What is Machine Capability (Normal Distribution)?
Machine capability, when discussed in the context of a normal distribution, typically refers to the ability of a machine or system to produce output or measurements that follow a normal or Gaussian distribution. The normal distribution, also known as the bell curve, is a statistical distribution characterized by its symmetric shape and specific properties.
In the context of machine capability, it implies that the machine's output or measurements are expected to exhibit a normal distribution with a specific mean (average) and standard deviation (measure of dispersion). This assumption of normality is often made in statistical process control and quality control to assess the performance and consistency of a machine or process.
When to use Machine Capability (Normal Distribution)?
Here are some situations where machine capability analysis using the normal distribution is typically employed:
- Quality control: Machine capability analysis is used to assess the capability of a manufacturing process to produce products that meet predefined quality standards. By analyzing the distribution of measurements, such as product dimensions or weights, against the desired specifications, it can be determined if the process is capable of consistently meeting those specifications.
- Process improvement: If a manufacturing process is found to be incapable of consistently producing products within the desired specifications, machine capability analysis can help identify areas for improvement. By analyzing the distribution of measurements and identifying sources of variability, steps can be taken to reduce process variation and increase capability.
- Setting tolerances: Machine capability analysis aids in setting appropriate tolerance limits for product specifications. By understanding the variation in the process, organizations can set realistic and achievable tolerances that balance quality requirements with production feasibility.
- Six Sigma projects: Machine capability analysis is often used as part of Six Sigma projects, which aim to improve the quality and efficiency of a process. It helps in identifying areas of improvement, defining process performance goals, and measuring the effectiveness of process improvements.
- Supplier evaluation: Machine capability analysis can be used to evaluate and compare the capabilities of different suppliers. By analyzing the distribution of measurements from different suppliers' processes, organizations can make informed decisions about supplier selection based on their ability to consistently meet quality requirements.
Guidelines for correct usage of Machine Capability (Normal Distribution)
- Understand the normal distribution: Familiarize yourself with the properties and characteristics of the normal distribution. It is a symmetric probability distribution that is defined by its mean and standard deviation. Understanding concepts like the 68-95-99.7 rule and the empirical rule will help you interpret results accurately.
- Choose appropriate parameters: When generating random numbers from a normal distribution, determine the desired mean and standard deviation that align with your problem domain or data. Ensure that these parameters accurately represent the distribution you are modeling.
- Validate data suitability: Before applying any analysis or modeling techniques based on the normal distribution, validate whether your data reasonably follows a normal distribution. You can utilize statistical tests like the Shapiro-Wilk test or visual methods like histograms or Q-Q plots.
- Central Limit Theorem: Remember that the Central Limit Theorem states that the sum or average of a large number of independent and identically distributed random variables will be approximately normally distributed, regardless of the underlying distribution. This theorem is relevant when dealing with sample means or sums.
- Sample size considerations: If you are working with small sample sizes, be cautious about relying too heavily on assumptions of normality. Small samples might not exhibit the expected properties of a normal distribution, and alternative methods may be more appropriate.
- Statistical inference: When performing hypothesis tests or constructing confidence intervals using the normal distribution, ensure that the assumptions are met. These assumptions may include independence, normality, and homogeneity of variances.
- Robust alternatives: If your data violates the assumptions of normality or if you're concerned about outliers, consider using robust statistical methods or non-parametric tests that do not rely on the normal distribution.
- Interpretation: Understand the implications of using the normal distribution in your analysis. For instance, when constructing confidence intervals, interpret them correctly as a range within which the true parameter is likely to fall, rather than as definitive bounds.
- Consult domain experts: If you are unsure about the appropriateness of using the normal distribution or need assistance with specific applications, consult with experts in the field, such as statisticians or data scientists.
Alternatives: When not to use Machine Capability (Normal Distribution)
- Six Sigma - If you are dealing with a process that exhibits significant variations, defects, or quality issues, Six Sigma can be a suitable approach. By applying Six Sigma methodologies, you can identify and address the root causes of the problems, reducing defects and improving overall process performance.
- Design of Experiments (DoE) - In cases where conducting physical experiments is necessary (e.g., testing the performance of a new material or prototype), DOE helps in efficiently exploring the parameter space and reducing the number of required experiments. This saves time and resources compared to conducting exhaustive testing.
Example of Machine Capability (Normal Distribution)?
In order to assess the Machine capability, quality engineers at an engine manufacturer utilize a forging Machine 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 and K as 6.
- After using the above mentioned tool, she fetches the output as follows:
How to do Machine 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 Machine Capability (Normal Distribution) under Process Capability.
- Click on Machine 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 put the values of lsl, usl and K.
- Finally, click on calculate at the bottom of the page and you will get desired results.
On the dashboard of Machine 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 Machine capability refers to the Lower Specification Limit. It is the lower boundary or threshold set for a specific parameter or characteristic. In Machine capability analysis, LSL is used to determine whether a Machine is capable of producing outputs within the desired range or specifications.
- Usl: USL in Machine capability refers to the Upper Specification Limit. It represents the upper boundary or threshold set for a specific parameter or characteristic. During Machine capability analysis, the USL is used to assess whether a Machine is capable of producing outputs within the desired range or specifications.
- K: In Machine capability, K is used to evaluate the capability of a process in relation to the specification limits.