Most useful statistical techniques in six sigma DMAIC are hypothesis testing and interval estimation. So this paper reviews and derives sample size formula by considering significance level, power of detectability and effect difference. The quality practioners can effectively interpret the practical and statistical significance with the rational sample sizing.

The paper reviews properties of hypothesis decision approaches using rejection region and significance probability. The study also presents the guidelines for quality practioners to implement most useful hypothesis testing techniques such as RR(Rejection Region) approach and P-Value approach.

This paper aims to develop a new chain metrics for obtaining lean Overall Equipment Effectiveness(OEE) and present implementation strategy which considers the properties for Total Productive Maintenance(TPM) to reduce machine losses, Performance Analysis and Control(PAC) to reduce labor losses, Lean Production System(LPS) to reduce floor wastes, and Theory of Constraints(TOC) to minimize the problem of Capacity Constrained Resource(CCR). The study reviews the related literatures and reformulates the structure of machine losses, labor losses and field wastes. The research also develops the integrated productivity metrics according to time, units, reliability and maintainability. It is found that the study develops the actual productivity measure in terms of efficiency, effectiveness and standard productivity. In addition to that, it outlines and develops by using the integrated LPS and TPM, lean OEE measures such as Time Based Productivity(TBP), Unit Based Productivity(UBP), and Reliability & Maintainability Based Availability(RMBA). Implication examples are proposed to make it easier and available for practioners to understand the implementation strategies about TPM OEE, lean OEE and TOC OEE. Futhermore related to other studies, the research contributes to create a new chain productivity measures to clear the interrelationship concepts of productivity, efficiency and effectiveness. Moreover the paper develops the enhanced OEE measures by integration of TPM, PAC, LPS and TOC with the perspective of schedule, throughput, reliability, maintainability and availability.

The Design of Experiment (DOE) is a most practical technique when establishing an optimal condition for production technology in Six Sigma innovation project. This research proposes the assessment of properties of error terms, such as normality, equal variance, unbiasedness and independence. The properties of six nonparametric ranking techniques for checking normality assumption are discussed as well as run test which is used to identify the randomness, and to check unbiased assumption. Furthermore, Durbin-Watson (DW) statistics and ARIMA (p,d,q) process are discussed to identify the serial correlation.

Based on latest research, the parametric quality statistics cannot be used in non-normal process with demand pattern of many-variety and small-volume, since it involves extremely small sample size. The research proposes nonparametric quality statistics according to the number of lot or batch in the non-normal process. Additionally, the nonparametric Process Capability Index (PCI) is used with 14 identified non-normal distributions.

Reliability measures of questionnaire and  contingency tests of categorized responses are most practical tools to analyze the characteristics of subjects of survey study. This research evaluates the Cronbaha’s reliability measures by using Repeated Measure Design (RMD) with illustrated MINITAB examples. In addition,  statistics of each cell of categorized tables can be effectively interpreted with the symmetric plot of correspondence analysis. The practical example is also discussed to provide comprehensive understanding of topic.

The research presents an application of Balanced ANOVA (BANOVA) by utilizing randomized orders for various Split-Plot Designs (SPDs) which include two cell designs, split-plot with one-way HTC (Hard to Control) factor, split-plot with two-way HTC factor, split-split-plot design and nested design. In addition, four MINITAB examples of 2-level split-plot designs based on the number of blocks and the type of whole-plots are presented for practitioners to obtain comprehensive understanding. Furthermore, the geometrical interrelated properties among three typical Designs of Experiments (DOE), such as Factorial Design (FD), Response Surface Design (RSD), and Mixture Design (MD) are discussed in this paper.

The research presents a guideline for quality practitioners to provide a full comprehension of differences in theoretical and practical interpretations of assumed sampling errors of and significance probability of calculated p-value. Besides, the study recommends the use of statistical inferences methods with known parameters to identify the improvement effects. In practice, the quality practitioners obtain the known parameters through systematic quality Database (DB) activities.

