# Practical engineering process and reliability statistics pdf

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*Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking principles to organize this body of knowledge. The individual outcome of such efforts, an engineered system , can be defined as a combination of components that work in synergy to collectively perform a useful function.*

Many objects consist of more components. The mutual arrangement of the individual elements influences the resultant reliability. The formulae are shown for the resultant reliability of series arrangement, as well as for parallel and combined arrangement. The possibility of reliability increasing by means of redundancy is explained, and also the principle of optimal allocation of reliabilities to individual elements. Everything is illustrated on examples.

## Systems engineering

In statistics and psychometrics , reliability is the overall consistency of a measure. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained.

Various kinds of reliability coefficients, with values ranging between 0. Reliability does not imply validity. That is, a reliable measure that is measuring something consistently is not necessarily measuring what you want to be measured. For example, while there are many reliable tests of specific abilities, not all of them would be valid for predicting, say, job performance. While reliability does not imply validity , reliability does place a limit on the overall validity of a test.

A test that is not perfectly reliable cannot be perfectly valid, either as a means of measuring attributes of a person or as a means of predicting scores on a criterion. While a reliable test may provide useful valid information, a test that is not reliable cannot possibly be valid. For example, if a set of weighing scales consistently measured the weight of an object as grams over the true weight, then the scale would be very reliable, but it would not be valid as the returned weight is not the true weight.

For the scale to be valid, it should return the true weight of an object. This example demonstrates that a perfectly reliable measure is not necessarily valid, but that a valid measure necessarily must be reliable. In practice, testing measures are never perfectly consistent. Theories of test reliability have been developed to estimate the effects of inconsistency on the accuracy of measurement. The basic starting point for almost all theories of test reliability is the idea that test scores reflect the influence of two sorts of factors: [7].

Factors that contribute to consistency: stable characteristics of the individual or the attribute that one is trying to measure. Factors that contribute to inconsistency: features of the individual or the situation that can affect test scores but have nothing to do with the attribute being measured.

These factors include: [7]. The goal of estimating reliability is to determine how much of the variability in test scores is due to errors in measurement and how much is due to variability in true scores. A true score is the replicable feature of the concept being measured. It is the part of the observed score that would recur across different measurement occasions in the absence of error. Errors of measurement are composed of both random error and systematic error.

It represents the discrepancies between scores obtained on tests and the corresponding true scores. The goal of reliability theory is to estimate errors in measurement and to suggest ways of improving tests so that errors are minimized. The central assumption of reliability theory is that measurement errors are essentially random. This does not mean that errors arise from random processes. For any individual, an error in measurement is not a completely random event. However, across a large number of individuals, the causes of measurement error are assumed to be so varied that measure errors act as random variables.

If errors have the essential characteristics of random variables, then it is reasonable to assume that errors are equally likely to be positive or negative, and that they are not correlated with true scores or with errors on other tests.

It is assumed that: [8]. Reliability theory shows that the variance of obtained scores is simply the sum of the variance of true scores plus the variance of errors of measurement. In its general form, the reliability coefficient is defined as the ratio of true score variance to the total variance of test scores.

Or, equivalently, one minus the ratio of the variation of the error score and the variation of the observed score :. Unfortunately, there is no way to directly observe or calculate the true score , so a variety of methods are used to estimate the reliability of a test.

Some examples of the methods to estimate reliability include test-retest reliability , internal consistency reliability, and parallel-test reliability. Each method comes at the problem of figuring out the source of error in the test somewhat differently. It was well known to classical test theorists that measurement precision is not uniform across the scale of measurement.

Tests tend to distinguish better for test-takers with moderate trait levels and worse among high- and low-scoring test-takers. Item response theory extends the concept of reliability from a single index to a function called the information function. The IRT information function is the inverse of the conditional observed score standard error at any given test score.

Four practical strategies have been developed that provide workable methods of estimating test reliability. Test-retest reliability method : directly assesses the degree to which test scores are consistent from one test administration to the next. The correlation between scores on the first test and the scores on the retest is used to estimate the reliability of the test using the Pearson product-moment correlation coefficient : see also item-total correlation.

The key to this method is the development of alternate test forms that are equivalent in terms of content, response processes and statistical characteristics. For example, alternate forms exist for several tests of general intelligence, and these tests are generally seen equivalent.

