Chapter 14: Q4RE (page 654)

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?

Expert verified

The following chart is the run chart constructed for the given values:

The values appear to be steadily increasing. As a result, it looks that there is a slight upward trend.

One point lies far too low and can largely affect the process.

As a result, the process does not appear to be statistically controlled.

Step by step solution

Data values are given for eightyears on the energy consumed (in kWh) in a two-month period.

The sample size for each of the eightyears is equal to 6.

Follow the given steps to construct the run chart:

Mark the values 0, 5, ...,50 on the horizontal axis and label the axis as 鈥淥bservations.鈥�
Mark the values 0, 1000, 2000, 鈥︹€�,6000 on the vertical axis and label the axis as 鈥淓nergy (kWh).鈥�
Plot a horizontal line parallel to the horizontal axis corresponding to the value 鈥�3157鈥� on the vertical axis.
Mark the 48 sample points means on the graph and join the dots using straight lines.

The following run chart is plotted:

The points seem to be gradually increasing. Thus, there appears to be aslight upward trend.

One point corresponding to one value of the energy consumption is too low and can be considered an exceptional value.

Thus, it can be said that the process does not appear to be within statistical control.

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