CQI common mistakes
CQI · Understand the traps and how to avoid them.
Computing the sample standard deviation by dividing the sum of squared deviations by n instead of n−1, and then carrying that value into a process capability or control-chart calculation.
The population formula is the one most people memorise first, and under exam pressure the denominator is the step most likely to be skipped over without checking whether the data set is a sample or a population.
What to do instead
Before computing, ask one question: 'Is this a sample used to estimate a larger population?' If yes, divide by n−1. Write the denominator explicitly on your scratch paper before squaring anything so the choice is made deliberately rather than by habit.
Converting between SI and inch-pound units for area or volume by applying the linear factor once (for example converting in² to cm² by multiplying by 2.54 rather than 6.4516).
The conversion factor is recalled as a length relationship, and the squared or cubed nature of the unit is invisible once the exponent is dropped from the written expression.
What to do instead
Carry units through every step as if they were algebraic quantities and let them cancel: (2.54 cm/in)² emerges automatically. If the units at the end are not the units the question asked for, the factor was wrong.
Applying the permutation formula nPr to a counting problem where selection order does not matter, producing an answer that is a multiple of the correct one.
Both formulas use the same n and r and look nearly identical in memory; the distinguishing phrase ('arrangements', 'order matters') is easy to read past in a word problem.
What to do instead
Before choosing a formula, construct one small trial case by hand with n=3, r=2 and list the outcomes. If the list contains the same pair in two orders, it is a combination. Verifying against a tiny case costs seconds and catches the error every time.
Reading a micrometer or vernier caliper without first checking the zero reading, and reporting the sleeve/thimble or main-scale/vernier combination as the measured value outright.
The instrument is treated as a direct-read display, so the zero-error correction step is never triggered; also, on a micrometer the thimble is the finer scale and candidates sometimes read the barrel graduation as the fractional part.
What to do instead
Adopt a fixed reading sequence that always begins with closing the instrument on its zero reference and recording any offset. Then read main scale first, fine scale second, and add or subtract the stored zero error before writing the answer.
Selecting 'precision' for a scenario that describes closeness to the true or reference value, or selecting 'accuracy' for a scenario describing repeatability of clustered readings.
The two words are used interchangeably in everyday speech, and exam items deliberately describe a tight cluster far from the target or a scattered cluster centred on it, which is the opposite of the naive intuition.
What to do instead
Reduce each scenario to two questions: are the readings close together (precision) and are they centred on the reference value (accuracy)? Answer them independently before looking at the options, then choose the option matching the one the stem actually names.
Treating calibration as an activity that improves or guarantees the accuracy of an instrument, or assuming a calibrated instrument means the product measured with it conforms.
Calibration is conflated with adjustment and with verification of product, because in practice a calibration visit often includes adjustment and the paperwork arrives alongside good parts.
What to do instead
Hold the definition precisely: calibration is a comparison against a traceable standard that establishes the relationship and reports as-found and as-left data; adjustment is a separate, optional action; and conformity of product is a separate decision made against specification limits.
Computing a position or other geometric tolerance at MMC without adding bonus tolerance equal to the amount the actual size has departed from MMC.
The tolerance value inside the feature control frame is read as the complete allowable deviation, and the modifier symbol is treated as decoration rather than as a variable boundary condition.
What to do instead
Whenever the MMC or LMC modifier appears, write three numbers down before calculating: MMC size, actual mating size, and the difference between them. That difference is bonus tolerance and is added to the stated tolerance before comparing to the measured deviation.
Interpreting AQL as the quality level that will always be accepted, or reversing producer's risk and consumer's risk when reading an operating characteristic curve.
The phrase 'acceptable quality level' reads as a guarantee, and the two risk regions sit on opposite sides of the curve so they are easy to swap when the curve is being read quickly from left to right.
What to do instead
Anchor both definitions to the curve: AQL is the quality level corresponding to a specified (high) probability of acceptance, and the risk of rejection there is the producer's risk; LTPD sits on the low-acceptance tail and its risk of acceptance is the consumer's risk. Sketch the curve and label both tails before answering.
Classifying internal failure, external failure, appraisal, and prevention costs by the activity's name rather than by when and on whom the cost lands - for example filing rework as prevention or calibration as prevention.
Activities like training, calibration, and inspection all feel like 'quality work', so they get grouped together instead of being split by the cost-of-quality model's two axes.
What to do instead
Route every item through two gates in order: did a defect already occur (failure) or not (appraisal/prevention)? If failure, was it found before or after delivery? If not failure, does the activity evaluate product (appraisal) or build capability before the fact (prevention)? Calibration evaluates, so it is appraisal.
Describing containment, sorting, or rework of a nonconforming lot as the corrective action, and describing an action on a nonconformity that has already occurred as preventive action.
Both the containment step and the corrective action appear in the same investigation report and both feel like 'fixing', and the corrective/preventive pair sounds like it maps onto before-and-after rather than onto existing-versus-potential.
What to do instead
Label each proposed action on the report with one of three tags: correction (fix the part), corrective action (remove the root cause of this occurrence), preventive action (remove the cause of a potential occurrence elsewhere). Only the action that changes the system so the cause cannot recur earns the corrective-action label.