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6 Steps of Machine learning Lifecycle Introduction to Predictive Modeling
Introduction to Exploratory Data Analysis & Data Insights Descriptive Statistics Inferential Statistics How to Understand Population Distributions?
Reading Data Files into Python Different Variable Datatypes
Probability for Data Science Basic Concepts of Probability Axioms of Probability Conditional Probability
Central Tendencies for Continuous Variables Spread of Data KDE plots for Continuous Variable Overview of Distribution for Continuous variables Normal Distribution Skewed Distribution Skeweness and Kurtosis Distribution for Continuous Variable
Central Tendencies for Categorical Variables Understanding Discrete Distributions Performing EDA on Categorical Variables
Dealing with Missing Values Understanding Outliers Identifying Outliers in Data Outlier Detection in Python Outliers Detection Using IQR, Z-score, LOF and DBSCAN
Sample and Population Central Limit Theorem Confidence Interval and Margin of Error
Bivariate Analysis Introduction
Covariance Pearson Correlation Spearman's Correlation & Kendall's Tau Correlation versus Causation Tabular and Graphical methods for Bivariate Analysis Performing Bivariate Analysis on Continuous-Continuous Variables
Tabular and Graphical methods for Continuous-Categorical Variables Introduction to Hypothesis Testing P-value Two sample Z-test T-test T-test vs Z-test Performing Bivariate Analysis on Continuous-Catagorical variables
Chi-Squares Test Bivariate Analysis on Categorical Categorical Variables
Multivariate Analysis A Comprehensive Guide to Data Exploration The Data Science behind IPL
Supervised Learning vs Unsupervised Learning Reinforcement Learning Generative and Descriminative Models Parametric and Non Parametric model
Machine Learning Pipeline Preparing Dataset Build a Benchmark Model: Regression Build a Benchmark Model: Classification
Evaluation Metrics for Machine Learning Everyone should know Confusion Matrix Accuracy Precision and Recall AUC-ROC Log Loss R2 and Adjusted R2
Dealing with Missing Values Replacing Missing Values Imputing Missing Values in Data Working with Categorical Variables Working with Outliers Preprocessing Data for Model Building
Understanding Cost Function Understanding Gradient Descent Math Behind Gradient Descent Assumptions of Linear Regression Implement Linear Regression from Scratch Train Linear Regression in Python Implementing Linear Regression in R Diagnosing Residual Plots in Linear Regression Models Generalized Linear Models Introduction to Logistic Regression Odds Ratio Implementing Logistic Regression from Scratch Introduction to Scikit-learn in Python Train Logistic Regression in python Multiclass using Logistic Regression How to use Multinomial and Ordinal Logistic Regression in R ? Challenges with Linear Regression Introduction to Regularisation Implementing Regularisation Ridge Regression Lasso Regression
Introduction to K Nearest Neighbours Determining the Right Value of K in KNN Implement KNN from Scratch Implement KNN in Python
Bias Variance Tradeoff Introduction to Overfitting and Underfitting Visualizing Overfitting and Underfitting Selecting the Right Model What is Validation? Hold-Out Validation Understanding K Fold Cross Validation
Introduction to Feature Selection Feature Selection Algorithms Missing Value Ratio Low Variance Filter High Correlation Filter Backward Feature Elimination Forward Feature Selection Implement Feature Selection in Python Implement Feature Selection in R
Introduction to Decision Tree Purity in Decision Tree Terminologies Related to Decision Tree How to Select Best Split Point in Decision Tree? Chi-Squares Information Gain Reduction in Variance Optimizing Performance of Decision Tree Train Decision Tree using Scikit Learn Pruning of Decision Trees
Introduction to Feature Engineering Feature Transformation Feature Scaling Feature Engineering Frequency Encoding Automated Feature Engineering: Feature Tools
Understanding how to solve Multiclass and Multilabled Classification Problem Evaluation Metrics: Multi Class Classification
Introduction to Ensemble Techniques Basic Ensemble Techniques Implementing Basic Ensemble Techniques Finding Optimal Weights of Ensemble Learner using Neural Network Why Ensemble Models Work well?
Introduction to Stacking Implementing Stacking Variants of Stacking Implementing Variants of Stacking Introduction to Blending Bootstrap Sampling Introduction to Random Sampling Hyper-parameters of Random Forest Implementing Random Forest Out-of-Bag (OOB) Score in the Random Forest IPL Team Win Prediction Project Using Machine Learning Introduction to Boosting Gradient Boosting Algorithm Math behind GBM Implementing GBM in python Regularized Greedy Forests Extreme Gradient Boosting Implementing XGBM in python Tuning Hyperparameters of XGBoost in Python Implement XGBM in R/H2O Adaptive Boosting Implementing Adaptive Boosing LightGBM Implementing LightGBM in Python Catboost Implementing Catboost in Python
Different Hyperparameter Tuning methods Implementing Different Hyperparameter Tuning methods GridsearchCV RandomizedsearchCV Bayesian Optimization for Hyperparameter Tuning Hyperopt
Understanding SVM Algorithm SVM Kernels In-depth Intuition and Practical Implementation SVM Kernel Tricks Kernels and Hyperparameters in SVM Implementing SVM from Scratch in Python and R
Introduction to Principal Component Analysis Steps to Perform Principal Compound Analysis Computation of Covariance Matrix Finding Eigenvectors and Eigenvalues Implementing PCA in python Visualizing PCA A Brief Introduction to Linear Discriminant Analysis Introduction to Factor Analysis
Introduction to Clustering Applications of Clustering Evaluation Metrics for Clustering Understanding K-Means Implementation of K-Means in Python Implementation of K-Means in R Choosing Right Value for K Profiling Market Segments using K-Means Clustering Hierarchical Clustering Implementation of Hierarchial Clustering DBSCAN Defining Similarity between clusters Build Better and Accurate Clusters with Gaussian Mixture Models
Understand Basics of Recommendation Engine with Case Study
8 Ways to Improve Accuracy of Machine Learning Models
Introduction to Dask Working with CuML
Introduction to Machine Learning Interpretability Framework and Interpretable Models model Agnostic Methods for Interpretability Implementing Interpretable Model Understanding SHAP Out-of-Core ML Introduction to Interpretable Machine Learning Models Model Agnostic Methods for Interpretability Game Theory & Shapley Values
Introduction to AutoML Implementation of MLBox Introduction to PyCaret TPOT Auto-Sklearn EvalML
Pickle and Joblib Introduction to Model Deployment
Deploying Machine Learning Model using Streamlit Deploying ML Models in Docker Deploy Using Streamlit Deploy on Heroku Deploy Using Netlify Introduction to Amazon Sagemaker Setting up Amazon SageMaker Using SageMaker Endpoint to Generate Inference Deploy on Microsoft Azure Cloud Introduction to Flask for Model Deploying ML model using Flask
Model Deployment in Android Model Deployment in Iphone

