This set of Statistical Quality Control Objective Questions & Answers focuses on “Statistical Process Control for Short Production Runs – 6”.
1. Which of the error probability does the acceptance control chart take into account?
a) Type I
b) Type II
c) Neither of the type I not the type II
d) Both, type I and type II
Explanation: The acceptance control charts were first designed by Freund. These charts take both, the probability of type I error and the probability of type II error into account.
2. How many approaches can be used to develop the acceptance control charts?
Explanation: The acceptance control charts can be designed by using two approaches. First uses the specified n, and a process fraction nonconforming γ that we would like to reject with probability 1-β. Another uses the values of n, δ and α.
Explanation: The Upper control limit of the acceptance control chart, when sample size n, and the fraction nonconforming for 1-β probability rejection are specified, is expressed as,
Explanation: The LCL value for the acceptance control chart uses the value of lower specification limit instead of the USL. The LCL value, when n, and γ are specified to reject with 1-β probability are specified, is
5. When n, γ, and β are specified, the values of control limits are between ____
a) μL And μU
b) LSL And μU
c) μL And USL
d) μL And LSL
Explanation: We know that the control limits of an acceptance control chart are,
By the above equations, we get the control limit values between μL and μU.
6. When the values of n, δ, and α, are specified, the LCL of the acceptance control charts, lie in between ____
a) μL And USL
b) μL And LSL
c) USL And μU
d) LSL And μU
Explanation: When the values of n, β, and γ are specified, the control limits for an acceptance control chart lie between μL and μU. But, when the values of n, δ, and α, are specified, the LCL lies in between μL and LSL.
7. When the values of δ and α are specified instead of the β and γ, what is the position of UCL of the acceptance control charts?
a) Between USL and μU
b) Between LSL and μU
c) Between μL and USL
d) Between μL and LSL
Explanation: The value of UCL lies between μL and μU when the sample size n, β and γ are specified, but when the values of δ and α are specified instead of β and γ, the UCL of acceptance control charts lies between the USL and μv.
Explanation: It is possible to choose a sample size for an acceptance control chart so that the specified values of α, β, γ, and δ are obtained. The required sample size will be,
9. if δ= 0.01, α=0.00135, γ=0.05, and β=0.2, what will be the sample size for the desired values of these?
10. Modified control chart design is not based upon____
a) Type I error probability
b) Sample size n
c) Type II error probability
d) Process fraction nonconforming
Explanation: The modified control chart design includes the development of the control limits for it, which includes only the sample size n, the process fraction nonconforming δ, and the type I error probability.
11. 2-sigma limits are recommended for the modified control charts. Which of these is not one of the reasons for this?
a) The spread must be low
b) The limits must be greater than the spread
c) Gives smaller β-risk
d) Gives higher β-risk
Explanation: The 2-sigma limits are recommended for the modified control charts, because the spread of the process is quite low than the limits, plus it also gives smaller β-risk.
12. Low type I error probability is obtained when 2-sigma limits are used for modified control chart.
Explanation: The use of 2-sigma limits gives the smaller β-risk, which is an indicator of low type II error probability. Thus the α-risk or the type I error probability is increased.
13. It is impossible to get desired values of α, β, γ, and δ in the acceptance control charts.
Explanation: It is possible to choose such a value for the sample size n for getting desired values of α, β, γ, and δ in the acceptance control charts. This may be done by using the following expression,
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