The Conditional Probability Integral Transformation and Applications to Obtain Composite Chi-Square Goodness-of-Fit Tests

O'Reilly, Federico J.; Quesenberry, C. P.

doi:10.1214/aos/1193342383

Cited by 60 publications

(11 citation statements)

References 15 publications

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“…In certain models it is possible to redefine the (Un) slightly so as to be exactly independent U[O, 1] variables under any P(J E r!J . This may be achieved through predictive fiducial pivotals in models with group-structure, or through the conditional probability integral transform (O'Reilly and Quesenberry, 1973) in those with suitable sufficient statistics. Such (Un) should provide more reliable small-sample diagnostics.…”

Section: Recursive Residualsmentioning

confidence: 99%

Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach

Dawid¹

1984

Journal of the Royal Statistical Society. Series A (General)

888

343

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SUMMARY The prequential approach is founded on the premiss that the purpose of statistical inference is to make sequential probability forecasts for future observations, rather than to express information about parameters. Many traditional parametric concepts, such as consistency and efficiency, prove to have natural counterparts in this formulation, which sheds new light on these and suggests fruitful extensions.

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Section: Recursive Residualsmentioning

confidence: 99%

Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach

Dawid¹

1984

Journal of the Royal Statistical Society. Series A (General)

888

343

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“…Zantek et al 89 addressed this problem by using the standardized recursive residuals (SRR)93 calculated from the measurements of different samples. The SRR values independently and identically follow a standard normal distribution94. An ordinary CUSUM chart was constructed to monitor the process stability based on a sequence of SRR calculated at each specific stage k .…”

Section: Spc Methods For Variation Reduction Of Mmpsmentioning

confidence: 99%

Variation reduction for multistage manufacturing processes: a comparison survey of statistical‐process‐control vs stream‐of‐variation methodologies

Liu

2010

Quality & Reliability Eng

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The performance of Multistage Manufacturing Processes (MMPs) can be measured by quality, productivity and cost, which are inversely related to the variation of key product characteristics (KPCs). Therefore, it is crucial to reduce KPCs' variations by not only detecting the changes of process parameters, but also identifying the variation sources and eliminating them with corrective actions. Recent developments in the Stream-of-Variation (SoV) and StatisticalProcess-Control (SPC) methodologies significantly improve the variation reduction for MMPs. This paper provides a review on the reported methodologies by comparing these two categories of methodologies in terms of their variation propagation modeling, process monitoring and diagnostic capability. With an illustrative case study, it is concluded that the recent advancements of SoV and SPC methodologies significantly improve the effectiveness of variation reduction. The discussion on the drawbacks of both methodologies also suggests the future research directions.

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“…, ε ij,n−1 . In the absence of a shift in the mean of ε ij , the distribution of u ij,n in Equation (11) is known to be Student's t with (n − b i − 2) degrees of freedom (see, e.g., O'Reilly and Quesenberry (1973)). Let F c (·) denote the distribution function of a Student-t random variable with c degrees of freedom, and denote the inverse of the standard normal distribution function by −1 (·).…”

Section: Case Ii: Parameters Unknownmentioning

confidence: 99%

“…These authors use theoretical results presented by O'Reilly and Quesenberry (1973) to devise a methodology that transforms recursive residuals to a sequence of independent standard normal variates. Hawkins (1991) and Hawkins and Olwell (1998, pp.…”

Section: Introductionmentioning

confidence: 99%

A self-starting procedure for monitoring process quality in multistage manufacturing systems

Zantek¹,

Wright²,

Plante³

2006

IIE Transactions

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Manufacturing systems typically contain processing and assembly stages whose output quality is significantly affected by the output quality of preceding stages. The deficiencies of using standard statistical process-monitoring procedures in such systems have been highlighted in the literature. This article proposes a procedure to monitor process and product quality in multistage systems. By accounting for the quality of the input to each stage, the procedure not only detects the presence of out-of-control conditions but also helps to identify the stages responsible for such departures. We extend previous research to the common case where the process parameters are unknown. An extensive performance study shows that the procedure is effective in detecting out-of-control conditions and that it convincingly outperforms existing methods. We illustrate the use of the procedure using production line data from a major electronics manufacturer.

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The Conditional Probability Integral Transformation and Applications to Obtain Composite Chi-Square Goodness-of-Fit Tests

Cited by 60 publications

References 15 publications

Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach

Present Position and Potential Developments: Some Personal Views: Statistical Theory: The Prequential Approach

Variation reduction for multistage manufacturing processes: a comparison survey of statistical‐process‐control vs stream‐of‐variation methodologies

A self-starting procedure for monitoring process quality in multistage manufacturing systems

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