What are Statistical Process Control (SPC) Charts?

mounish12439
mounish12439 30 Jul, 2024
4 min read

Introduction

In quality management, Statistical Process Control (SPC) charts are the key for organizations to help oversee, control, and improve their processes. Through statistical methods, SPC charts highlight variations and identify patterns to ensure consistent product quality. Let’s explore the types of SPC charts, their mechanisms, and their applications.

SPC Charts

Overview

  • Understand the fundamentals of SPC charts
  • Learn about their types.
  • Explore the benefits of using them in quality management
  • Discover how to implement them effectively
  • Learn to create SPC charts using Python and Excel

Table of contents

What are SPC Charts? 

SPC charts, also called control charts, they help in visually displaying data points (over time). They distinguish between common cause variations (inherent) and special cause variations (unusual). This separation aids in maintaining process stability and pinpointing improvement areas.

Types of SPC Charts

SPC charts come in various types, each suited for specific data and process characteristics. The main types include:

  • X-Bar and R Chart: These charts monitor a process’s mean and range. The X-bar chart tracks the average of subgroups, while the R chart monitors the range within subgroups.
  • P-Chart: It’s Designed to monitor the proportion of a process with defective items. This is useful for categorical data where each item is either defective or non-defective.
  • C-Chart: This chart counts the number of defects in a single unit of product. It is ideal for processes where the number of defects per unit is counted.
  • U-Chart: This chart is similar to the C-chart, but it accounts for varying sample sizes. It monitors the number of defects per unit, allowing for more flexibility in sample size.

Benefits of SPC Charts

Implementing SPC charts offers several advantages to organizations:

  • Improved Quality Control: They help monitor and control processes, consistently ensuring products meet quality standards.
  • Early Detection of Issues: They enable prompt identification of deviations, allowing for immediate corrective actions to prevent defects.
  • Data-Driven Decision Making: They visually represent process data, supporting informed decisions based on real-time insights.

How to Implement SPC Charts Effectively?

To successfully implement SPC charts, follow these steps:

  1. Select the Right Chart: Choose the appropriate type of SPC chart based on the data and process characteristics.
  2. Collect Data: Gather data points systematically, ensuring accuracy and consistency.
  3. Calculate Control Limits: Based on historical data, determine the upper and lower control limits to identify acceptable variation ranges.
  4. Plot Data Points: Plot the data points on the chart, marking any points that fall outside the control limits.
  5. Analyze and Act: Analyze the chart to identify trends or unusual variations. Take corrective actions for any points outside the control limits.

