CQT - 2. Statistical Techniques

Free sample questions

3 questions from this set, shown in full with the correct answer and the reasoning behind it. Read them as a study resource.

1. Q1.The individuals chart below tracks the melt temperature on an extrusion line. No point falls outside the control limits, yet the technician stops the run and starts an investigation.

   

   • A.Nine points in a row on one side of the centre line✓ Correct answer
   • B.One point beyond three standard deviations above or below the centre line
   • C.Six points in a row steadily rising or steadily falling
   • D.Two out of three points in a row beyond two standard deviations

   Explanation

   Samples $4$ to $12$ are nine points in a row below the centre line, which is a run. A run says the process has settled at a new level, even though no point has crossed a limit. Looking only for a point outside the limits is the nearest wrong answer, and it is the habit this item is meant to break. A trend rule would need the points to climb or fall steadily, and these points scatter at a lower level instead.

   Reference: CQT BoK II

2. Q2.A cable assembly plant inspects exactly $100$ harnesses every hour. Until now the team recorded only how many harnesses were rejected. They now want the chart to show the total number of faults found each hour, because one harness can carry three or four separate faults.
   
   Which control chart suits the new count?

   • A.p chart
   • B.c chart✓ Correct answer
   • C.np chart
   • D.u chart

   Explanation

   The team is now counting faults, not faulty harnesses, and the amount inspected each hour is fixed at $100$ harnesses. A c chart plots the count of defects for a constant area of opportunity, so it fits. The u chart is the nearest rival: it plots defects per unit and is needed when the amount inspected changes from sample to sample, which is not the case here. The p and np charts both count defective units, which is what the team has decided to stop doing.

   Reference: CQT BoK II

3. Q3.A moulding process has been stable for a month. Its capability study gives $C_p = 1.50$ and $C_{pk} = 0.80$.
   
   What does this pair of values show?

   • A.The process spread is too wide for the tolerance
   • B.The process is not stable enough for capability to be judged
   • C.The spread fits the tolerance, but the average sits off centre✓ Correct answer
   • D.The measurement system is adding error to the readings

   Explanation

   $C_p$ of $1.50$ says the tolerance is comfortably wider than the natural spread of the process, so variation is not the problem. $C_{pk}$ of $0.80$ is much lower, and the two indices separate only when the average drifts away from the middle of the tolerance. Blaming the spread is the nearest wrong answer, but a wide spread would have pulled $C_p$ down as well. Moving the process back to the centre would raise $C_{pk}$ toward $C_p$ without any change to the equipment.

   Reference: CQT BoK II

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