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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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. 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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Introduction

In the article “PCA I”, the main process performance indices were defined. In the article “PCA II”, ways to calculate the percent defective were introduced. In this article, the mathematical connection between the Cp index and percent defectives is made.

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Introduction

In my prior article, PCA was defined for prototype samples and serial production. It’s application to one and two sided distributions was discussed. The P_p, P_pk, C_p, and C_pk indices were defined. 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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Introduction

Vehicle operation is highly variable causing parameter and states data to change unpredictably. A way to deal with this data is Markov Analysis.

Markov Processes

A Markov Process is defined a having a finite number of states and the probability of transitioning from the current state to another state is between 0 and 1. A Markov transition matrix is used to count these transitions, table 1. [Read more…]

Introduction

Telematics data presents the opportunity to characterize the vehicle lifetime usage. This information is used to validate development and testing targets. Because there can be bad or incomplete data, it needs to be reviewed prior to any analysis to have confidence in the results. [Read more…]

Introduction

In my prior article, “A Primer on Probability Distributions”, the usage of different types of histograms to display data was discussed. The histogram would acquire a bell shape if the data were normally distributed. The main limitation of the histogram approach is that the shape of the histogram can change radically with the selection of the bins used. Instead, a probability plot could be used.

This article discussed probability plots. They are extremely useful for the analysis of big and small data sets.

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Introduction

Frequently, data collection is the most time consuming and expensive part of a project. Consequently, people work with small sample data. There is too little data to plot a histogram, so the analysis assumes the underlying population is normally distributed.

A frequent error is to assume the sample average and standard deviation are the population normal mean and standard deviation. When small sample sizes are being analyzed, these assumptions lead to estimation errors.

Methods to make better estimates are discussed in this article. [Read more…]

Introduction

Working with product engineers to develop a reliability test early in a program can be a satisfying experience. My interactions with the product engineers are the most fruitful when there is mutual respect. I ask the product engineer questions about his goals, the product features, the supplier, and rely on his product expertise. I like to examine prototype parts and review an engineering drawing or the circuit diagrams.

A good example was when a product engineer, let’s call him Jim,  approached me to develop a safety switch reliability test.

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 Vehicle Warranty Big Data

Automobile companies pay dealers to perform vehicle prep and make warranty repairs on customer vehicles. A lot of data is collected thus warranty is considered big data.

Generally, vehicle warranty covers 3 years or 36,000 miles. When a vehicle is serviced, the customer, vehicle, repair, and text data are collected. Claims are entered into a transaction database, may be rejected for a number of reasons, and then resubmitted until resolved. The transaction database covers many model years, millions of vehicles, and a number of warranty claims for each vehicle. As a rough estimate, assuming 10 years, 2 million vehicles/year, and 2 claims for each vehicle, yields 40 million records. The actual number is higher due to the submission, rejections, and resubmission cycle.

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