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on Tools & Techniques

A listing in reverse chronological order of articles by:

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Nonparametric Forecasts From Left-Censored Data

Nonparametric Forecasts From Left-Censored Data

Nonparametric Forecasts From Left-Censored Data

“Component D” had some failures in its first 12 months. How many more would fail in 36-month warranty? ASQ’s Quality Progress Statistics Roundtable published the data and Weibull analysis. The data included left-censored failure counts collected at one calendar time. The Weibull analysis included actuarial failure forecasts. This article describes nonparametric alternatives to Weibull and quantifies extrapolation uncertainty. The nonparametric forecasts are larger than the Weibull forecasts. Alternative extrapolations of nonparametric failure rates from data subsets quantify uncertainty. [Read more…]

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How Should the Sample Size be Selected for an X-bar Chart? (Part I)

How Should the Sample Size be Selected for an X-bar Chart? (Part I)

How Should the Sample Size be Selected for an X-bar Chart? (Part I)

The purpose of control charts is to detect significant process changes when they occur.  In general, charts that display averages of data/measurements (X-bar charts) are more useful than charts of individual data points or measurements.  Charts of individuals are not nearly as sensitive as charts of averages at detecting process changes quickly.  X-bar charts are far superior at detecting process shifts in a timely manner, and the sample size is a crucial element in ensuring that appropriate chart signals are produced. [Read more…]

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How do I know what product or process characteristics to control?

How do I know what product or process characteristics to control?

How do I know what product or process characteristics to control?

While the construction of control charts is relatively straight-forward, often a more difficult question is “how do I know what process characteristic to control in the first place?”  Clearly, controlling “everything” is not feasible or a smart use of limited resources.   [Read more…]

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Actuarial Forecasts, Least Squares Reliability, and Martingales

Actuarial Forecasts, Least Squares Reliability, and Martingales

Actuarial Forecasts, Least Squares Reliability, and Martingales

I learned actuarial methods working for the USAF Logistics Command. We used actuarial rates to forecast demands and recommend stock levels for expensive engines tracked by serial number, hours, and cycles. I had a hunch that actuarial methods could be applied to all service parts, without life data. [Read more…]

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Basic DOE Terminology

Basic DOE Terminology

Basic DOE Terminology

In this article post, we formally define or describe the basic terminology that is commonly used in Design of Experiments.  Some of the terms we have already been using in prior posts, but they will also be presented here for completeness.  This is Part I of a two part article covering DOE Terminology.  [Read more…]

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Ergodicity, Toilet Paper, and Field Reliability

Ergodicity, Toilet Paper, and Field Reliability

Ergodicity, Toilet Paper, and Field Reliability

Ergodicity means that cross-section probabilities equal longitudinal lifetime probabilities. (“Ergos” is Greek for “work.” Think of “ergonomics”.) Ergodicity means that we can estimate age-specific field reliability functions from cross-section data: ships (installed base) and returns (complaints, failures, service parts’ sales, etc.). Ships and returns provide information about lifetimes. Returns are the superpositions of failures of products or their parts started at different times. What does ergodicity have to do with toilet paper? [Read more…]

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Relationship between FMEA and Risk Management

What is the relationship between FMEA and Risk Management?

“If no one ever took risks, Michelangelo would have painted the Sistine floor.” – Neil Simon

FMEA and Risk Management are two distinct bodies of knowledge. This article explores some of the interactions between these two important methods. It is not intended to be a complete analysis of the similarities, differences, and linkages between FMEA and risk management. Rather, it is a high-level overview.

[Read more…]

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The Tragedy of the Commons

The Tragedy of the Commons

The Tragedy of the Commons

Imagine you were a rancher with a herd of cattle and a small field in which to graze them. One of your primary concerns include determining how many cattle the field could support. With too few cattle, you give up potential earnings that the field could readily sustain. But too many cattle consume the grass faster than the field could replenish it, resulting in malnourished cattle and degraded land quality.