The research discusses interrelationship of structural and reliability importance measures which used in the probabilistic safety assessment. The most frequently used component importance measures, such as Birnbaum's Importance (BI), Risk Reduction (RR), Risk Reduction Worth (RRW), RA (Risk Achievement), Risk Achievement Worth (RAW), Fussel Vesely (FV) and Critically Importance (CI) can be derived from two structure importance measures that are developed based on the size and the number of Minimal Path Set (MPS) and Minimal Cut Set (MCS). In order to show an effectiveness of importance measures which is developed in this paper, the three representative functional structures, such as series-parallel, k out of n and bridge are used to compare with Birnbaum's Importance measure. In addition, the study presents the implementation examples of Total Productive Maintenance (TPM) metrics and alternating renewal process models with exponential distribution to calculate the availability and unavailability of component facility for improving system performances. System state structure functions in terms of component states can be converted into the system availability (unavailability) functions by substituting the component reliabilities (unavailabilities) for the component states. The applicable examples are presented in order to help the understanding of practitioners.

The study proposes three types of production lead time according to the production or demand pattern. First of all, it discusses the difference of three lead times. While pitch time and cycle time are used in push system with process stock and mass conveyor production, the tact time is used in pull system like as JIT based lean production system.

This research presents an implementation strategy of Process Capability Index ( PCI) according to the types of process characteristics. The types of process feature are classified as four perspectives of variation range, time period, error position, and process stage. The paper examines short-term or long-term PCI, within or between variation, position of precision or accuracy, and inclusion of measurement or calibration stage. Moreover, the study proposes normality test of unilateral PCI.

The research reviews the logical approach based on the creative thoughts. The two logical approaches, including deductive convergent and inductive divergent are discussed with why-why techniques and how-how techniques. While the deductive thinking is vertical logic for interconnected hierarchical and deep domains, the inducive thinking is horizontal logic for mutually exclusive and collectively exhausted frameworks. The creative thinking comes from the reversing the logic and lessening the premise of convergent and divergent approaches.

The research shows misuse cases of quantitative regression analysis used in QC circle activity and six sigma movement which presents guidelines of correct use for quality practitioners. Additionally, the qualitative regression analysis that responses nonconforming ratio of variable y, is reviewed based on misuse cases for proper use by practitioners in the field. In most cases, there are frequent errors that involve the correlation analysis or ANOVA, regardless of using quantitative regression analysis. In addition, qualitative regression analysis for the nonconforming ratio that has dependent variable of discrete and categorical data, is often applied with quantitative regression and result in ineffective quality improvement.

The papaer reviews four theoretical acceptance sampling plans as OC (Operating Characteristics) curve based inspection, rectifying inspection, switching inspection, and continuous inspection. In addition, the study presents practical limitations of theoretical acceptance sampling by attribute and by variable. Finally, following research also recommends the sampling inspection based on production technology. However, the inspection method requires quality expertise with various experience and implicit knowledge of the field.

The research proposes seven elimination rules of redundant gates and blocks in Fault Tree Analysis (FTA) and Reliability Block Diagram (RBD). The computational complexity of cut sets and path sets is NP-hard. In order to reduce the complexity of Minimal Cut Set (MCS) and Minimal Path Set (MPS), the paper classifies generation algorithms. Moreover, the study develops six implementation steps which reflect structural importance (SI) and reliability importance (RI) from Reliability Centered Maintenance (RCM) that a priority of using the functional logic among components is to reduce (improve) the system unavailability (or availability). The proposed steps include efficient generation of state structure function by Rare Event Enumeration (REA). Effective use of importance measures, such as SI and ill measures, is presented based on the number and the size of MCS and MPS which is generated from the reference[5] of this paper. In addition, numerical examples are presented for practitioners to obtain the comprehensive understanding of six steps that is proposed in this research.

The study focuses on the Repeated Measurements Design (RMD) which observations are periodically made for identical subjects within definite time periods. One of the purposes of this design is to monitor and keep track of replicated records within regular period over years. This paper also presents the classification models of RMD that is developed according to the number of factors in Between-Subject (BS) variates and Within-Subject (WS) variates. The types of models belong to each number of factors: One factor is 0BS 1WS. Two factors are 1BS 1WS and 0BS 2WS. Three factors are 1BS 2WS and 2BS 1WS. Lastly, the four factors include model of 2BS 2WS In addition, the study explains the generation mechanism of models for RMD using Generalizability Design (GD). GD is a useful method for practitioners to identify linear model of experimental design, since it generates a Venn diagram. Lastly, the research develops three types of 1BS 2WS RMDs with crossed factors and nested factors. Those are random models, mixed models and fixed models and they are presented by using Generalizability Design, (S:A×B)×C. Moreover, the example of applications and its implementation steps of models developed in the study are presented for better comprehension.