Study of a Memory Type Shrinkage Estimator of Population Mean in Quality Control Process

Abstract

Controlling and improving quality is a major business strategy for various organizations. A company gains an advantage over its competitors by maintaining a high level of quality for products or services and pleasing its customers or clients. Control charts are a tool used in Statistical Process Control for the purpose of reducing variability in a process as well as estimating certain parameters. In the current manuscript, auxiliary information has been utilized to propose an estimator for process mean using hybrid exponentially moving average statistic. The proposed memory-type estimator utilizes prior information to provide better estimates from data which is time-scale based than conventional estimators which were designed for data collected at a single point of time. The properties of the estimator have been studied under Simple Random Sampling as well as Stratified Sampling structure. Simulation study has been conducted to illustrate its efficiency over contemporary estimators. Application to real data on datasets "Machine", "Automobile" and "Auto MPG" is introduced to illustrate the method.

Mean Estimation for Time-Based Surveys Using Memory-Type Logarithmic Estimators

“…By employing simple random sampling without replacement, 25 samples of size 5 are drawn from the population at regular intervals, and the results are compiled in Table 7. Each sample provides the usual mean estimators as ȳ and x, while the classical ratio estimator r , logarithmic estimator a , memory-type ratio estimator m r , and MTLE m a are computed using (1), ( 7), (12), and (18). Each sample is used to construct the EWMA statistic with η = 0.25.…”

“…The population-mean-based memory-type ratio and product estimators were suggested by [17] in stratified sampling. A memory-based shrinkage estimator of the population mean was presented by [18] for statistical quality control. Memory-type population variance estimators employing the EWMA statistic were proposed by [19] for time-scaled surveys.…”

Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression

“…Building upon this, Aslam et al [25,26] defined similar product and ratio estimators within the context of ranked-based and stratified sampling methods, respectively. Further exploration by Singh et al [27] led to the development of an EWMA-based shrinkage estimator for the population mean in quality control processes. In the realm of time-based surveys, readers interested in this topic can refer to Chhaparwal and Kumar [28] and Qureshi et al [29].…”

Calibrated EWMA estimators for time-scaled surveys with diverse applications

“…Subsequently, Aslam et al [13] , [14] defined same kind of mean estimators under ranked set sampling. Moving on to time-based surveys, interested readers, see [15] , [16] , [17] and [18] . Bhushan et al [19] , [20] emphasize the importance of investigating logarithmic type estimators.…”