Tabtrainer Minitab: One Sample Poisson Rate

Achieve top-level expertise in Minitab with Prof. Dr. Murat Mola, recognized as Germany's Professor of the Year 2023.

What you'll learn

Total Occurrences and defect rates of poisson distributed data

Graphical derivation of the Poisson distribution

Interpreting the probability density of the Poisson distribution

Normal approximation in the context with the Poisson distribution

Determine total occurrences in Poisson distribution

Hypothesis definitions for poisson distributed data

Working with the sum function in the context of the Poisson distribution

Working with the function “tally individual variables” in the context of Poisson distribution

Requirements

No Specific Prior Knowledge Needed: all topics are explained in a practical step-by-step manner.

Description

Learning Description: One Sample Poisson RateIn this training unit, students are introduced to a realistic quality control scenario in the shock pad production at Smartboard Company. The goal is to assess whether the production process meets the customer’s strict requirement: a maximum of 25 surface defects per batch of 500 shock pads, equivalent to a 5% defect rate.Since inspecting every shock pad would be economically unfeasible, students work with sample data consisting of 50 randomly selected batches. Each batch contains 500 parts, and the number of defects per batch was measured using an automatic surface inspection system. Based on this data, the students perform a statistical analysis using the one-sample Poisson hypothesis test.By completing this unit, students will learn to:Understand the background and relevance of quality control in a production environment with tight customer specifications.Work with real sample data and interpret its structure, including batch numbers, sample sizes, and detected defects.Learn key statistical terms:Total Occurrences – the total number of defects in all samples combinedSample Rate – the average number of defects per single partSample Mean – the average number of defects per batchUnderstand why the Poisson distribution is the appropriate choice for modeling such defect data, and how it compares to the Binomial, Normal, and Chi-square distributions.Visualize and interpret the Poisson probability distribution and understand its parameterization based on the mean (λ or μ).Perform a hypothesis test to estimate the population defect rate and assess whether the process is still in control.Learn the correct formulation of:Null Hypothesis (H₀): The average number of defects per batch is ≤ 25.Alternative Hypothesis (H₁): The average number of defects per batch is > 25.Select the exact Poisson method over the normal approximation due to its higher accuracy and better selectivity in low-count situations.Interpret the results of the hypothesis test, including:The calculated Poisson rate (λ) and mean (μ)The p-value and its implications for decision-makingRecognize the difference between sample-based values and population-based estimations, and how a hypothesis test can bridge this gap.Make data-driven quality management decisions:Even if the sample appears just above the customer threshold, the test might show the process is statistically still in control—with 95% confidence.In conclusion, students will be able to make informed, statistically sound recommendations to management—deciding whether immediate process improvements are necessary or if the current process performance is acceptable despite being close to the critical limit.This unit demonstrates how Six Sigma tools like the Poisson distribution and hypothesis testing are applied in real-world production environments, combining statistical theory with business impact.

Overview

Section 1: Einführung

Lecture 1 Introduction and Business Case

Lecture 2 What You Need to Know Before You Start: Key Terms

Lecture 3 Choosing the Right Distribution: Why Poisson Fits Our Scenario

Lecture 4 From Sample to Population: Understanding the Poisson Approach

Lecture 5 Conducting a One-Sample Poisson Hypothesis Test to Assess Process Quality

Lecture 6 From Sample Insights to Population Estimates: Understanding λ or μ

Lecture 7 Making Decisions with Confidence: Interpreting the Poisson Hypothesis Test Resul

Lecture 8 Summary of the Most Important Findings

Quality Assurance Professionals: Those responsible for monitoring production processes and ensuring product quality will gain practical tools for defect analysis.,Production Managers: Managers overseeing manufacturing operations will benefit from learning how to identify and address quality issues effectively.,Six Sigma Practitioners: Professionals looking to enhance their expertise in statistical tools for process optimization and decision-making.,Engineers and Analysts: Individuals in manufacturing or technical roles seeking to apply statistical methods to real-world challenges in production.,Business Decision-Makers: Executives and leaders aiming to balance quality, cost, and efficiency in production through data-driven insights and strategies.