Process Capability Analysis in Minitab: Algorithms and Features

In the realm of quality control and process improvement, Process Capability Analysis is a cornerstone technique to evaluate whether a process can consistently meet customer requirements. Minitab, a leading statistical software, provides multiple algorithms and methodologies to execute this analysis effectively. This article explores various process capability analysis algorithms in Minitab, including the new and enhanced Automated Capability Analysis feature.

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Overview of Process Capability Analysis

Process Capability Analysis (PCA) is a crucial methodology in quality control and process improvement that allows businesses to assess their ability to consistently produce products that meet customer requirements. In manufacturing and service industries, it's essential to determine whether a process can produce output within specified limits. By comparing the spread of the process to the spread of the specifications, PCA helps identify whether a process is stable and capable of meeting desired quality levels.

This technique evaluates several important factors, such as the centering of the process and its variability, to determine how well the process performs in relation to established specifications. The core goal of PCA is to ensure that the process is consistent and capable of delivering products within acceptable quality standards, which can ultimately help improve customer satisfaction, reduce costs, and minimize defects.

There are several algorithms and approaches used in PCA, depending on the nature of the data being analyzed. The method chosen will depend on factors such as the distribution of data, the type of process being analyzed, and the level of precision required. In Minitab, a leading statistical software, you have access to a variety of tools designed for performing PCA efficiently and effectively, including the traditional normal capability analysis and the newer automated capability analysis feature.

The primary steps in performing a process capability analysis include:

  • Step 1: Data Collection: Gather data from the process, ensuring it's representative and accurate. This data typically includes measurements of product or process characteristics.
  • Step 2: Data Analysis: Assess the data to determine whether it follows a normal distribution or a non-normal distribution. This step may involve transforming data or selecting the appropriate model for analysis.
  • Step 3: Capability Indices Calculation: Compute key metrics like Cp, Cpk, Pp, and Ppk to determine the process's ability to meet specification limits.
  • Step 4: Interpretation of Results: Compare the calculated indices to industry standards or customer requirements to evaluate whether the process is capable of meeting expectations.

Overall, process capability analysis provides valuable insights into whether a process is well-designed and capable of meeting production goals. By performing PCA regularly, companies can ensure that their processes remain under control, identify potential areas for improvement, and make data-driven decisions for enhancing quality and efficiency.

In minitab as well as other software, there are many techniques that fit to different data / process characteristics, which is essential for accurate analysis of Process Capability. The following models are popular and well equipped in Minitab:

  • Normal Capability Analysis
  • Nonnormal Capability Analysis
  • Binomial Capability Analysis
  • Poisson Capability Analysis
  • Automated Capability Analysis (new feature)
  • Normal Capability Sixpack (to check data assumptions)

Algorithms for Process Capability Analysis in Minitab

Normal Capability Analysis

Purpose: Normal Capability Analysis evaluates a process's ability to produce output within specification limits, assuming that the data follows a normal distribution. This method is primarily used to assess the potential and overall capability of a process in meeting quality standards, ensuring that the process operates in a state of statistical control. It helps to identify whether the process can produce items consistently within the desired specification range, with minimal variation.

Key Metrics:

  • Cp (Process Capability Index): Measures the potential capability of a process. It compares the width of the process spread to the width of the specification limits. A Cp value greater than 1 indicates that the process has the potential to produce within specification limits.
  • Cpk (Process Capability Index, Adjusted for Centering): Similar to Cp, but accounts for how well the process is centered within the specification limits. If the process is not centered, Cpk will be less than Cp, indicating a lower capability.
  • Pp (Process Performance Index): Similar to Cp but considers the overall spread of the data, including potential shifts or drifts in the process over time.
  • Ppk (Process Performance Index, Adjusted for Centering): Like Cpk, this metric adjusts for process centering, but it uses actual performance data, accounting for any shifts or changes in the process.
  • Proportion of Nonconforming Products: The percentage of items produced outside the specification limits, providing an indication of overall quality.

Applications: Normal Capability Analysis is used when the process data is assumed to be normally distributed and in statistical control. This analysis is particularly useful in manufacturing environments where the process is stable, and the product characteristics follow a normal distribution, such as in processes that involve measurements like weight, length, or thickness of a product. It helps to assess whether the process is capable of producing goods consistently within customer specifications.

Real-Case Example: Consider a manufacturer of aluminum cans, where the process involves the measurement of the can's diameter. The company sets a specification limit for the diameter, which must be between 4.90 cm and 5.10 cm. Over a period, the company collects data on the diameter of cans produced from the process. After performing a normality test on the data, the results show that the diameter measurements follow a normal distribution.

