Introduction

A state variable is a parameter that is categorized into a countable number of defined states. Examples would include transmission gear states, PRNDL positions, ignition switch states, and others. Sometimes continuous variable, like pedal positions, may be binned into discrete states to be displayed as a histogram.  State  change timing is unpredictable since vehicle operation is highly variable. A way to deal with this data is Markov Analysis.

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Introduction

Reliability and durability are essential in today’s competitive market place. However, component reliability verification tests and system durability tests take a long time, cycles, or miles to complete. This puts these tests in direct conflict with program timing, product development budgets, and limited testing resources. To minimize this conflict, it is essential to accelerate these tests.

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Test To Bogy Sample Sizes

Introduction

Reliability verification is a fundamental stage in the product development process. It is common for engineers to run a test to bogy (TTB).  What sample size is required for a TTB?

Reliability Testing

Reliability is the probability of a part successfully functions under specified life, duty cycle and environmental conditions. Many functions are specified during the design process. Each reliability test will be focused to validate a specific function. The targeted verification level depends on the criticality of the function and potential failure modes. The life could be specified as a count of cycles, an operating time, or perhaps a mileage or mileage equivalent. The duty cycle is a description of how the device is used. Environmental stresses are generally included in the test. 

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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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Process Capability VII – Confidence Limits

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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Process Capability – Non-Normal Variables

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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Process Capability V – Variation Reduction

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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Telematics Analytics

This post provides a list of my telematics analytics articles, a short description and a link. The goal is to make it easy for the reader to locate any of the articles. It is recommended to read these articles in the order presented.  This post will be updated when additional posts are written on this topic.

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Process Capability Articles

This post provides a list of my process capability articles, a short description and a link. The goal is to make it easy for the reader to locate any of the articles. It is recommended to read these articles in the order presented.  This post will be updated when additional posts are written on the Process Capability topic.

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Process Capability IV – Improve the Process

In prior articles of this series, the process was not capable. The Cp ~0.46 so even if centered, a high percentage of parts would be non-conforming! In industry, it is common to see a Cp of about 1. The paradigm is that if the process range is just contained within the tolerance range, it is satisfactory.  Such processes are marginally capable. A process mean shift away from the target or an increase in variation significantly increases the number of non-conforming parts.  Process Capability needs to be increased. At a minimum, Cp should be greater than 1.33, but larger is better.

There are two approaches to improving process capability. One is to center the process and the other is to reduce variation. Both need to be accomplished.

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