Classical Statistical Inference Extended to Truncated Populations for Continuous Process Improvement: Test Statistics, P‐values, and Confidence Intervals

Abstract

Statistical hypothesis testing is useful for controlling and improving processes, products, and services. This most fundamental, yet powerful, continuous improvement tool has a wide range of applications in quality and reliability engineering. Some application areas include statistical process control, process capability analysis, design of experiments, life testing, and reliability analysis. It is well-known that most parametric hypothesis tests on a population mean, such as z-test and t-test, require a random sample from the population under study. However, there are special situations in engineering, where the specification limits, such as the lower and upper specification limits, on the process are implemented externally, and the product is typically reworked or scrapped if the performance of a product does not fall in the range. As such, a random sample needs to be taken from a truncated distribution; however, there has been little work on the theoretical foundation of statistical hypothesis procedures under this special situation. The objective of this paper is twofold. First, we provide the mathematical justifications that the central limit theorem works quite well for a large sample size, given samples taken from a truncated distribution. We also verify this finding using simulation. Second, we then develop the new one-sided and two-sided z-test and t-test procedures, including their test statistics, confidence intervals, and P-values, using appropriate truncated statistics.

Measurement Error Effect on the Power of Control Chart for Doubly Truncated Normal Distribution under Standardization Procedure

“…It has been observed from the table that ARL values increase as there is an increase in the range of truncation. Also ARL values increase as there is an increase in the values of 2 R for fixed  and .…”

A new measure of ecological network structure based on node overlap and segregation

“…However, we propose a test that is able to overcome these difficulties. First, the truncation and non‐normality of the Ɲ ij distribution can be overcome by invoking the central limit theorem (CLT), which has been recently demonstrated to be effective also for truncated distributions (Cha & Cho ). According to the CLT, the distribution of as a random expectation (i.e.…”

An approximation to the inverse of left-sided truncated gaussian cumulative normal density function using Polya's model to generate random variates for simulation applications

“…The simplest method is inverse transform sampling (ITS), a method for pseudo-random number sampling which randomly generates variates using the CDF inverse. In the literature, ITS appears in different names, such as inversion sampling (e.g., [1][2]), inverse probability integral transform (e.g., [3][4]), inverse transformation method (e.g., [5][6]), Smirnov transform (e.g., [7][8]) and golden rule (e.g., [9][10]). ITS method can be performed in two steps: 1.…”