ISS (Statistical Services) Statistics Paper IV: Questions 31 - 33 of 92

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Question 31

Describe in Detail


When should R-Chart be Analyzed? Six samples which contain 20 observations per sample have been collected and the sample means and sample ranges are computed as shown below. Test whether the sample means are within control limits of ?

Test Mean Samples and Check if They Are in Control Limits of R Chart


  • Range chart should be analyzed before the mean chart since variability of the process must be in control before the mean chart can be analyzed.
  • If the R chart indicates that the dispersion of the quality by the process is out of control, generally it is better not to construct chart, until the quality dispersion is brought under control.
  • The sample …

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Question 32


Describe in Detail


a) What is major difference between X bar Chart and R chart?

b) What is OC plot?

c) What is Average outgoing Quality (AOQ) ?

d) What is Average Total Inspection (ATI) ?


a) is used to control the process mean, R chart is used to control process variation. reveals undesirable variations between samples as far as their averages are concerned while the R chart reveals any undesirable variations within samples.

b) Operating Characteristic (O. C.) curve is a graphic representation of the relationship between the probab…

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Question 33

Describe in Detail


a) In welding of seams, defects included pinholes, cracks, cold laps, etc. A record was made of the number of defects found in one seam each hour and given below. Obtain the 3-σ limits for number of defects.

Finding Limits for Number of Defects
1 - 12 - 19838 A. M.212 A. M.6
9 A. M.41 P. M.4
10 A. M.72 P. M.9
11 A. M.33 P. M.9
12 A. M.13 - 12 - 19838 A. M.6
1 P. M.49 A. M.4
2 P. M.810 A. M.3
3 P. M.911 A. M.9
2 - 12 - 19838 A. M.512 A. M.7
9 A. M.31 P. M.4
10 A. M.72 P. M.7
11 A. M.113 P. M.12

b) The number of daily customer complaints are monitored at a telephone exchange. Complaints have been recorded over the past twenty days. Develop three-sigma control limits for the following data.

Finding Control Limits for the Given Data
DaysNo. of complaintsDaysNo. of complaints


a) Average number of defects per sample is

= 6 + = 13.35

= 6-

Since number of defects cannot be negative, can be considered as zero.

b) Average number of defects per sample is

= 2.2 + = 6.65

= 2.2- ⇾ 0

Since number of defects cannot be negative, can be considered as zero. (rounded up to zero)

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