimation method:
- Pooled: The pooled standard deviation estimation method, also known as the pooled variance method, is a statistical technique used to estimate the common standard deviation of two or more groups or populations when they are assumed to have the same underlying variance.
- Rbar: The "R-bar" standard deviation estimation method is used in process capability analysis when working with data collected in rational subgroups. It involves calculating the average range, denoted as R-bar, within each subgroup and using it as an estimate of the standard deviation of the process.
- Sbar: The "S-bar" standard deviation estimation method is another approach used in process capability analysis, particularly when working with data collected in rational subgroups. It involves calculating the average standard deviation, denoted as S-bar, within each subgroup and using it as an estimate of the overall standard deviation of the process.
- Within stdev estimation method for subgroup size = 1:
- Average Moving Range: It is calculated as the average of the absolute differences between consecutive observations within each subgroup.
- Median Moving Range: It is calculated as the median of the absolute differences between consecutive observations within each subgroup.
- Square root of MSSD: The MSSD is calculated by taking the squared difference between consecutive observations, averaging these squared differences, and then taking the square root of the resulting value.
- Moving range of length: In process capability analysis, the moving range (MR) refers to the absolute difference between consecutive observations within a subgroup or set of data. The "moving range of length" specifically refers to the calculation of the moving range when the data consists of lengths or measurements.
- Unbiasing Constant: The unbiasing constant, also known as the correction factor or bias correction factor, is a mathematical adjustment applied to the estimation of process capability indices to correct for potential bias in small sample sizes.