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In the wake of the many changes that business and industry has gone through during the past 20 years, one thing holds as sure as ever - measurement and data. That processes are best managed by taking appropriate data, by using clear metrics, and by scientific analysis is the very core of the way things are now done. In this paper we examine several of the mainstream metrics for process quality that have emerged as a standard by which quality is judged. We look at Normal distribution based metrics such as the indices Pp, Ppk, Cp and Cpk; the general fraction or percent non-conforming metric, defects per million opportunities; and the new “6-sigma” process capability standard. We consider the relations among these metrics and some aspects of the use of statistical confidence with respect to these metrics.

The requirement of “zero defects” is rapidly finding its way as a “standard” of quality in numerous quarters. This phrase has great psychological appeal, and is often taken literally at all levels in an organization even though quality motivation may be the intention. It is common to believe that when zero defects are found in the sample, this must be the case for “all the rest” as well. In this paper the technical side of “zero defects” is examined. We look at the statistics of zero defects and show what is implied about lot or process quality when zero defects is the actual sample outcome. The focus is on attribute measurements and includes some special cases where a significant measurement error exists and cases where a Bayesian statistical analysis may be appropriate.

The Weibull distribution is a widely used statistical model for studying fatigue and endurance life in engineering devices and materials. Many examples can be found among the aerospace, electronics, materials, and automotive industries. Recent advances in Weibull theory have also created numerous specialized Weibull applications. Modern computing technology has made many of these techniques accessible across the engineering spectrum. The purpose of this paper is to give a brief expository review of the Weibull distribution with a discussion and illustration of some of the more popular Weibull techniques. A short list of resources taken from the literature of Weibull analysis is also included.

This paper addresses a common problem associated with data analysis when a 1st failure in n, Weibull analysis is used. This is known among Weibull practitioners as the method of “sudden death”. Weibull analysis is a widely used reliability assessment and prediction technique. The “sudden death” method was initially developed to help reduce test time. In a “sudden death” test, k groups of n parts each are tested. In each test group testing is halted when the first failure occurs. This is referred to as the “first failure in n” and is usually detected by periodic inspection or by automatic/electronic test shut-off when the first failure occurs. It may happen that the first failure is not detected and there are two or more failures found upon inspection. In such cases the first failure time is lost since there are now 2 or more failures. If the second or third failure time is used as if it were the first failure time, overestimation of the reliability will result.

This paper concerns the analysis of data for cases where there are NO occurrences of “failures” when there is reason to assume a Weibull distribution with known slope parameter for the characteristic being studied. All samples survive a time t in an unfailed condition. In a series of n independent tests conducted under similar conditions, if we observe no failures by time t we call this a “success” run of length n. In this paper the classical non-parametric success run is first reviewed and it is shown what can be said about the relationship among reliability, confidence and sample size. Next, the Weibull distribution is explored for modeling the success run test when it is reasonable to assume a value for the Weibull slope parameter, b.

This paper reviews the theory and application of the “success run” test, found in reliability assessment applications, among others. A “success run” is a series of n independent tests without failure. The mathematical basis of the classical, non parametric success run test is reviewed, and it is shown with examples what can be said about the relation among reliability, confidence and sample size. The Bayesian success run is developed using the uniform distribution as prior distribution of reliability. This is further extended to include cases of uniform priors where 0< A < R < 1. The classical non-parametric case is reexamined and a natural prior distribution is revealed for the special case when one's only prior assumption is: 0 < A ≤ R ≤ 1. Finally, some comparisons are made among these models and it is shown that the lower confidence bounds on reliability, using these conservative priors, converge rather rapidly to results obtained using the classical non-parametric model.