Statistical Quality Control Questions and Answers – Variable Charts – Shewhart Control Chart for Individual Measurements

This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Variable Charts – Shewhart Control Chart for Individual Measurements”.

1. The Shewhart control charts for sample size n=1 are called _________
a) Single Sample control charts
b) Stationary control charts
c) Control charts for zero variance
d) Control charts for individual measurements
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2. In the case of automatic manufacturing, the sample size is ___________
a) 1
b) 2
c) 4
d) Greater than 5
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3. In the case of individuals control charts, which of these is used?
a) Relative range
b) Process standard deviation
c) Mean of the highest observations
d) Moving range
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4. MR (Moving Range) is defined as
a) The difference of highest observation and the lowest observation
b) The difference between any two successive observations
c) The difference between the highest observation and mean of observations
d) The difference between the lowest observation and mean of the observations
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5. What is the correct expression for the UCL for an Individuals Control Chart?
a) UCL=\(\bar{x}+\frac{3\overline{MR}}{d_2}\)
b) UCL=\(\bar{x}+\frac{2\overline{MR}}{d_2}\)
c) UCL=\(\bar{x}+\frac{3\overline{MR}}{d_3}\)
d) UCL=\(\bar{x}+\frac{\overline{MR}}{d_2}\)
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6. The center line for any individuals control chart represents the value equal to __________
a) The process mean
b) The moving range
c) The mean of moving ranges
d) The process standard deviation
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7. The value of ARL for any x bar control chart having 3-σ limits is __________
a) 482
b) 310
c) 370
d) 270
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8. The average number of points that must be plotted before an out-of-control point is plotted on an Individuals control chart?
a) ARL
b) ATS
c) MTBF
d) Hazard rate
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9. The ARL for any individuals control chart with the 1 sigma limits, and the β=0.972, is ____
a) 2
b) 6.3
c) 43.96
d) 13
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10. Which of this stands correct for the relation between the ARL for a shewhart control chart and the individual control chart ARL?
a) ARL_{individual control chart}=1/ ARL_{shewhart control chart}
b) ARL_{individual control chart}= ARL_{shewhart control chart}
c) ARL_{individual control chart}≪ARL_{shewhart control chart}
d) ARL_{individual control chart}≫ ARL_{shewhart control chart}
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11. What is the correct expression for average moving range for any individuals control chart?
a) \(\overline{MR} = \sum_{i=2}^m \frac{MR_i}{m-1}\)
b) \(\overline{MR} = \sum_{i=1}^m \frac{MR_i}{m}\)
c) \(\overline{MR} = \sum_{i=2}^{m-1} \frac{MR_i}{m-1}\)
d) \(\overline{MR} = \sum_{i=1}^m \frac{MR_i}{m-1}\)
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12. The estimator of the process standard deviation for any individuals control chart is written as?
a) \(\frac{\overline{MR}}{2}\)
b) \(\overline{MR}/0.8865\)
c) \(\overline{MR}/1.128\)
d) \(1.128\overline{MR}\)
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13. The estimation of the process standard deviation for any individuals control chart is expressed as ____ in the terms of sample standard deviation.
a) \(\widehat{σ_2}=\frac{s}{c_4}\)
b) \(\widehat{σ_2}=\frac{s}{c_1}\)
c) \(\widehat{σ_2}=\frac{s}{c_2}\)
d) \(\widehat{σ_2}=\frac{s}{c_3}\)
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14. Moving range can only be calculated by the two successive observations.
a) True
b) False
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15. “\(\widehat{σ_3} = 1.047\overline{MR}\); where \(\overline{MR}\) is the median of the span-two moving ranges.”
a) True
b) False
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