Two economically optimized nonparametric schemes for monitoring process variability

Abstract

Controlling and reducing process variability is an essential aspect for maintaining the product or service quality. Even though most practitioners believe that an increasing process variability is often a more severe concern than a shift in location, barely a few research paid attention to the cost‐efficient monitoring of process variability. Some of the existing studies addressed the dispersion aspect, assuming that the quality characteristic is Gaussian. Non‐normal and complex distributions are not uncommon in modern production processes, time to event processes, or processes involving service quality. Unfortunately, we find no literature on economically designed nonparametric (distribution‐free) schemes for monitoring process variability. This article introduces two Shewhart‐type cost‐optimized nonparametric schemes for monitoring the variability of any unknown but continuous processes to fill the research gap. The proposed monitoring schemes are based on two popular two‐sample rank statistics for differences in scale parameters, known as the Ansari–Bradley statistic and the Mood statistic. We assess their actual performance for a set of process scenarios and illustrate the design along with the implementation steps. We discuss a practical problem related to product quality management. It is expected that the proposed schemes will be beneficial in various industrial operations.

Deciles‐based EWMA‐type sign charts for process dispersion

“…In line with this direction, the works of Villanueva‐Guerra et al 50 . and Li and Mukherjee 51 can be useful. Moreover, the considered nonparametric EWMA‐type charts can be extended to composite charts, by adding a Shewhart limit.…”

Economic Design of EWMA Control Charts with Variable Sampling Intervals for Monitoring the Mean and Standard Deviation under Preventive Maintenance and Taguchi’s Loss Functions

“…Li and Mukherjee [16] presented two distribution-free cost-efficient Shewhart-type schemes for sequentially monitoring process location with restricted false alarm probability, based, respectively, on the Sign and Wilcoxon rank-sum statistics. Li and Mukherjee [17] proposed two economically optimized nonparametric schemes for monitoring process variability based on two popular two-sample rank statistics for differences in scale parameters, known as the Ansari-Bradley statistic and the mood statistic. In addition to the above research, many scholars have carried out the economic design and reliability group of the sampling plan, for example [18][19][20][21][22][23].…”