With the parallel test model it is possible to develop two forms of a test that are equivalent in the sense that a person's true score on form A would be identical to their true score on form B. If both forms of the test were administered to a number of people, differences between scores on form A and form B may be due to errors in measurement only. The correlation between scores on the two alternate forms is used to estimate the reliability of the test. This method provides a partial solution to many of the problems inherent in the test-retest reliability method.

For example, since the two forms of the test are different, carryover effect is less of a problem. Reactivity effects are also partially controlled; although taking the first test may change responses to the second test.

However, it is reasonable to assume that the effect will not be as strong with alternate forms of the test as with two administrations of the same test. This method treats the two halves of a measure as alternate forms. It provides a simple solution to the problem that the parallel-forms method faces: the difficulty in developing alternate forms. The correlation between these two split halves is used in estimating the reliability of the test.

This halves reliability estimate is then stepped up to the full test length using the Spearman—Brown prediction formula. There are several ways of splitting a test to estimate reliability. For example, a item vocabulary test could be split into two subtests, the first one made up of items 1 through 20 and the second made up of items 21 through However, the responses from the first half may be systematically different from responses in the second half due to an increase in item difficulty and fatigue.

In splitting a test, the two halves would need to be as similar as possible, both in terms of their content and in terms of the probable state of the respondent. The simplest method is to adopt an odd-even split, in which the odd-numbered items form one half of the test and the even-numbered items form the other. This arrangement guarantees that each half will contain an equal number of items from the beginning, middle, and end of the original test.

Internal consistency : assesses the consistency of results across items within a test. The most common internal consistency measure is Cronbach's alpha , which is usually interpreted as the mean of all possible split-half coefficients. These measures of reliability differ in their sensitivity to different sources of error and so need not be equal.

Also, reliability is a property of the scores of a measure rather than the measure itself and are thus said to be sample dependent. Reliability estimates from one sample might differ from those of a second sample beyond what might be expected due to sampling variations if the second sample is drawn from a different population because the true variability is different in this second population.

This is true of measures of all types—yardsticks might measure houses well yet have poor reliability when used to measure the lengths of insects. Reliability may be improved by clarity of expression for written assessments , lengthening the measure, [9] and other informal means. However, formal psychometric analysis, called item analysis, is considered the most effective way to increase reliability. This analysis consists of computation of item difficulties and item discrimination indices, the latter index involving computation of correlations between the items and sum of the item scores of the entire test.

From Wikipedia, the free encyclopedia. Overall consistency of a measure in statistics and psychometrics. For other uses, see Reliability. Main article: Classical test theory.

This article includes a list of general references , but it remains largely unverified because it lacks sufficient corresponding inline citations.

Please help to improve this article by introducing more precise citations. July Learn how and when to remove this template message. Toronto: Pearson. Essentials of abnormal psychology. Murphy, Charles O. Upper Saddle River, N. Theory of mental tests.

Hillsdale, N. Erlbaum Associates. What Is Coefficient Alpha? An Examination of Theory and Applications. Journal of Applied Psychology, 78 1 , 98— Understanding a widely misunderstood statistic: Cronbach's alpha. International Journal of Public Health.

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## Practical Reliability Engineering (eBook, PDF)

Most complex systems, such as automobiles, communication systems, aircraft, aircraft engine controllers, printers, medical diagnostics systems, helicopters, train locomotives, etc. When these systems are fielded or subjected to a customer use environment, it is often of considerable interest to determine the reliability and other performance characteristics under these conditions. Areas of interest may include assessing the expected number of failures during the warranty period, maintaining a minimum mission reliability, addressing the rate of wearout, determining when to replace or overhaul a system and minimizing life cycle costs. In general, a distribution, such as the Weibull distribution, cannot be used to address these issues. In order to address the reliability characteristics of complex repairable systems, a process is often used instead of a distribution.

Jetzt bewerten Jetzt bewerten. With emphasis on practical aspects of engineering, this bestsellerhas gained worldwide recognition through progressive editions asthe essential reliability textbook. This fifth editionretains the unique balanced mixture of reliability theory andapplications, thoroughly updated with the latest industry bestpractices. Each chapter is supportedby practice questions, and a solutions manual is available tocourse tutors via the companion website. DE Als Download kaufen. Jetzt verschenken.

## Reliability (statistics)

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In statistics and psychometrics , reliability is the overall consistency of a measure. Scores that are highly reliable are precise, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.

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