Asian Journal of Probability and Statistics

Statistical process improvement is frequently inferred from lower defect rates, favourable capability indices, or an absence of control-chart signals, although these indicators address different dimensions of process behaviour and may be affected by sampling variation. This study develops and evaluates a reproducible Monte Carlo framework for examining the operating behaviour of Statistical Process Control (SPC) charts and process capability/performance indices in a simulated sachet-water production system. The simulation followed an Aims–Data-generating mechanism–Estimands–Methods–Performance measures (ADEMP) structure and generated 10,000 independent 60-day production replications. Each replication comprised three shifts per day and 50 sachets per shift (9,000 sachets; 180 rational subgroups). The first 30 days represented a baseline process and the final 30 days an improved process. Fill volume was generated as a continuous quality characteristic, while leakage, printing failure and overall defective status were represented as attribute outcomes. The study evaluated the X-bar and S charts, a p-chart, and the Cp, Cpk, Pp and Ppk indices. Three one-subgroup special causes were also embedded to assess immediate detection: a sealing-temperature drop, a machine-speed surge and a post-improvement fill-volume drift. Under the primary data-generating mechanism, the mean defective-sachet proportion declined from 14.978% to 2.040%, an absolute reduction of 12.938 percentage points and an approximate 86.36% relative reduction. The within-subgroup standard deviation declined from 4.600 to 1.9995 mL, while mean Cpk increased from 0.5435 to 1.6623. All 10,000 replications recovered the expected direction of change for defective proportion, within-subgroup variance and Cpk. Control-chart performance was less uniform: the X-bar chart detected the Day-48 mean shift in 94.60% of replications, whereas the S chart detected the associated dispersion increase in 33.29%; the p-chart detection rate for the Day-12 sealing disturbance was 68.74%. Sensitivity analysis showed that the sustained improvement conclusion remained stable under heavy-tailed errors, autocorrelation, subgroup heterogeneity and attribute overdispersion, but false-alarm and detection characteristics changed materially under dependence and heterogeneity. The findings demonstrate that defect reduction, capability and statistical stability should be interpreted as complementary evidence. The article's primary contribution is methodological: it shows how repeated simulation can distinguish reliable recovery of known process changes from the less certain detection of short-lived disturbances.