on Tools & Techniques

Sample Size – Measuring a Continuous Variable

Introduction

When planning a test on a continuous variable, the most common question was “How many should I test”? Later, when the test results were available, the questions were “What is the confidence?” or “How precise was the result?” This article focuses on planning the measurements of a continuous variable and analyzing the test results. 

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Introduction

In some of my articles, I have referred to The Central Limit Theorem, a development in probability theory. It can be stated

“When independent identically distributed random variables are added, their normalized sum tends toward a normal distribution (informally a “bell curve”) even if the original variables themselves are not normally distributed.”

We can apply this principle to many practical problems to analyze the distribution of the sample mean. In this article, I provide graphical and mathematical descriptions and a practical example.

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Sample Sizes – Surveys

Introduction

How many responses are needed for a survey? This question requires specifying the desired confidence and the accuracy of the survey results.

The Bernoulli Trial

A Bernoulli trial is an event that has two possible outcomes. Consider the case where the only possible outcomes are success or failure. Let the probability of a success is p and the probability of failure equals q.  The probabilities of all possible events must equal 1, so q = 1-p. These relationships are expressed mathematically as 

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Introduction

In prior articles on process capability, sample statistics and SPC statistics were assumed to be population parameters and ignored sampling variability. This article reviews the analytic methods that can be used to develop confidence bounds on the process capability indices.

$-P_p-$ Index

The P_p index calculation requires an estimate of the parameter σ. The index is calculated as:

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The Situation

You have a process that is not capable because sample measurements or SPC data indicate that some characteristics have too much variability. The calculated Cpk’s are too small. What do you do?

Assuming the data is correct, a course of action is to review the assumption is that the measurements are normally distributed. For most situations, this is a reasonable assumption, but other statistical distributions may provide a better description of the data variation. 

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Introduction

In the prior article, Process Capability IV, vehicle wheel toe alignment showed excessive variation. Because the vehicle assembly process is very long and involves many steps, the toe alignment problem required brainstorm which serial production steps, factors, and levels could be responsible for the variation. The most likely process steps were examined and the problem area identified as a wheel alignment machine that needed maintenance and calibration.

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