Question

The following samples have been taken from an on-going process. Use these values to create both an X bar and an R chart, and then answer the questions below. Please show work.

Sample 1: 56 48 53 58 52

Sample 2: 50 59 57 56 54

Sample 3: 61 59 56 55 58

Sample 4: 57 51 49 57 50

Sample 5: 50 49 57 55 56

Sample 6: 56 55 60 58 57

**A)** What is the value of the centerline for an X
bar chart?

**B)** The upper control limit for the X bar chart
is:

**C)** The lower control limit for the X bar chart
is:

**D)** The upper control limit for the R chart
is:

**E) **The lower control limit for the R
chart is:

Answer #1

mean | range | ||||||

sample 1 | 56 | 48 | 53 | 58 | 52 | 53.4 | 10 |

sample 2 | 50 | 59 | 57 | 56 | 54 | 55.2 | 9 |

sample 3 | 61 | 59 | 56 | 55 | 58 | 57.8 | 6 |

sample 4 | 57 | 51 | 49 | 57 | 50 | 52.8 | 8 |

sample 5 | 50 | 49 | 57 | 55 | 56 | 53.4 | 8 |

sample 6 | 56 | 55 | 60 | 58 | 57 | 57.2 | 5 |

total | 329.8 | 46 | |||||

average | 54.967 | 7.667 |

a) value of the centerline for an X bar chart =54.967

b)

for sample size n=5 ; critical value of A2 =0.577

hence upper control limit for the X bar chart is =Xbar+A2*Rbar=54.967+0.577*7.667=59.391

c) lower control limit for the X bar chart ==Xbar-A2*Rbar=54.967-0.577*7.667=50.543

d)

for n=5 ; constant D3=0 and D4 =2.115

upper control limit for the R chart=D4*Rbar=2.115*7.667=16.215

e) lower control limit for the R chart =D3*Rbar=0*7.667=0

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52
59
57
64
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54
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57
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58
52
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62
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50
53
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63
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56
58
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61
62
63
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53
55
57
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61
62
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64
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