Therefore, as a rancher with long-term prospects, inspecting and maintaining the field, planting new grass, and limiting the number of new cattle in the field all become a cornerstone of your business model. [Read more…]

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How is Formal Experimentation different from Simplistic Approaches? (Part II)

How is Formal Experimentation different from Simplistic Approaches? (Part II)

How is Formal Experimentation different from Simplistic Approaches? (Part II)

Statistically based DOE provides several advantages over more simplistic approaches such “one-factor-at-a-time” experimentation.  These advantages include:

  • The use of statistical methodology to determine which factors are actually (statistically) significant
  • Balanced experimental designs to allow stronger conclusions with respect to cause and effect relationships (as opposed to just finding correlations)
  • The ability to understand and estimate interactions between factors
  • The development of predictive models that are used to find optimal solutions for one or more responses

[Read more…]

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Gozinto Theory and Parts’ Installed Base

Gozinto Theory and Parts’ Installed Base

Gozinto Theory and Parts’ Installed Base

Andrew Vázsonyi led an interesting life. He collaborated with mathematician Paul Erdös, he was co-founder of The Institute of Management Sciences, and he wrote “Which Door has the Cadillac: Adventures of a Real-Life Mathematician”. Around 1970, Andrew Vázsonyi interviewed for a teaching job in Sauder School of Business, University of British Columbia. During the job interview, he taught us Gozinto Theory. [Read more…]

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How do I Choose the Appropriate Type of Control Chart?

How do I Choose the Appropriate Type of Control Chart?

How do I Choose the Appropriate Type of Control Chart?

Proper control chart selection is critical to realizing the benefits of Statistical Process Control.  Many factors should be considered when choosing a control chart for a given application.  These include:

  • The type of data being charted (continuous or attribute)
  • The required sensitivity (size of the change to be detected) of the chart
  • Whether the chart includes data from multiple locations or not
  • The ease and cost of sampling
  • Production volumes

[Read more…]

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Andragogy – How Adults Learn to Learn

Andragogy – How Adults Learn to Learn

Andragogy – How Adults Learn to Learn

This strange word andragogy was popularized in the early 1970’s by educational researcher, Malcolm Knowles. It is etymologically rooted in the Greek language from two words “aner”, which means “man” and “agogos”, which means “to lead”. Fused together, andragogy means “leading men”, or to paraphrase, leading or educating adults. Andragogy is often contrasted with pedagogy, typically referring to the education of children. [Read more…]

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The Dark Side of the HALT

The Dark Side of the HALT

The Dark Side of the HALT

Thems that die’ll be the lucky ones.
~ Robert Louis Stevenson

This post is a continuation of the series “Is the HALT a Life Test or not?”

Test two samples and demonstrate reliability R=0,99 over a lifetime with CL=0,99. This is real. But what payment will we pay, besides the duration of the test on triple lifetime, which can be significantly accelerated by the way? [Read more…]

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How is Formal Experimentation different from Simplistic Approaches (Part I)

How is Formal Experimentation different from Simplistic Approaches (Part I)

How is Formal Experimentation different from Simplistic Approaches (Part I)

Statistically based DOE provides several advantages over more simplistic approaches such “one-factor-at-a-time” experimentation.  These advantages include:

  • The use of statistical methodology to determine which factors are actually (statistically) significant
  • Balanced experimental designs to allow stronger conclusions with respect to cause and effect relationships (as opposed to just finding correlations)
  • The ability to understand and estimate interactions between factors
  • The development of predictive models that are used to find optimal solutions for one or more responses

This article will explore the first two advantages in a bit more detail.  The second two advantages will be discussed in the next article post.  [Read more…]

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How Can You Estimate Reliability Without Life Data?

How Can You Estimate Reliability Without Life Data?

How Can You Estimate Reliability Without Life Data?

Myron Tribus’ UCLA Statistical Thermodynamics class introduced me to entropy, -Sp(t)ln(p(t)). (p(t) is the probability of state t of a system.) Professor Tribus later advocated maximum-entropy reliability estimation, because that “…best represents the current state of knowledge about a system…” [Principle of maximum entropy – Wikipedia] Caution! This article contain statistical neurohazards.

Claude Shannon wrote that entropy (log base 2) represents information bits, “…an absolute mathematical limit on how well data from the source can be losslessly compressed onto a perfectly noiseless channel.”  [Beirlant et al.]

Maximum likelihood estimation is one way to estimate reliability from data. It maximizes the probability density function of observed data, Pp(t), e.g., for observed failures at ages t. It is equivalent to maximize -Sln(p(t). Maximum entropy reliability estimation maximizes entropy -Sp(t)ln(p(t). That’s same as maximizing the expected value, -Sp(t)ln(p(t), of the log likelihood -ln(p(t). Fine, if you have life data, ages at failures t censored or not. [Read more…]