Big Data & Analytics

Extended Bogy Testing

Introduction

Extended bogy testing builds on test to bogy (TTB), discussed in a prior article. TTB focused on calculating the number (N) of parts tested to one life bogy, with 0 failures allowed, to a specified reliability (R) and confidence (C) levels.

Using TTB to verify conformance to high reliability and confidence targets requires very large sample sizes, increasing testing cost. The capacity to test large samples may require large facility capital expenditures. Also, the zero failures allowed paradigm removes the opportunity to learn about product failure modes and the opportunity to improve the product through design or manufacturing process changes.

This article focuses on extended bogy test plans as an alternative to TTB.

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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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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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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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In the article Process Capability I – Overview and Indices, the main process performance indices were defined. In the article Process Capability Analysis II – Estimating Percent Defective, ways to calculate the percent defective were introduced.

Next, a way to estimate estimate the percent defective was discussed in Process Capability III – Cp vs Percent Defective. The data showed the process had a  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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Introduction

In my prior article, Process Capability I – Overview and Indices, the process capability concept was defined for prototype samples and serial production. The data is assumed to be normally distributed and P_p, P_pk, C_p, and C_pk indices were defined. Its application to one-sided and two-sided tolerances was discussed. This article provides methods to estimate the percent defective.

The Data

The engineering tolerance for a critical characteristic is 10±0.2. So the lower specification limit (LSL) is 9.8 and the upper specification limit (USL) is 10.2. A sample of 30 parts provided measurements of the critical characteristic. The sample mean ($-\bar{x}-$) was 9.951 and the sample standard deviation (s) was 0.1825.

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Introduction

The analysis of telematics data with two or more parameters is a complex process. The analysis of multiple parameters using contour plots is a powerful tool since a lot of information is captured in the graphics.

The best results come from a team effort. For engineering data, the team may consist of the design/development engineers, a programmer, and a reliability engineer or a statistician. The following is an analysis of engine speed, engine torque, and the transmission gear state to describe the process.

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