Question

Energy Consumption. Exercises 1–5 refer to the amounts of energy consumed in the author’s 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?

Short answer

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

Given information

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.

Construction of run Chart

Follow the given steps to construct the run chart:

• Mark the values 0, 5, ...,50 on the horizontal axis and label the axis as “Observations.”
• Mark the values 0, 1000, 2000, ……,6000 on the vertical axis and label the axis as “Energy (kWh).”
• Plot a horizontal line parallel to the horizontal axis corresponding to the value “3157” on the vertical axis.
• Mark the 48 sample points means on the graph and join the dots using straight lines.

	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

The following run chart is plotted:

Analysis of the run chart

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.