Garcia\'s Garage desires to create some colorful charts and graphs to illustrate

Question

Garcia's Garage desires to create some colorful charts and graphs to illustrate how reliably its mechanics "get under the hood and fix the problem." The historic average for the proportion of customers that return for the same repair within the 30-day warranty period is 0.09. Each month, Garcia tracks 120 customers to see whether they return for warranty repairs. The results are plotted as a proportion to report progress toward the goal. If the control limits are to be set at two standard deviations on either side of the goal, determine the control limits for this chart. In March, 15 of the 120 customers in the sample group returned for warranty repairs. Is the repair process in control? The UCLp equals and the LCLp equals Enter your responses rounded to three decimal places.)

Explanation / Answer

This is a case of p-chart

The given data is

pbar = 0.09

n = 120

Upper Control Limit = UCLp = pbar + 2 * sqrt (pbar*(1-pbar)/n)

So, UCLp = 0.09 + 2 * sqrt (0.09 * (1-0.09)/ 120) = 0.142

Lower Control Limit = LCLp = pbar - 2 * sqrt (pbar*(1-pbar)/n)

So, LCLp = 0.09 - 2 * sqrt (0.09 * (1-0.09)/ 120) = 0.038

So, the answers are

UCLp = 0.142 and LCLp = 0.038

Now, we get 15 customers returned from 120 customers, so p = 15/120 = 0.125

As, p=0.125 is withing UCLp and LCLp, we can say that the repair process is in control

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