Using Normal Capability Analysis, the company calculates the Cp and Cpk indices:

  • The Cp is 1.33, indicating that the process has the potential to produce within the specification limits. This suggests that, in theory, the process should be able to meet the customer requirements.
  • The Cpk is 1.10, which is slightly lower than the Cp, indicating that while the process is capable, it is not perfectly centered. This suggests that there is some room for improvement in process centering to reduce variation and improve product consistency.
By using these metrics, the company can assess whether they need to make adjustments in the process, such as fine-tuning the machinery or adjusting production conditions to improve centering and capability.

This example demonstrates how Normal Capability Analysis can be applied in real-world scenarios to assess and improve manufacturing processes, ensuring products consistently meet customer expectations while minimizing defects and variability.

Nonnormal Capability Analysis

Purpose: Nonnormal Capability Analysis is used when the process data does not follow a normal distribution, such as data that may follow distributions like Weibull, exponential, or lognormal. This analysis fits the most appropriate nonnormal distribution to the data to evaluate the process's capability. In cases where the data exhibits skewness, heavy tails, or other deviations from normality, nonnormal analysis provides more accurate insights into process performance.

Key Metrics:

  • Cp (Process Capability Index): Measures the potential capability of the process, adjusted for the selected nonnormal distribution. A Cp greater than 1 suggests that the process could meet specification limits under ideal conditions.
  • Cpk (Process Capability Index, Adjusted for Centering): Similar to Cp, but adjusts for process centering. A Cpk value closer to the Cp value indicates a well-centered process, while a large discrepancy suggests that the process may need adjustment.
  • Pp (Process Performance Index): Similar to Cp, but reflects the actual spread of the process data over time, considering natural variations and potential shifts.
  • Ppk (Process Performance Index, Adjusted for Centering): A measure of process performance that accounts for both the process spread and centering over time.
  • Proportion of Nonconforming Products: The percentage of products that fall outside the specification limits, adjusted for the nonnormal nature of the data.

Applications: Nonnormal Capability Analysis is ideal for processes where data distribution deviates significantly from normality. It is used when traditional normal distribution assumptions do not hold true, such as in processes dealing with failure rates, time to failure, or count data. It is particularly valuable in industries like healthcare, manufacturing, and service sectors, where the data may be more complex than what a normal distribution can capture.

Real-Case Example: A pharmaceutical company manufactures pills, and they are monitoring the time it takes for a drug to degrade under certain conditions. The degradation data is known to follow a Weibull distribution, as the degradation rate is more rapid at the start and slows over time. Using Nonnormal Capability Analysis, the company can assess whether their process meets the specifications for the drug's shelf life.

The company fits a Weibull distribution to the data and calculates the following:

  • Cp: 1.25, which suggests the process has the potential to meet the specification limits for degradation time, given ideal conditions.
  • Cpk: 1.00, indicating that the process is well-centered within the specification limits, but not perfectly centered.
  • Pp: 1.10, reflecting the overall variation in the process, including factors like machine wear and environmental influences.
  • Ppk: 0.95, which signals that there is some room for improvement in the process to reduce variability over time.
By using Nonnormal Capability Analysis, the company can adjust their production processes to ensure that the degradation of the drug remains consistent and within specifications, even when the data does not follow a normal distribution.

This real-world example highlights how Nonnormal Capability Analysis can be applied to processes with skewed or complex data distributions, offering a more accurate reflection of process performance and helping companies make informed decisions about improving quality and consistency.

Binomial Capability Analysis

Purpose: Binomial Capability Analysis is used to evaluate processes that involve binary outcomes, typically in situations where data can be classified as pass/fail, yes/no, or defective/non-defective. This analysis helps assess the ability of a process to produce units that meet quality standards, by determining the proportion of defective units or the probability of failure. The analysis is based on the binomial distribution, which is ideal for situations where each observation is independent and has only two possible outcomes.

Key Metrics:

  • Proportion Defective: The proportion of units that fail to meet the specified quality standards, usually represented as a percentage. A lower proportion defective indicates a more capable process.
  • Confidence Intervals: Confidence intervals provide a range of values within which the true proportion defective is likely to fall. This helps assess the reliability of the proportion defective estimate and account for variability in sample data.

Applications: Binomial Capability Analysis is commonly used in quality control scenarios where products or processes are evaluated based on binary attributes, such as pass/fail outcomes, defect/no defect, or on/off conditions. It is ideal for attribute data (non-measurement data), often seen in manufacturing, service industries, and inspection processes. This method is frequently applied to quality control tests, inspections, and audits where each item is either classified as "defective" or "non-defective."

Real-Case Example: A manufacturing company that produces electronic components, such as circuit boards, uses Binomial Capability Analysis to evaluate the proportion of boards that pass a quality inspection. Each board is inspected for a variety of potential defects (e.g., broken components, poor soldering) and classified as either pass or fail based on the inspection criteria. Over a sample of 500 boards, 25 are found to be defective. The company uses Binomial Capability Analysis to assess the process's ability to produce defect-free boards.

