Question 1

What is a Shewhart control chart?

Accepted Answer

A Shewhart control chart plots individual measurements against a centre line (the process mean) and upper/lower control limits, usually set at plus or minus three standard deviations. A point that falls outside those limits is flagged as a statistically significant departure from normal process behaviour. Shewhart charts are excellent at catching large, sudden shifts but are comparatively slow to react to small, sustained drifts because a small shift rarely pushes any single point past a wide three-sigma limit.

Question 2

What is a CUSUM chart and how does it differ from Shewhart limits?

Accepted Answer

A cumulative sum (CUSUM) chart accumulates the signed deviation of each new reading from a target value, resetting to zero whenever the running sum would go negative. Because it remembers a history of small deviations rather than judging each point in isolation, CUSUM is far more sensitive to small, sustained shifts in the mean than a single-point Shewhart limit, at the cost of being slightly slower to react to very large one-off spikes that Shewhart limits catch instantly.

Question 3

What do the CUSUM parameters k and h control?

Accepted Answer

k is the reference or slack value, expressed in standard-deviation units, and is usually set to half the size of the shift you want to detect quickly; it is subtracted from each standardised deviation before accumulating. h is the decision interval: the cumulative sum must exceed h standard deviations before an alarm is raised. Lowering h or k makes the chart more sensitive to small drifts but increases the rate of false alarms during normal operation; raising them makes the chart calmer but slower to detect real faults.

Question 4

Why does this simulation freeze the baseline mean and standard deviation after calibration?

Accepted Answer

Real SPC deployments separate a Phase I calibration period, used only to estimate the in-control process mean and standard deviation, from Phase II monitoring, which compares new data against those frozen values. If the control limits kept re-estimating themselves from every new reading, a slow drift would gradually be absorbed into the 'normal' baseline and would never trigger an alarm — freezing the baseline is what lets both charts actually detect a sustained drift rather than adapting to it.

Question 5

Why can a small sustained drift slip past the Shewhart chart but still get caught by CUSUM?

Accepted Answer

A drift of, say, half a standard deviation per sample rarely pushes any single reading three standard deviations away from the frozen baseline, so the Shewhart chart can stay silent for a long time. CUSUM instead keeps a running total of every small deviation in the same direction; even tiny persistent shifts eventually accumulate past the decision threshold h, which is exactly why CUSUM charts are the standard tool for catching slow degradation that per-point limits miss.