# Statistical Quality Control Questions and Answers – Control Charting Techniques – Statistical Process Control for Short Production Runs – 2

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This set of Statistical Quality Control Multiple Choice Questions & Answers (MCQs) focuses on “Control Charting Techniques – Statistical Process Control for Short Production Runs – 2”.

1. What is the UCL of the standardized R chart for short production runs?
a) D4
b) D5
c) D1
d) D2

Explanation: The standardized R chart is the best way to study the short production run data when the part standard deviations are not same. This chart has UCL value of D4.

2. What is the value of LCL of the standardized R chart for short runs?
a) D4
b) D2
c) D1
d) D3

Explanation: The standardized R chart is used to study the short production runs. The effectiveness of this chart depends on the control limits chosen. It has UCL and LCL of values, D4 and D3 respectively.

3. What is the value of standard variable plotted in the standardized x bar chart for short run production?
a) $$\bar{x}_i^s=\frac{\bar{M}_i-T_j}{2\bar{R}_j}$$
b) $$\bar{x}_i^s=\frac{\bar{M}_i+T_j}{\bar{R}_j}$$
c) $$\bar{x}_i^s=\frac{\bar{M}_i-T_j}{\bar{R}_j}$$
d) $$\bar{x}_i^s=\frac{2\bar{M}_i-T_j}{\bar{R}_j}$$

Explanation: The standardized charts are plotted for both R and x bar. The x bar chart has the value of the standard variable as,
$$\bar{x}_i^s=\frac{\bar{M}_i-T_j}{\bar{R}_j}$$

4. The standardized x bar chart has the value of LCL when used for short production runs is ____________
a) 3
b) –A2
c) 1
d) A2

Explanation: The standardized x bar chart is used to find the process performance of short production runs. This chart has the LCL value equal to –A2.

5. Which of these has the same difference between the LCL and Center line, and the UCL and the center line?
a) Standardized R chart for short production runs
b) Standardized x bar charts for short production runs
c) Both, standardized x bar and R charts for short production runs
d) Neither one of the standardized R chart and standardized x bar charts for short production runs

Explanation: The x bar chart (standardized) for short production runs, has the LCL and UCL values equal to ∓A2respectively. So the difference from the centerline for them is equal.

6. The term Mi, which is used in the expression of the standard variable used in standardized x bar charts for short production runs, is defined as ___________
a) Average of averages of standard deviations
b) Average of original mean measurements
c) Moving average
d) Exponentially weighted moving average

Explanation: The term Mi is the average of original mean measurements. It is used in the expression of the standard variable used in the standardized x bar charts for short production runs.

7. Rj is the ____________
a) Target value for range
b) Target value for ratios
c) Result of jth part
d) Ratio of jth part

Explanation: Rj is used in the expression of the standard value variable in the standardized R chart. It is defined as the target value for range for each part number.

8. Tj stands for __________
a) Target value for relative range
b) Target value for relative mean
c) target value for x bar for each part number
d) Target value for tested value of the variable

Explanation: The term Tj is used in the expression of the standardized x bar variable, which is used in the standardized x bar chart for the short production runs. It is the target value for the x bar for each part number.

9. Which of these is correct?
a) $$\bar{R}_j=\frac{Sd_2}{c_4}$$
b) $$\bar{R}_j=\frac{Sd_2}{c_2}$$
c) $$\bar{R}_j=\frac{Sd_2}{2c_2}$$
d) $$\bar{R}_j=\frac{d_2}{c_4}$$

Explanation: The value of target for the range and the x bar, i.e. Rj and Tj are specified using the specifications for Tj, and using the history for Rj. Here we can say that,
$$\bar{R}_j=\frac{Sd_2}{c_4}$$

10. Standardized control chart approach for short production runs was presented by ____________
a) Rodriguez
b) Roberts
c) Crowder
d) Farnum

Explanation: Farnum (1992) has presented a generalized approach to the DNOM procedure. The standardized control chart approach is a special case of his method.

11. According to Farnum, the coefficient of variation is _____________
a) $$\frac{σ}{μ}$$
b) $$\frac{μ}{σ}$$
c) $$\frac{2σ}{μ}$$
d) $$\frac{2μ}{σ}$$

Explanation: Farnum was the first person to present the generalized approach to the DNOM procedure. He defined the coefficient of variation as σ/μ.

12. Which of these is true according to Farnum?
a) The coefficient of the variation should be randomly varying
b) The coefficient of the variation should be systematically varying
c) The coefficient of the variation should be varying, maybe randomly or systematically
d) The coefficient of the variation must be constant

Explanation: Farnum defined the coefficient of variation as σ/μ, which he used to give his generalized approach to DNOM procedure. According to him, the coefficient of variation should be constant, which probably occurs fairly often in practice.

13. Which of these is correct target value for standardized control chart for fraction nonconforming for shorter production runs?
a) p
b) np
c) c
d) R̅

Explanation: The short production runs concept can also be used for attributes control chart. The standardized p chart for short production runs uses the target value equal to p.

14. The standardized control chart approach for short production runs can only be applied on variable control charts.
a) True
b) False

Explanation: The standardized control chart approach for short production runs is generally applied to the x bar and R charts but, it can also be applied on the attributes charts such as p-chart, c-chart, and np-chart.

15. The DNOM approach does not need the measurements to be taken at all.
a) True
b) False

Explanation: The DNOM is calculated by,
xi=Mi-TA
Where Mi stands for the measurements of the dimension. So to calculate DNOM value we need to have the value of the dimension measured.

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