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Cell Design produces cell phone covers for all makes and models of cell phones. Cell Design sells 1,050,000 units each year at a price of $10 per unit and a contribution margin of 40%.

A survey of Cell Design customers over the past 12 months indicates that customers were very satisfied with the products but a disturbing number of customers were disappointed because the products they purchased did not fit their phones. They then had to hassle with returns and replacements.

Cell Design’s managers want to modify their production processes to develop products that more closely match Cell Design’s specifications because the quality control in place to prevent ill-fitting products from reaching customers is not working very well.

The current costs of quality are as follows:

Prevention costs$210,000Appraisal costs$100,000Internal failure costsRework$420,000Scrap$21,000External failure costsProduct replacements$315,000Lost sales from customer returns$787,500The QC manager and controller have forecast the followingadditional costs to modify the production process.CAD design improvement$150,000Improve machine calibration to specifications$137,500\begin{array}{lr} \text{Prevention costs}& \$210,000\\ \text{Appraisal costs}& \$100,000\\ \text{Internal failure costs}&\\ \quad\text{Rework}& \$420,000\\ \quad\text{Scrap}& \$ 21,000\\ \text{External failure costs}&\\ \quad\text{Product replacements}& \$315,000\\ \quad\text{Lost sales from customer returns}& \$787,500\\ \text{The QC manager and controller have forecast the following}& \\ \quad\text{additional costs to modify the production process.}&\\ \text{CAD design improvement}& \$150,000\\ \text{Improve machine calibration to specifications}& \$137,500\\ \end{array}

  1. Which cost of quality category are managers focusing on? Why?

  2. If the improvements result in a 60% decrease in customer replacement cost and a 70% decrease in customer returns, what is the impact on the overall COQ and the company’s operating income? What should Cell Design do? Explain.

  3. Calculate prevention, appraisal, internal failure, and external failure costs as a percentage of total quality costs and as a percentage of sales before and after the change in the production process. Comment briefly on your results.

Question

A one-sided confidence interval for p can be expressed as p<p^+E or p>p^Ep<\hat{p}+E \text { or } p>\hat{p}-E, where the margin of error E is modified by replacing zα/2z_{\alpha / 2} with zαz_{\alpha}. If Air America wants to report an on-time performance of at least x percent with 95% confidence, construct the appropriate one-sided confidence interval and then find the percent in question. Assume that a simple random sample of 750 flights results in 630 that are on time.

Solution

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The best - point estimate of pp is the number of successes xx divided by the sample size nn:

p^=xn=6307500.84\hat{p}=\dfrac{x}{n}=\dfrac{630}{750}\approx 0.84

Determine zα/2z_{\alpha/2} using table A-2:

zα/2=z0.05=1.645z_{\alpha/2}=z_{0.05}=1.645

The margin of error is then:

E=zα/2p^(1p^)n=1.6450.84(10.84)7500.0220E=z_{\alpha/2}\cdot \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}=1.645\cdot \sqrt{\dfrac{0.84(1-0.84)}{750}}\approx 0.0220

The confidence interval then becomes:

81.80%=0.8180=0.840.0220=p^E<p81.80\%=0.8180=0.84-0.0220=\hat{p}-E<p

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