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Chapter 14: Q1BSC (page 654)

Minting Quarters Specifications for a quarter require that it be 8.33% nickel and 91.67% copper; it must weigh 5.670 g and have a diameter of 24.26 mm and a thickness of 1.75 mm; and it must have 119 reeds on the edge. A quarter is considered to be defective if it deviates substantially from those specifications. A production process is monitored, defects are recorded and the accompanying control chart is obtained. Does this process appear to be within statistical control? If not, identify any out-of-control criteria that are satisfied. Is the manufacturing process deteriorating?

Short Answer

Expert verified

No, the process does not appear to be within statistical control.

The following out-of-control criteria are noticeable, which imply that the process is out of control:

  • There is a downward trend.
  • There are at least 8 points above the centerline.

No, the manufacturing process is not deteriorating. Rather, the process appears to be improving as the proportion of defective quarters are declining.

Step by step solution

01

Given information

A p-chart is plotted to examine if the process is under control or not.

Here, the p-chart depicts the proportion of defective quarters manufactured a series of times.

02

Analysis of the p-chart

The p-chart depicts the following two out-of-control criteria:

  • There is a downward trend in the proportion of defective quarters as the points move from the upper left corner to the lower right corner.
  • More than 8 points lieabove the central line.

Since the above two features imply that the process is not stable, it can be said that the process is not under statistical control.

Moreover, the proportion of defective quarters produced have decreased over time.

This indicates that the manufacturing process is bettering and not deteriorating.

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Energy Consumption. Exercises 1鈥�5 refer to the amounts of energy consumed in the author鈥檚 home. (Most of the data are real, but some are fabricated.) Each value represents the energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. Data are available for download at www.TriolaStats.com.


Jan.-Feb.

Mar.-April

May-June

July-Aug.

Sept.-Oct.

Nov.-dec.

Year 1

3637

2888

2359

3704

3432

2446

Year 2

4463

2482

2762

2288

2423

2483

Year 3

3375

2661

2073

2579

2858

2296

Year 4

2812

2433

2266

3128

3286

2749

Year 5

3427

578

3792

3348

2937

2774

Year 6

4016

3458

3395

4249

4003

3118

Year 7

4016

3458

3395

4249

4003

3118

Year 8

4016

3458

3395

4249

4003

3118

Energy Consumption: Run Chart Construct a run chart for the 48 values. Does there appear to be a pattern suggesting that the process is not within statistical control?

\(\bar x\)- Chart Based on Standard Deviations An x chart based on standard deviations (instead of ranges) is constructed by plotting sample means with a centerline at x and control limits at x + A3s and x - A3s, where A3 is found in Table 14-2 on page 660 and s is the mean of the sample standard deviations. Use the data in Table 14-1 on page 655 to construct an xchart based on standard deviations. Compare the result to the x chart based on sample ranges in Example 5 鈥渪 Chart of Altimeter Errors.鈥�

Energy Consumption. Exercises 1鈥�5 refer to the amounts of energy consumed in the author鈥檚 home. (Most of the data are real, but some are fabricated.) Each value represents energy consumed (kWh) in a two-month period. Let each subgroup consist of the six amounts within the same year. Data are available for download at.


Jan.-Feb.

Mar.-April

May-June

July-Aug.

Sept.-Oct.

Nov.-dec.

Year 1

3637

2888

2359

3704

3432

2446

Year 2

4463

2482

2762

2288

2423

2483

Year 3

3375

2661

2073

2579

2858

2296

Year 4

2812

2433

2266

3128

3286

2749

Year 5

3427

578

3792

3348

2937

2774

Year 6

4016

3458

3395

4249

4003

3118

Year 7

4016

3458

3395

4249

4003

3118

Year 8

4016

3458

3395

4249

4003

3118

Energy Consumption: R Chart Let each subgroup consist of the 6 values within a year. Construct an R chart and determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation
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