Improving Shewhart control chart performance for monitoring the Weibull mean

2021

This paper proposes a procedure to improve the performance for the attribute control charts: X𝑡𝑛 and 𝑆 2 𝑡𝑛 . In these control charts, a simple size 𝑛 is collected periodically and each item is allocated into one of the five categories defined by a go-no-go gauge. After that, a random value is generated for each item according to a truncated normal distribution with its upper and lower limits defined by the cut points of the go-no-go gauge. With the 𝑛 generated values, the sample mean X𝑡𝑛 and the sample variance 𝑆 2 𝑡𝑛 are calculated and compared with the their respective control limits. In this paper, a procedure was implemented in order to improve the performance of these control charts, which consists of the sequential switches between two sample sizes 𝑛 𝑎 and 𝑛 𝑏 (with 𝑛 𝑎 > 𝑛 𝑏 ) and checking whether the sample mean (or sample variance depending) exceeds the control limits or not. The proposal is relatively easy for practitioners to implement it. Extensive computational experiments showed that the procedure improved both control charts to detect small shifts in term of 𝐴𝑅𝐿 1 . With this procedure, the "Improved X𝑡𝑛 " (shortly X𝑡𝑛(𝐼) ) control chart performs similarly to X chart for small shifts in the process mean provided that the sample sizes are raised by approximately two additional sample units and the "Improved 𝑆 2 𝑡𝑛 " (shortly 𝑆 2 𝑡𝑛(𝐼) ) control chart also has a similar performance to 𝑆 2 chart with more or less double sample size in the range of small shifts of the variance. Two numerical examples are presented to illustrate the use of the procedure.

Section: 𝒕𝒏mentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improving the performance of the attribute charts: X¯tn$\bar{X}_{tn}$ and Stn2$S^2_{tn}$

Yamauchi

2021

“…The performances were compared in terms of 𝐴𝑅𝐿 in scenarios of shift sizes (𝛿) in the process mean. This same scheme of inspection was previously studied by Ho et al 14 to improve the performance of 𝑋 control chart to monitor a Weibull mean. The design simplifies the decision-making, because it is a predetermined fixed sequence, facilitates its operation, minimizes the need for specialized training, and can reduce the possibility of errors in the elaboration of the control chart and, consequently, the decision-making in the long term.…”

Section: Introductionmentioning

confidence: 89%

The use of npx$np_{x}$‐type attribute charts to monitor the variance

Silva

2021

Self Cite

First, the 𝑛𝑝 𝑥 -type attribute control charts have been proposed to monitor the process mean. The main contribution of this paper is to show the good performances of the "pure 𝑛𝑝 𝑥 " (shortly 𝑛𝑝 𝜎 2 𝑥 ) and "improved 𝑛𝑝 𝑥 " (shortly 𝑛𝑝 𝜎 2 𝑥(𝐼) ) attribute charts to monitor the variance. The results confirmed that they are also good alternatives to 𝑆 2 control chart. To have an equal performance (in terms of speed to detect abnormal cases), the sample size needed for these charts is slightly higher than those practiced for an 𝑆 2 control chart. This is an advantage since an attribute inspection is faster and cheaper as no measurements on the examined units are taken (mainly if we are dealing with destructive experiments). A numerical example illustrates our proposal.

“…Recently, Ho et al 33 . proposed a simplified variable sample size (SVSS) procedure to improve the

\overline{X}_{{\rm std}}

for the Weibull mean.…”

Section: Performance Of the X¯$\overline{x}$ Control Chart With Klein...mentioning

confidence: 99%

Klein's supplementary runs rules on X¯$\overline{X}$ chart to control the mean of a Weibull random variable

Fernandes

et al. 2021

Self Cite

Most of the papers found in the literature concerned monitoring a process mean of a quality characteristic normally distributed. However, in several practical situations (like in reliability studies), the engineering team also desires to monitor a process mean in which the quality characteristic follows other probabilistic distributions, such as the Weibull. In this paper, we monitor a process mean of a random variable following a Weibull distribution using the traditional X¯$\overline{X}$ control chart. To improve the performance, Klein's two of two supplementary run rule is included in the X¯$\overline{X}$ chart. Such adoption promotes better performance, producing faster signals of abnormal situations (in terms of average run length) than the traditional X¯$\overline{X}$ chart in a great variety of shifts. An empirical example illustrates the proposed scheme.