Statistical Process Control Activities in Daily Routine

Statistical Process Control

Activities in Daily Routine

Application of Statistical Process Control and Solving the Problem

(a) Statistical Process Control: X-bar Charts

(b) Weekly Morning Time Utilization Chart

Observations from the chart

Effect of Seasonal Factors

Seasonal Factors

Usefulness of Confidence Intervals

This paper is on process control of activities that happen on daily basis. Statistical Process Control (SPC) involves application of statistical methods and procedures (such as control charts) to analyze the inherent variability of a process or its outputs to achieve and maintain a state of statistical control, and to improve the capability, also called statistical quality control . (Business Dictionary, 2010). The total time taken from waking up till reaching the office after going through various chores is 85 minutes. The person wants to cut it down to 60 minutes. He thinks of foregoing his leisurely sipping of coffee and watching news for 20 minutes and substitute it with taking coffee in the car and listening to radio for news. That is a way a common man looks at the problem.

Sipping coffee in the car and listening to radio form for news is not the same as doing the same in comfort at home. So an alternate solution is to be chalked out. This is exactly where the Process Selection Control and design step in. Let us now see how the concept can be applied to the problem.

2. Application of Statistical Process Control and Solving the Problem

Details of total time spent on taking bath, getting ready, taking coffee and watching news and travel to office for six days in a week are given below.

Day

Time Consumed (in min)

Monday

84

Tuesday

85

Wednesday

83

Thursday

87

Friday

86

Saturday

84

Average

84.83

(a) Statistical Process Control: X-bar Charts

Let us start by calculating the average for the data points.

Where

is the individual result and 'n' is the total number of results.

minutes.

Let us now calculate the upper control limit, UCL and lower control limit LCL.

UCL (calculated) =

LCL (calculated) =

Where

in which

is the Standard Deviation and the number of results.

The Standard Deviation

is given by,

minutes

Now,

minutes

We are applying 3-sigma system ("Statistical Process Control: Process and Quality Views," 2008) for the problem.

As such UCL and LCL are now,

UCL =

LCL =

Now let us draw the X-bar chart.

(b) Weekly Morning Time Utilization Chart

Average =84.83 minutes Standard Deviation =1.47 min

LCL=83.03 minutes UCL= 86.63 minutes

3. Observations from the Chart

(a)The daily utilization is mostly within UCL and LCL.

(b)Only one point lies slightly above the UCL.

(c.) The utilizations are equally using above and below average.

4. Conclusion

It is quite obvious from the above chart analysis that it is not possible to reduce the overall time below 83 minutes (LCL) even after cutting off daily deviations.

5. Solution

The only solution seems to be reducing the average utilization to 60 minutes and reduce the individual utilizations proportionately. The suggested utilization after proportionate reduction will be as shown in the table below.

Activity

Earlier Utilization

(in minutes)

Suggested Utilization

(in minutes)

Taking Shower

20

14

Watching news and drinking coffee

20

14

Changing and getting ready

30

21

Driving to Office

15

11

85

60

This way, he need not forego any of his routine activities but still can manage to perform all of them in 60 minutes.

6. Effect of Seasonal Factors

Seasonal factors affect process performance data. Seasonal factors can be referred to as weather changes, body clock changes and seasonal items used like dressing. In the given process design time change would be the seasonal factor that will be affecting the process performance data. The duration of day changes basing on the season each year. Depending upon change of the duration of the day, one may spend less time preparing for work or more time based on clock settings. When the day length reduces one is forced to wake up earlier but might not be able to make the adjustment promptly and needs more time to sleep and adjust over a period of time. When the duration of the day reduces, one might get up earlier depending on the individual.

7. Confidence Intervals

A confidence interval is used to describe the amount of uncertainty associated with a sample estimate of a population parameter. ("Statistical Tutorial: Confidence Intervals," 2010).To express a confidence interval, three pieces of information are needed. (1) Confidence level (2) Statistic (3) Margin of error

The range of the confidence interval is defined by the sample statistic + margin of error. The uncertainty associated with the confidence interval is specified by the confidence level.

Where the margin of error is not given; it must be calculated.

There are four steps to constructing a confidence interval. ("Statistical Tutorial: Confidence Intervals," 2010 ).

(a) Identifying a sample statistic: Choose the statistic (e.g., mean, standard deviation) that is used to estimate a population parameter.

(b) Selecting a confidence level: Often 90%, 95%, or 99% confidence levels are chosen, but any percentage can be used.

(c) Finding the margin of error: If you are working on a homework problem or a test question, the margin of error may be given. Often, however, you will need to compute the margin of error, based on one of the following equations.