Empirical Comparisons of X‐bar Charts when Control Limits are Estimated

A control chart is a very common tool used to monitor the quality of business processes. An estimator of the process variability is generally considered to obtain the control limits of a chart when parameters of the process are unknown. Assuming Monte Carlo simulations, this paper first compares the efficiency of the various estimators of the process variability. Two empirical measures used to analyze the performance of control charts are defined. Results derived from various empirical studies reveal the existence of a linear relationship between the performance of the various estimators of the process variability and the performance of charts. The various Monte Carlo simulations are conducted under the assumption that the process is in both situations of in‐control and out‐of‐control. Copyright © 2015 John Wiley & Sons, Ltd.     

A Single Sampling Plan Based on Exponentially Weighted Moving Average Model for Linear Profiles

The exponentially weighted moving average (EWMA) model has been successfully used in acceptance sampling plans. The EWMA model provides the quality information of the current lot and the preceding lots. In addition, a multiple dependent state (MDS) sampling plan considers the quality information of the preceding lots. In this study, we present two new sampling plans for linear profiles. One is based on EWMA model with yield index using the single sampling plan, and the other is based on EWMA model with yield index using the MDS sampling plans. The plan parameters are determined by a nonlinear optimization approach. As the smoothing parameter value equals to one, the first proposed plan becomes the traditional single sampling plan. In addition, we compare the proposed plans with the traditional single sampling plan. The results indicate that the MDS sampling plan based on EWMA model with yield index with smaller value of smoothing parameter performs better than the traditional single sampling plan and the single sampling plan based on EWMA model with yield index in terms of the sample size required. One real example is used to illustrate the proposed plan. Copyright © 2015 John Wiley & Sons, Ltd.     

Reference Range Estimation: Accounting for Measurement System Errors

Reference range is a statistic that is used in health related fields to represent the range of the most likely values for a variable of interest. Based on this range, individuals are classified as being healthy or unhealthy. In biostatistics, the reference range is calculated as the (1 ? α)% prediction interval, where this prediction interval is based on the estimated population variance from the data. Such estimation of population variance is not precise, because obtained test results do usually have errors associated with them. These errors are due to the imprecise test procedure or gauge used. In this paper, the total variability in the data is decomposed into two categories. The first is the patient‐to‐patient variability and the other is the variability due to the measurement system used. Estimation of the two kinds is performed through a gauge repeatability and reproducibility study, then the reference range is calculated, taking into account only the patient‐to‐patient variability. The revised reference range procedure is illustrated through a case study of vitamin B12 test results. A closed form formula is given to calculate the probability of a given test result being within the revised reference range. Copyright © 2015 John Wiley & Sons, Ltd.     

Multiple Comparisons with the Best for Process Selection for Linear Profiles with One‐sided Specifications

In this study, we propose the multiple comparisons with the best method based on the yield index to compare the process yields of K (K ≥ 2) suppliers for linear profiles with one‐sided specifications. The performance analysis of the proposed method is conducted. The numbers of profiles required for different power levels are also provided. A simulated data set from a leather dyeing process is presented to illustrate the applicability of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Control Charts with Variable Dimension for Linear Combination of Poisson Variables

This article analyzes the simultaneous control of several correlated Poisson variables by using the Variable Dimension Linear Combination of Poisson Variables (VDLCP) control chart, which is a variable dimension version of the LCP chart. This control chart uses as test statistic, the linear combination of correlated Poisson variables in an adaptive way, i.e. it monitors either p₁ or p variables (p₁ < p) depending on the last statistic value. To analyze the performance of this chart, we have developed software that finds the best parameters, optimizing the out‐of‐control average run length (ARL) for a shift that the practitioner wishes to detect as quickly as possible, restricted to a fixed value for in‐control ARL. Markov chains and genetic algorithms were used in developing this software. The results show performance improvement compared to the LCP chart. Copyright © 2015 John Wiley & Sons, Ltd.     

Reliability Analysis Method on Repairable System with Standby Structure Based on Goal Oriented Methodology

This paper presents a reliability analysis method on repairable system with standby structure based on goal oriented (GO) methodology. Firstly, a new combination of GO operator, which is composed of a new logical GO operator named Type 18A operator and a new auxiliary GO operator named Type 20 operator, is created to represent standby mode. The availability formula of standby equipment with translation exception is deduced based on Markov process theory. Then, the application method of combination of GO operator for standby mode and the analysis process of repairable system with standby structure based on GO method are proposed. Thirdly, this new combination of GO operator is applied in availability analysis of the hydraulic oil supply system of power‐shift steering transmission. Finally, the results obtained by the new GO method are compared with the results of fault tree analysis, Monte Carlo simulation, GO methods using Type 2 operator and Type 18 operator to represent the standby mode, respectively. And the comparison results show that this new GO method is applicable and reasonable for reliability analysis of repairable system with standby structure. All in all, this paper provides guidance for reliability analysis of repairable systems with standby structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Control Charts for the Lognormal Mean

Among a set of tools that form the core of statistical process control, statistical control charts are most commonly used for controlling, monitoring, and improving processes. The conventional control charts are based on the assumption that the distribution of the quality characteristic to be monitored follows the normal distribution. However, in real applications, many process distributions may follow a positively skewed distribution such as the lognormal distribution. In this study, we discuss the construction of several control charts for monitoring the mean of the lognormal distribution. A real example is used to demonstrate how these charts can be applied in practice. Copyright © 2015 John Wiley & Sons, Ltd.     

Modelling and Thermal Analysis of Tray‐layered Fruits inside Ventilated Packages during Forced‐air Precooling

Ventilated packaging is widely used in the forced‐air precooling practice for horticultural produce. Fresh fruits are living organisms which are sensitive to temperature in turn related to airflow and heat transfer inside package. In this study, a transient mathematical model considering heat of respiration and evaporation is developed to predict the thermal response of tray‐layered fruits in ventilated packages during forced‐air precooling. Specifically, the heat source is combined with the energy conservation equation and loaded into numerical solution by User Defined Function (UDF). Temperature profiles of three variously distributed circular and oblong vents in three different patterns (spaced, paralleled and crossed stacking) are simulated, separately. The results show that the heat source affects fruit cooling process, and the layered fruit in paralleled stacking pattern tends to be cooled better than others. Furthermore, the results indicate that vertical oblong vent could improve the longitudinal and lateral airflow, while non‐central vent design could greatly improve the overall cooling performance. Definitely a triangular distribution of three circular vents was superior to laterally distributed centre vents with 66.5% higher uniformity and 2.5°C lower of the highest temperature. Compared with the three identical vertical oblong vent conditions, vent design with one hand hole and two side vertical oblong vents can be cooled more uniformly with an increase of 6.5%. It is revealed that vents with large major‐to‐minor axis ratio could be applied to balance airflow and ease cooling differences for a rapid but uniform cooling. Experimental validations were performed for Sim2, Sim4 and Sim6, Sim8, Sim9, and good agreement was obtained considering the five vent conditions with the error less than 3.5°C but coordinated later (within the limits of the experimental uncertainty).Thus the numerical model can be used to predict and optimize temperature distribution within precooling packages. Copyright © 2016 John Wiley & Sons, Ltd.