The analysis provides the following results:

  • Proportion Defective: 5% (25 defective boards out of 500 total boards inspected).
  • Confidence Interval: The 95% confidence interval for the true proportion defective is 3.5% to 6.5%. This means that, based on the sample data, the company is 95% confident that the true proportion of defective boards lies within this range.

By conducting Binomial Capability Analysis, the company can assess the effectiveness of their current manufacturing process. With a 5% defect rate, they can investigate potential causes of defects and determine whether the process is capable of meeting the desired quality standards. If the company's quality standard allows no more than 2% defective products, the company may decide to implement corrective actions, such as improving the soldering process or enhancing inspection protocols, to bring the defect rate within acceptable limits.

This example illustrates how Binomial Capability Analysis helps companies in quality control to evaluate their processes, identify issues, and make informed decisions to improve product quality and reduce defects.

Poisson Capability Analysis

Purpose: Poisson Capability Analysis is used to assess the capability of processes that generate count data, specifically for defects or events occurring per unit of measurement (such as defects per unit, errors per item, or failures per time period). This analysis assumes that the data follows a Poisson distribution, which is appropriate for rare or infrequent events occurring within a fixed time or space. It helps evaluate the process's ability to produce products or services with an acceptable level of defects or failures, making it especially useful in high-volume or repetitive manufacturing scenarios.

Key Metrics:

  • Defects per Unit (DPU): The average number of defects or failures occurring in each unit produced or processed. DPU gives insight into how frequently defects occur in the process, and a lower value indicates a more capable process.
  • Defects per Million Opportunities (DPMO): A metric used to evaluate the process capability by scaling defects to a million opportunities for defects to occur. DPMO is often used in high-volume manufacturing to provide a standard measure of defect rates, regardless of the volume produced.

Applications: Poisson Capability Analysis is commonly applied in high-volume manufacturing processes or service environments where the number of defects or failures is relatively low but significant in terms of quality impact. This includes industries such as electronics, automotive manufacturing, semiconductor production, and any process where defects are counted rather than measured on a continuous scale. The analysis is particularly helpful in defect monitoring, failure analysis, and reliability engineering, where understanding the frequency of defects is critical for quality control.

Real-Case Example: Consider a semiconductor manufacturing company that produces microchips. In this case, defects such as scratches, cracks, or other physical imperfections on the chips are counted. Each chip produced represents a unit, and the company tracks the number of defects observed on each unit. Over a sample of 10,000 chips, 50 defects are identified. The company wants to assess the capability of their manufacturing process to meet a standard of fewer than 5 defects per million opportunities.

The analysis provides the following results:

  • Defects per Unit (DPU): 50 defects / 10,000 chips = 0.005 defects per chip.
  • Defects per Million Opportunities (DPMO): (50 defects / 10,000 chips) * 1,000,000 = 5,000 DPMO.

With a DPMO of 5,000, the company can compare this result with industry benchmarks or customer specifications for acceptable defect rates. If their target is to maintain fewer than 1,000 DPMO, the company would recognize that their current process is not meeting the desired quality standards and would need to implement corrective actions, such as improving the handling process to prevent scratches or refining inspection techniques to detect defects earlier in the production cycle.

This example demonstrates how Poisson Capability Analysis helps manufacturers monitor the frequency of defects or failures in their processes. By calculating DPU and DPMO, companies can make data-driven decisions to improve their processes and maintain high levels of product quality, especially in high-volume production environments where defects, although rare, can have significant consequences on overall product quality.

Normal Capability Sixpack

Purpose: The Normal Capability Sixpack is a diagnostic tool used to verify whether process data meets the assumptions required for normal capability analysis. This tool is designed to check if the data follows a normal distribution before applying traditional capability analysis methods, such as Cp and Cpk. By ensuring the data meets the normality assumption, the Sixpack helps prevent misleading results from being used in decision-making. The tool evaluates aspects such as the shape of the distribution, skewness, and kurtosis, as well as performing normality tests to assess the appropriateness of applying normal capability analysis techniques.

Key Features:

  • Histogram and Normality Plot: Visualizes the distribution of the data, helping users identify if it appears approximately normal or deviates significantly (e.g., skewness or bimodal distribution).
  • Normality Tests: Conducts statistical tests (such as Anderson-Darling, Anderson-Darling for Exponential, or Ryan-Joiner) to assess whether the data fits a normal distribution.
  • Skewness and Kurtosis: Analyzes the skewness (asymmetry) and kurtosis (tailedness) of the data to detect deviations from normality. Large values may indicate the presence of outliers or nonnormality in the data.
  • Capability Indices: Provides initial estimates of Cp and Cpk, assuming normality, to determine if the process meets the required standards.

