Sample size is an important factor in statistical process control (SPC), which is a method of monitoring and improving the quality of a process. Choosing the right sample size can affect the accuracy, reliability, and cost of your SPC charts and analysis. In this article, you will learn some of the best ways to determine sample sizes in SPC, based on different criteria and scenarios.
The sample size is the number of units or observations that you collect from a process to calculate a statistic, such as the mean, standard deviation, or range. The sample size affects the variability and precision of your statistic, and therefore the sensitivity and stability of your SPC charts. A larger sample size can reduce the sampling error and the width of the control limits, making it easier to detect shifts or changes in the process. However, a larger sample size also means more time, effort, and resources spent on data collection and analysis. Therefore, you need to balance the benefits and costs of increasing the sample size, and choose the optimal one for your SPC objectives and constraints.
It is not possible to correctly assess the impact of sample sizes on your SPC and experiments without having extended knowledge of statistical theory and sampling. Particularly for sensitive applications where fine grained effect measurement is vital, without knowing sampling techniques, distributions, assumptions etc incorrect conclusions might be drawn.
Here are major methods: 1. Central Limit Theorem: CLT can detect if process data is normally distributed. Smaller samples can work if so. 2. Margin of Error: A smaller MOE needs a larger sample to be precise. 3. Confidence: Higher confidence requires larger samples to reduce ambiguity. 4. Process variability: Larger samples may be needed to capture the true mean and detect changes with high variability. 5. Effect Size: Detecting smaller effect sizes may require larger samples. 6. Resource constraints: Smaller samples save resources but reduce precision. 7. Continuous Monitoring: It may allow you to use smaller samples more often to adjust to changing conditions. 8. Analyse historical data to assess process variability and guide sample size.
Determining the sample size in SPC can be done through formulas that are based on statistical theory and assumptions. These formulas can help you estimate the sample size needed to reach a specific level of confidence, precision, or power in your SPC charts and analysis. For example, if you want to use an X-bar and R chart to monitor the mean and range of a process, the formula n = (Zα/2 * σ / E)^2 can be used to calculate the sample size, where n is the sample size, Zα/2 is the critical value for a given confidence level, σ is the standard deviation of the process, and E is the margin of error or the maximum allowable difference between the sample mean and the true mean. However, utilizing formulas can have some limitations and challenges such as not knowing values of parameters such as σ and having to estimate them from historical or pilot data which can introduce uncertainty and bias. Furthermore, assumptions may need to be made about the distribution and behavior of the process which may not hold true in reality. Additionally, adjustments may need to be made for different types of SPC charts and statistics such as attribute charts or non-normal data. Other factors that can affect sample size such as frequency of sampling, subgroup size, process stability, and type of variation must also be taken into account.
Blind folded usage of sample size formulas can be more dangerous than you might guess. I have seen several serious failures just due to this. So, make sure to check distributions of mean samples etc before using a simple z-test formula. And always aspire to understand the statistical logic behind sample and effect size.
Another way to determine the sample size in SPC is to use tables derived from formulas and simulations. These tables provide recommended sample sizes for different types of SPC charts and statistics, based on criteria and scenarios such as a P chart with a 95% confidence level and a 10% margin of error. Using tables can have its benefits, such as saving time and effort, as well as being able to compare different sample sizes for different scenarios. However, there are some drawbacks, such as not finding a table that matches your exact situation or having to rely on the source and quality of the table. Therefore, it is important to check if the table is based on sound and updated statistical methods and data.
Using statistical formulas and simulation tables is pragmatic. Based on confidence levels and margins of error, these tables suggest SPC chart and statistical measure sample sizes. Tables speed up sample size determination, making it easier for practitioners. They also enable scenario-wide sample size comparison for informed decision-making. However, this method has drawbacks. Table accuracy depends on statistical methods and data sources, which may not match your context. SPC sample size determination tables should be based on solid statistical principles and updated with the latest data. Tables make generalised recommendations, so statistical rigour must be balanced with practicality and quality control goals.
A third way to determine the sample size in SPC is to use software that can perform the calculations and simulations for you. There are many software tools and applications available that can help estimate the sample size for different types of SPC charts and statistics, based on various criteria and scenarios. For example, if you want to use a CUSUM chart to monitor the cumulative sum of deviations from a target value in a process, you can input the parameters into such a software and get the sample size. This software assumes that you want to have a 5% false alarm rate and a 90% detection rate in your CUSUM chart.
Using software for sample size determination has both benefits and drawbacks. It can automate and simplify the process, as well as customize and modify the parameters for specific SPC needs. However, it may require some training and expertise to learn how to use the software, as well as paying for it or subscribing to it. Additionally, you must ensure its compatibility and security with your data and system.
Utilising software to determine sample sizes in SPC provides numerous benefits. It automates complex calculations and simulations, thereby streamlining the estimation of sample size. It is essential to consider the following factors. First, acquiring proficiency with the software may require training and knowledge, but the investment is well worth it due to the increased efficiency. Second, there may be costs associated with purchasing or subscribing to the software, but the benefits in terms of time saved and accuracy typically outweigh these costs. Lastly, it is essential to ensure that the selected software is compatible with your data and system and that data security is maintained.
Consider putting everything regarding the statistical experimentations and SPC in a DevOps like structure through the projects, robust and reactive to dynamical landscape of statistics. I call it StatOps.