Example of SPC Chart in Python

Here’s how you can create an X-bar and R chart using Python:

import numpy as np
import matplotlib.pyplot as plt
# Sample data
data = np.array([[5, 6, 7], [8, 9, 7], [5, 6, 7], [8, 9, 6], [5, 6, 8]])
# Calculate subgroup means and ranges
x_bar = np.mean(data, axis=1)
R = np.ptp(data, axis=1)
# Calculate overall mean and average range
x_double_bar = np.mean(x_bar)
R_bar = np.mean(R)
# Control limits for X-bar chart
A2 = 0.577  # Factor for X-bar chart control limits
UCL_x_bar = x_double_bar + A2 * R_bar
LCL_x_bar = x_double_bar - A2 * R_bar
# Control limits for R chart
D4 = 2.114  # Factor for R chart upper control limit
D3 = 0      # Factor for R chart lower control limit
UCL_R = D4 * R_bar
LCL_R = D3 * R_bar
# Plot X-bar chart
plt.figure(figsize=(12, 6))
plt.subplot(211)
plt.plot(x_bar, marker='o', linestyle='-', color='b')
plt.axhline(y=x_double_bar, color='g', linestyle='-')
plt.axhline(y=UCL_x_bar, color='r', linestyle='--')
plt.axhline(y=LCL_x_bar, color='r', linestyle='--')
plt.title('X-Bar Chart')
plt.xlabel('Subgroup')
plt.ylabel('Mean')
# Plot R chart
plt.subplot(212)
plt.plot(R, marker='o', linestyle='-', color='b')
plt.axhline(y=R_bar, color='g', linestyle='-')
plt.axhline(y=UCL_R, color='r', linestyle='--')
plt.axhline(y=LCL_R, color='r', linestyle='--')
plt.title('R Chart')
plt.xlabel('Subgroup')
plt.ylabel('Range')
plt.tight_layout()
plt.show()
SPC Chart in Python

Code Explanations

This Python script helps display X-bar and R-control charts using sample data. As you can see, these control charts help track the statistical process of control of stability over time.

  • numpy for numerical operations.
  • matplotlib.pyplot for plotting graphs.
  • Creates a 2D array representing five subgroups with three observations each.
  • x_bar: Mean of each subgroup.
  • R: Range of each subgroup.
  • x_double_bar: Overall mean of subgroup means.
  • R_bar: Average range of the subgroups.
  • Calculates upper (UCL_x_bar) and lower (LCL_x_bar) control limits.
  • Calculates upper (UCL_R) and lower (LCL_R) control limits.

Example of SPC Chart in Excel

Here are the examples of SPC Chart in Excel:

  1. Collect Data: Input your data in an Excel spreadsheet, with subgroups in rows and observations in columns.
  2. Calculate Averages and Ranges
    • You can use the AVERAGE function to calculate the mean of every subgroup.
    • Then, the MAX and MIN functions are used to calculate the range of each subgroup.
  3. Determine Control Limits
    • Calculate the overall average (X-double-bar) and average range (R-bar).
    • Apply appropriate constants (A2, D3, D4) to calculate the control limits.
  4. Create the Chart
    • Select the data and insert a line chart for the X-bar and R values.
    • You can add horizontal lines for control limits using the `Insert Shapes` feature or as additional data series.

Conclusion

Familiarity with the different types of SPC charts and their applications allows organizations to improve quality control measures, leading to superior product quality and greater efficiency. They serve as valuable instruments in quality management, providing a systematic method for overseeing and refining processes.

Frequently Asked Questions

Q1. Can SPC charts be used in service industries?

Ans. Yes, they can be applied in service industries to monitor and improve process quality, such as response times, customer satisfaction, and error rates.

Q2. What do control limits mean in SPC charts?  

Ans. Control limits are the lower and upper boundaries on an SPC chart that indicate the acceptable range of variation in a process. Data points outside these limits should be considered as potential issues.

Q3. How can SPC charts aid in regulatory compliance?

Ans. They help maintain consistent quality standards, provide evidence of process control, and support documentation requirements, aiding in compliance with industry regulations and standards.

ChartsGuidepythonstatistical
mounish12439
mounish12439 30 Jul, 2024

I'm a tech enthusiast, graduated from Vellore Institute of Technology. I'm working as a Data Science Trainee right now. I am very much interested in Deep Learning and Generative AI.

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