A hypothesis testing procedure for random changepoint mixed models

Most of the existing research in multi-state systems relies on point estimation for modeling and optimization. The assessment of uncertainty during design is essential, yet variability in system performance is commonly ignored. Unfortunately, unlimited testing which could provide these arbitrarily accurate estimates is not economical. This paper describes a statistical inference technique to quantify the uncertainties inherent in limited testing. The methodology enables estimation of joint confidence intervals for both system and component performance distributions and subsequently provides a hypothesis testing procedure to perform objective assessments. This builds on previous research which has only addressed confidence bounds for system reliability. Instead of dichotomizing systems into acceptable and unacceptable classes, our approach can handle the case when a system exhibits three or more distinct performance levels. Thus, the method does not place restrictions on the flexibility of the underlying multi-state system concept. The value of the approach is illustrated using a case study and several experiments. The results indicate that joint confidence intervals produced by this procedure are accurate for a range of common confidence levels and sample sizes. It is also demonstrated how hypothesis testing and uncertainty assessment may be used to objectively measure system readiness.

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An Insight of Linear Regression Analysis

Scientific Research Journal ◽

10.24191/srj.v15i2.9347 ◽

2018 ◽

Vol 15 (2) ◽

pp. 1

Author(s):

Set Foong Ng ◽

Yee Ming Chew ◽

Pei Eng Chng ◽

Kok Shien Ng

Keyword(s):

Regression Analysis ◽

Linear Regression ◽

Regression Model ◽

Hypothesis Testing ◽

Linear Regression Analysis ◽

Testing Procedure ◽

Coefficient Of Determination ◽

P Value ◽

Hypothesis Testing Procedure ◽

Independent Variable

Regression models are developed in various field of applications to help researchers to predict certain variables based on other predictor variables. The dependent variables in the regression model are estimated by a number of independent variables. Model utility test is a hypothesis testing procedure in regression to verify if there is a useful relationship between the dependent variable and the independent variable. The hypothesis testing procedure that involves p-value is commonly used in model utility test. A new technique that involves coefficient of determination R2 in model utility test is developed in this paper. The effectiveness of the model utility test in testing the significance of regression model is evaluated using simple linear regression model with the significance level α = 0.01, 0.025 and 0.05. The study in this paper shows that a regression model that is declared to be a significant model by using model utility test, however it fails to guarantee a strong linear relationship between the independent variable and dependent variable. Based on the evaluation presented in this paper, it is shown that the p-value approach in model utility test is not a good technique in evaluating the significance of a regression model. The results of this study could serve as a reference for other researchers applying regression analysis in their studies.

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An Insight of Linear Regression Analysis

Scientific Research Journal ◽

10.24191/srj.v15i2.5477 ◽

2018 ◽

Vol 15 (2) ◽

pp. 1

Author(s):

Set Foong Ng ◽

Yee Ming Chew ◽

Pei Eng Chng ◽

Kok Shien Ng

Keyword(s):

Regression Analysis ◽

Linear Regression ◽

Regression Model ◽

Hypothesis Testing ◽

Linear Regression Analysis ◽

Testing Procedure ◽

Coefficient Of Determination ◽

P Value ◽

Hypothesis Testing Procedure ◽

Independent Variable

Regression models are developed in various field of applications to help researchers to predict certain variables based on other predictor variables. The dependent variables in the regression model are estimated by a number of independent variables. Model utility test is a hypothesis testing procedure in regression to verify if there is a useful relationship between the dependent variable and the independent variable. The hypothesis testing procedure that involves p-value is commonly used in model utility test. A new technique that involves coefficient of determination R2 in model utility test is developed in this paper. The effectiveness of the model utility test in testing the significance of regression model is evaluated using simple linear regression model with the significance level α = 0.01, 0.025 and 0.05. The study in this paper shows that a regression model that is declared to be a significant model by using model utility test, however it fails to guarantee a strong linear relationship between the independent variable and dependent variable. Based on the evaluation presented in this paper, it is shown that the p-value approach in model utility test is not a good technique in evaluating the significance of a regression model. The results of this study could serve as a reference for other researchers applying regression analysis in their studies.

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The Fallacy of a Pseudo-Replication Hypothesis Testing Procedure

American Educational Research Journal ◽

10.3102/00028312008002379 ◽

1971 ◽

Vol 8 (2) ◽

pp. 379-383

Author(s):

Paul A. Games

Keyword(s):

Hypothesis Testing ◽

Testing Procedure ◽

Hypothesis Testing Procedure

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ILI Performance Verification and Assessment Using Statistical Hypothesis Testing

Volume 2: Integrity Management; Poster Session; Student Paper Competition ◽

10.1115/ipc2006-10325 ◽

2006 ◽

Author(s):

Guy Desjardins ◽

Mike Reed ◽

Randy Nickle

Keyword(s):

Hypothesis Testing ◽

Testing Procedure ◽

Statistical Hypothesis ◽

Statistical Hypothesis Testing ◽

Performance Verification ◽

Certainty Level ◽

Hypothesis Testing Procedure ◽

Degree Of Confidence ◽

High Degree

Following an inspection, API 1163 recommends that operators verify the accuracy of the ILI measurements. This paper examines the performance of an ILI tool from two separate perspectives. The first question is whether the ILI tool’s performance meets expectations and contractual requirements. The second question is to what level of accuracy the ILI tool can be relied upon for making integrity related decisions. This paper develops a method of determining the number of excavations and the number of anomalies to be investigated in the field to verify and assess the accuracy of the ILI reported depths. The verification and assessment of the ILI accuracy are two separate questions, and each is addressed as a hypothesis testing procedure. The first hypothesis states that the tool meets expected and contractual standards. That hypothesis is tested against the excavation data. Its acceptance means that the excavation data is consistent with the expected accuracy of the tool, but it does not specifically verify that accuracy. A second hypothesis states that the tool fails to meet some level accuracy as stated by a tolerance and certainty level. That hypothesis is constructed so that when it is tested against the excavation data it is rejected. Its rejection means that the tool exceeds the stated level of accuracy with a high degree of confidence.

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