Statistical Quality Control Questions and Answers – Time-Weighted – Cumulative Sum Control Chart – 5

This set of Statistical Quality Control Questions & Answers for Exams focuses on “Time-Weighted – Cumulative Sum Control Chart – 5”.

1. What are the graphical displays of tabular cusum called?
a) Cusum regular charts
b) Cusum regulated display
c) Cusum level display
d) Cusum status charts
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2. Which of these is a correct statement for cusum status charts?
a) A plot between C_i⁺ or C_i^– and the sample number
b) A plot between the C_i⁺ or C_i^– and the sample mean
c) A plot between the C_i⁺ or C_i^– and the sample variance
d) A plot between the C_i⁺ or C_i^– and the sample standard deviation
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3. Each vertical bar in cusum status chart represents __________
a) The value of C_i⁺ and C_i^–
b) The value of C_i^–
c) The value of C_i⁺
d) Neither the value of C_i⁺ nor C_i^–
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4. What is analogous to the control limits as in Shewhart control charts, in the cusum status charts?
a) The reference value
b) The allowance value
c) The value of the decision intervals
d) The value of C_i⁺ and C_i^–
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5. In the Minitab version of the cusum control charts, which of these is used?
a) \(C_i^+=max⁡\left\{0,x_i-μ_0+k+C_{i-1}^-\right\}\)
b) \(C_i^-=min⁡\left\{0,x_i-μ_0+k+C_{i-1}^-\right\}\)
c) \(C_i^-=max⁡\left\{0,x_i-μ_0-k+C_{i-1}^-\right\}\)
d) \(C_i^-=min⁡\left\{0,x_i-μ_0-k-C_{i-1}^-\right\}\)
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6. Which of these is true for the Minitab version of tabular cusum charts?
a) \(C_i^-≥0\)
b) \(C_i^-≥9\)
c) \(C_i^-≤0\)
d) \(C_i^-≤5\)
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7. Which of these steps, is not carried out when the process becomes out-of-control when using the cusum control charts?
a) Search for an assignable cause
b) Taking corrective action
c) Restarting the control chart from zero
d) Continuing the control chart
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8. Which of these control charts may accurately tell when the assignable cause has occurred?
a) Cusum control charts
b) p-charts
c) c-charts
d) x bar and s charts
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9. Which of these can be used to calculate the estimate of mean of the process in the case of the tabular cusums when C_i⁺ > H?
a) \(\hat{μ}=\left\{μ_0-K+\frac{C_i^+}{N^+}\right\}\)
b) \(\hat{μ}=\left\{μ_0+K+\frac{C_i^+}{N^+}\right\}\)
c) \(\hat{μ}=\left\{μ_0+K-\frac{C_i^+}{N^+}\right\}\)
d) \(\hat{μ}=\left\{μ_0+K+\frac{C_i^-}{N^-}\right\}\)
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10. Which of these following expressions can be used to calculate the estimate of mean of the process in the case of the tabular cusums when C_i^– > H?
a) \(\hat{μ}=\left\{μ_0+K+\frac{C_i^-}{N^-}\right\}\)
b) \(\hat{μ}=\left\{μ_0-K-\frac{C_i^-}{N^-}\right\}\)
c) \(\hat{μ}=\left\{μ_0-K+\frac{C_i^-}{N^-}\right\}\)
d) \(\hat{μ}=\left\{μ_0+K-\frac{C_i^-}{N^-}\right\}\)
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11. What of these can be used as the decision interval for the tabular cusum charts?
a) 2σ
b) 1σ
c) 5σ
d) 4σ
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12. What is the expression for the two sided cusum ARL?
a) \(\frac{1}{ARL}=\frac{1}{2ARL^-}+\frac{1}{2ARL^+}\)
b) \(\frac{1}{ARL}=\frac{1}{ARL^-}±\frac{1}{ARL^+}\)
c) \(\frac{1}{ARL}=\frac{1}{2ARL^-}-\frac{1}{2ARL^+}\)
d) \(\frac{1}{ARL}=\frac{1}{ARL^-}+\frac{1}{ARL^+}\)
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13. Which of these is an expression for Siegmund’s approximation?
a) \(ARL=\frac{exp⁡(-2∆b)+2∆b-1}{2∆^2}\)
b) \(ARL=\frac{exp⁡(-2∆b)+2∆b-1}{2∆}\)
c) \(ARL=\frac{exp⁡(-2∆b)-2∆b+1}{2∆^2}\)
d) \(ARL=\frac{exp⁡(-2∆b)-2∆b-1}{2∆^2}\)
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14. The value of K and H should be determined according to the ARL required for the corresponding cusum chart.
a) True
b) False
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15. The desired ARL is obtained by using the Siegmund’s approximation.
a) True
b) False
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