CQE Full 160 Questions Mock Exam (300 Minutes)

Free sample questions

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

1. Q1.What is the formula for calculating availability?

   • A.$\frac{MTTR}{MTBF + MTTR}$
   • B.$\frac{MTBF - MTTR}{MTBF}$
   • C.$\frac{MTBF}{MTBF + MTTR}$✓ Correct answer
   • D.$\frac{MTBF}{MTBF - MTTR}$

   Explanation

   Availability is the fraction of total time the system is up:
   
   $$A = \frac{MTBF}{MTBF + MTTR}$$
   
   $MTBF$ represents uptime and $MTTR$ represents downtime, so the denominator is total time. $\frac{MTTR}{MTBF + MTTR}$ is the complement, the unavailability.

   Reference: CQE BoK III

2. Q2.What is the probability of a system with an MTBF of 10 hours failing within the first 2 hours of operation?

   • A.0.18✓ Correct answer
   • B.0.63
   • C.0.82
   • D.0.997

   Explanation

   With a constant failure rate, the probability of failing by time $t$ is the cumulative distribution function, which is one minus the reliability:
   
   $$P(\text{failure}) = 1 - e^{-t/MTBF} = 1 - e^{-2/10} = 1 - 0.8187 = 0.1813$$
   
   So the probability is about $0.18$. The value $0.82$ is the complement, $e^{-0.2}$, which is the probability the system survives the first 2 hours. This formula applies only in the constant failure rate region of the bathtub curve.

   Reference: CQE BoK III

3. Q3.In a hospital, $40\%$ of patients have diabetes, $25\%$ have high blood pressure, and $10\%$ have both conditions.
   
   If a patient is chosen at random, what is the probability that the patient has neither of these two conditions?

   • A.$32.50\%$
   • B.$35\%$
   • C.$45\%$✓ Correct answer
   • D.$85\%$

   Explanation

   Let $A$ be the event 'has diabetes' and $B$ be the event 'has high blood pressure', so $P(A) = 0.40$, $P(B) = 0.25$ and $P(A \cap B) = 0.10$. The addition rule gives:
   
   $$P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.40 + 0.25 - 0.10 = 0.55$$
   
   Having neither condition is the complement of the union:
   
   $$P(A' \cap B') = 1 - P(A \cup B) = 1 - 0.55 = 0.45$$
   
   The $35\%$ foil comes from forgetting to add back the $10\%$ overlap.

   Reference: CQE BoK VI

4. Q4.A company wants to determine if there is a significant difference in the average number of defects in products produced on three different machines. They perform an ANOVA and construct the following ANOVA table.
   
   What is the missing value for the Sum of Squares in the ANOVA table?

   

   • A.60✓ Correct answer
   • B.80
   • C.100
   • D.120

   Explanation

   The sums of squares are additive: Total $SS$ = $SS_{Between}$ + $SS_{Within}$. With a total $SS$ of 300 and $SS_{Within}$ of 240:
   
   $$SS_{Between} = 300 - 240 = 60$$

   Reference: CQE BoK VI

5. Q5.Four improvement projects compete for a single funding slot.
   
   $$\begin{array}{l|c|c|c} \hline \textbf{Project} & \textbf{Cost} & \textbf{Annual benefit} & \textbf{Life (yr)} \\ \hline \text{P1} & \$130{,}000 & \$65{,}000 & 3 \\ \text{P2} & \$200{,}000 & \$90{,}000 & 2 \\ \text{P3} & \$40{,}000 & \$25{,}000 & 4 \\ \text{P4} & \$75{,}000 & \$30{,}000 & 5 \\ \hline \end{array}$$
   
   Ranking on benefit-cost ratio over the full project life, which project should be funded first?

   • A.Project P1
   • B.Project P2
   • C.Project P3✓ Correct answer
   • D.Project P4

   Explanation

   Benefit-cost ratio compares lifetime benefit with cost:
   
   $$BCR_{P3}=\frac{25{,}000 \times 4}{40{,}000}=2.50$$
   
   P2 is the primary foil because it has the largest annual benefit, but its ratio is $\frac{90{,}000 \times 2}{200{,}000}=0.90$, below $1.00$, so it destroys value over its short life. P4 has the largest net benefit at $\$75{,}000$ but a ratio of only $2.00$, and P1 has the largest total benefit at $\$195{,}000$ with a ratio of $1.50$; when funding is the constraint, the ratio decides.

   Reference: CQE BoK I

6. Q6.At the end of week 8 a project manager reviews the schedule below, in which the shaded portion of each bar shows the work already completed.
   
   Which task requires corrective action for schedule slippage?

   

   • A.Task B
   • B.Task C✓ Correct answer
   • C.Task D
   • D.Task E

   Explanation

   A task is behind only when its shading stops short of the status line while its bar extends past it; Task C should be complete through week 8 but is shaded only to week 6, a two-week slip. Task D is the primary foil because nothing is shaded at all, but its planned start is week 9, so at the status date it is not yet due to begin.

   Reference: CQE BoK I

Practise CQE the way the exam actually asks it

• 160 exam-style CQE questions randomly drawn from a pool
• Full explanation for every question (on completing the exam)
• Mobile friendly, no install required
• Each time you take this quiz, it draws random questions from the database

Questions about this practice test

Related CQE practice tests

• CQE Free Practice Questions (Review Mode) 30 practice questionsReviewEasyFreeView quiz→
• CQE Free Mock Exam (60 Minutes)20 practice questionsExam · 60 minMediumFreeView quiz→
• CQE Practice Questions (Review Mode) - 2. Quality Tools25 practice questionsReviewMediumView quiz→
• CQE Practice Questions (Review Mode) - 1. Reliability20 practice questionsReviewMediumView quiz→