Applications: The Normal Capability Sixpack is primarily used as a diagnostic tool in quality control processes to detect potential issues in the data before proceeding with detailed capability analysis. It is especially helpful in identifying special cause variation or nonnormality in data that might lead to inaccurate or biased conclusions if normal capability analysis were applied without validation. The Sixpack is typically used during the initial stages of process improvement efforts, particularly when assessing manufacturing processes, product quality, and production consistency.

Real-Case Example: Imagine a company that produces plastic parts for automotive interiors. The company uses normal capability analysis to assess whether their injection molding process is capable of consistently producing parts within specified dimensions. However, before running the full capability analysis, they use the Normal Capability Sixpack to ensure the data is normally distributed. Upon reviewing the Sixpack results, the company notices the following:

  • The histogram shows a slight skew towards the higher end of the target specification, suggesting the data is not perfectly symmetrical.
  • The normality test (Anderson-Darling) fails, indicating that the data does not fit a normal distribution.
  • Skewness and kurtosis values exceed the acceptable range, further supporting the conclusion that the data is nonnormal.
Given these findings, the company decides to perform a Nonnormal Capability Analysis rather than a standard normal capability analysis. By using an appropriate analysis method for nonnormal data, they can more accurately assess their process capability, leading to more reliable decisions on potential process improvements. This scenario demonstrates how the Normal Capability Sixpack helps identify data issues early in the process and ensures that the most suitable analysis method is applied, ultimately leading to more accurate and actionable insights for process improvement.

Spotlight on Automated Capability Analysis (New Feature)

What is Automated Capability Analysis?

The Automated Capability Analysis feature in Minitab simplifies the selection of the most appropriate method to evaluate process capability. This innovative approach automatically evaluates your process data to determine:

  • Whether the data follow a normal distribution.
  • Whether a transformation is necessary to normalize the data.
  • The best-fitting distribution if the data are nonnormal.

Key Advantages

  • Ease of Use: No need for users to manually decide the best analysis approach. The algorithm automatically selects the most appropriate method.
  • Comprehensive Evaluation: Examines multiple distributions and transformations, providing results for the most suitable method.
  • Non-Parametric Options: If no satisfactory distribution or transformation is found, the algorithm defaults to non-parametric methods.
  • Detailed Insights: Provides both visual and statistical evaluations of data fit.

Key Metrics and Outputs

  • Distribution fit statistics.
  • Capability indices (Cp, Cpk, Pp, Ppk).
  • Non-parametric estimates for processes without a reliable distribution fit.
  • Proportion of nonconforming products.

Comparing Normal and Automated Capability Analysis

Feature Normal Capability Analysis Automated Capability Analysis
Data Assumptions Requires normally distributed data Automatically checks and adjusts
Distribution Selection Manual selection Automatic, based on fit
Transformation Support Available but not automated Fully automated
Best Use Case Known normal data Unknown or complex data

Hỏi và trả lời

  1. What is process capability?

    Process Capability Analysis is a method used to evaluate a process's ability to produce products within specification limits. It helps determine whether a process can consistently meet customer requirements.

  2. What is Normal Capability Analysis?

    Normal Capability Analysis evaluates the potential (within) and overall capability of a process assuming the data follows a normal distribution. This method uses metrics like Cp, Cpk, Pp, and Ppk to assess the process's ability and the proportion of nonconforming products.

  3. What are the applications of Normal Capability Analysis?

    Normal Capability Analysis is used when the process data follows a normal distribution and is in statistical control. It is particularly useful for stable manufacturing processes, such as in electronics, pharmaceuticals, or automotive production.

  4. How can you check data normality before performing Normal Capability Analysis?

    The Normal Capability Sixpack tool can be used to check data before performing Normal Capability Analysis. It examines factors like skewness, kurtosis, and conducts normality tests such as Anderson-Darling to determine whether the data fits a normal distribution.

  5. When should Nonnormal Capability Analysis be used?

    Nonnormal Capability Analysis should be used when data does not follow a normal distribution, such as data with a Weibull or exponential distribution. This method is used to assess process capability when the data distribution significantly deviates from normality.

  6. What are the applications of Poisson and Binomial Capability Analysis?

    Poisson Capability Analysis is used to assess the capability of processes with count data (e.g., defects per unit), while Binomial Capability Analysis evaluates the proportion of defective units in binary data (e.g., pass/fail). These methods are typically applied in high-volume manufacturing and quality control scenarios.

  7. To learn more about Lean Six Sigma and how it can improve performance and quality in your organization, join the program: Lean Six Sigma
  8. Which course should I take to understand Lean Six Sigma and process improvement better?

    There are many courses available in the market. Courses like Lean Six Sigma White Belt and Yellow Belt, following ISO18404 and ISO13053 standards, have international recognition.

    For more information:

Which Lean Six Sigma expert communities are available for businesses in Vietnam?

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