SETTING CONTROL LIMITS FOR NUMBER OF DEFECTS. Red Top Cab Company receives several complaints per day about the behavior of its drivers. Over a 9-day period (where days are the units of measure), the owner, Gordon Hoft, received the following numbers of calls from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8, for a total of 54 complaints. Hoft wants to compute 99.73% control limits.
APPROACH $\blacktriangleright$ He applies Equation (S6–12).

Question

SETTING CONTROL LIMITS FOR NUMBER OF DEFECTS. Red Top Cab Company receives several complaints per day about the behavior of its drivers. Over a 9-day period (where days are the units of measure), the owner, Gordon Hoft, received the following numbers of calls from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8, for a total of 54 complaints. Hoft wants to compute 99.73% control limits.
APPROACH [latex]\blacktriangleright[/latex] He applies Equation (S6–12).

Control limits = [latex]\bar{c} \pm 3\sqrt{\bar{c}}[/latex] (S6-12)

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] [latex]\bar{c} = \frac{54}{9} = 6[/latex] complaints per day
Thus:

[latex]UCL_c = \bar{c} + 3\sqrt{\bar{c}} = 6 + 3\sqrt{6}[/latex] = 6 + 3(2.45) = 13.35, or 13

[latex]LCL_c = \bar{c} - 3\sqrt{\bar{c}} = 6 - 3\sqrt{6}[/latex] = 6 - 3(2.45) = 0 ← (since it cannot be negative)

INSIGHT [latex]\blacktriangleright[/latex] After Hoft plotted a control chart summarizing these data and posted it prominently in the drivers’ locker room, the number of calls received dropped to an average of three per day. Can you explain why this occurred?

LEARNING EXERCISE [latex]\blacktriangleright[/latex] Hoft collects 3 more days’ worth of complaints (10, 12, and 8 complaints) and wants to combine them with the original 9 days to compute updated control limits. What are the revised [latex]UCL_c and LCL_c[/latex]? [Answer: 14.94, 0.]

RELATED PROBLEMS [latex]\blacktriangleright[/latex] S6.21, S6.22, S6.23, S6.24
EXCEL OM Data File Ch06SExS5.xls can be found in MyOMLab.

Question 6.S5: SETTING CONTROL LIMITS FOR NUMBER OF DEFECTS. Red Top Cab Co...

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