Hotelling's T² control charts with fixed and variable sample sizes for monitoring short production runs

Abstract

Short production runs are common in enterprises that require a high degree of flexibility and variety in manufacturing processes. To date, past research on short production runs has little focus on the multivariate control charts. In view of this, fixed sample size (FSS) and variable sample size (VSS) Hotelling's T2 charts are designed to monitor the process mean when the production horizon is finite. Optimal parameters to minimize the out‐of‐control (1) truncated average run length (TARL) and (2) expected TARL (ETARL) are provided such that the in‐control TARL is equal to the number of inspections (say I). The numerical study considers the run length performances of the FSS and VSS T2 short‐run charts for both known and unknown shift sizes. The VSS T2 short‐run chart performs well in swiftly detecting various mean shifts in comparison with the FSS T2 short‐run chart. Additionally, the VSS T2 short‐run chart is superior to the FSS T2 short‐run chart, in terms of the truncated standard deviation of the run length, expected truncated standard deviation of the run length, probability that the chart signals an alarm within the I inspections, ie, P(I) and expected P(I). A case study on the impurity profile of a crystalline drug substance illustrates the implementation of the VSS T2 short‐run chart.

An improved Hotelling's T2 chart for monitoring a finite horizon process based on run rules schemes: A Markov‐chain approach

“…Let { Y 1 , Y 2 , …, Y n ( i ) } be a normally distributed multivariate random variable with sample size n ( i ) from the p ‐variate mean vector, μ 0 and covariance matrix, ∑ 0 . Then, the statistic of Hotelling's T 2 is obtained as 22 …”

“…Celano et al 20 and Khatun et al 21 then developed the joint Shewhart charts and one‐sided Shewhart multivariate coefficient of variation charts in a finite horizon process, respectively. More recently, Chong et al 22 developed the SH and variable sample size (VSS) Hotelling's T 2 charts to monitor the short production runs.…”

Effect of Measurement Errors on the Performance of Coefficient of Variation Chart With Short Production Runs

“…Their results showed that the choice of the monitoring scheme does not heavily depend on the distribution of the quality characteristic. Chong et al [47] proposed the multivariate fixed sample size and VSS Hotelling's T 2 short-run charts to monitor the mean shift in short production runs. Based on the comparison between the control charts, the VSS Hotelling's T 2 short-run chart surpasses its fixed sample size counterpart for most shift sizes.…”

Robust T2 control chart using median‐based estimators

“…19 Shepherd et al 20 proposed a Hotelling T 2 control chart based on shrunken covariance estimator. Many researchers have studied the aspects of Hotelling T 2 control chart including Chew et al, 21 Chong et al, 22 Dargopatil and Ghute, 23 and Sabahno et al 24 These estimators have some weaknesses. One is their high sensitivity to the presence of outliers, which leads to malfunction of the Hotelling T 2 control chart.…”