Sample Flashcards

A quality technician uses a stratified random sampling plan on a production run of 2,400 parts divided equally among 4 shifts. If 60 total samples are required, how many parts should be sampled per shift to maintain proportional representation?

Answer: 15

Stratified random sampling requires proportional allocation across strata (shifts). With 4 equal shifts and 60 total samples, each shift contributes 60 ÷ 4 = 15 samples. This ensures each stratum is represented in proportion to its size in the population.

When using a systematic sampling method on a conveyor line producing 900 units per hour, a technician must collect 30 samples per hour. What is the correct sampling interval, and from which unit should the first sample be randomly selected?

Answer: Every 30th unit; first unit selected randomly between 1 and 30

Systematic sampling interval = population size ÷ sample size = 900 ÷ 30 = 30. The first unit must be chosen randomly within the first interval (1 to 30) to avoid introducing bias; every subsequent unit is selected at the fixed 30-unit interval from there.

A process engineer examines a control chart and notices 7 consecutive sample means falling on the same side of the centerline, even though all points remain within the control limits. What is the MOST appropriate conclusion?

Answer: The pattern indicates a non-random special cause requiring investigation

The 'run rule' states that 7 or more consecutive points on one side of the centerline signal a non-random, special-cause variation — even if all points are within control limits. The probability of this occurring by chance is less than 1%, indicating a systematic shift in the process mean that must be investigated.

A sampling plan specifies an Acceptable Quality Level (AQL) of 1.0% and a Lot Tolerance Percent Defective (LTPD) of 6.0%. If a batch is submitted with a true defect rate of exactly 1.0%, which risk is MOST directly relevant to the producer?

Answer: Producer's risk (Alpha risk) — probability the lot is rejected despite meeting AQL

When the true defect rate equals the AQL, the producer's risk (alpha risk, or Type I error) is the concern — the probability that a good lot will be incorrectly rejected by the sampling plan. Consumer's risk (beta risk) applies when a bad lot is incorrectly accepted, which is relevant at the LTPD level.

A dimensional inspection uses a sample of n = 25 parts and calculates a sample mean of 50.4 mm and a sample standard deviation of 0.8 mm. What is the standard error of the mean for this sample?

Answer: 0.16 mm

Standard error of the mean (SEM) = s ÷ √n = 0.8 ÷ √25 = 0.8 ÷ 5 = 0.16 mm. The SEM measures how much the sample mean is expected to vary from the true population mean — it decreases as sample size increases, which is why larger samples yield more reliable estimates.

During incoming inspection, a technician applies a double-sampling plan. The first sample of 50 units yields 2 defectives. The plan specifies: Accept on 0, Reject on 4, and take a second sample if 1–3 defectives are found. The second sample of 50 units yields 1 additional defective (cumulative: 3). What is the correct disposition of the lot?

Answer: Accept the lot — the combined sample total is below the combined acceptance number

In a double-sampling plan, the final accept/reject decision after the second sample is based on the cumulative defective count across both samples. With a combined sample of 100 and a cumulative total of 3 defectives, acceptance requires that the combined count fall at or below the combined acceptance number — which in standard MIL-STD-1916 / ANSI plans is typically set higher than the first-stage acceptance number. The lot is accepted since 3 cumulative defectives do not reach the combined rejection threshold of 4.