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**Cycle-Time Analysis**

Variability is often considered to be the enemy of efficient and effective management. One approach to managing cycle times to improve delivery dependability is to map out the associated activities in a value-added process using a process flow diagram. This allows the manager to identify and measure the specific activities so that the management process can be made more effective. The following problem illustrates the use of cycle time analysis.

**Problem**

Company X has recently completed an analysis of its primary value-added process. As part of this analysis, the major flows have been mapped such that the process has been broken down into 10 major activities. To better understand the process, the times to complete each of these activities have been carefully monitored over the past month. The results of this monitoring follow:

| Activity | Mean (hours) | Standard Deviation (hours) |
|----------|--------------|----------------------------|
| 1 | 8 | 2.4 |
| 2 | 15 | 2.1 |
| 3 | 10 | 3.0 |
| 4 | 8 | 3.3 |
| 5 | 15 | 2.8 |
| 6 | 20 | 4.5 |
| 7 | 10 | 6.0 |
| 8 | 5 | 2.8 |
| 9 | 20 | 1.3 |
| 10 | 4 | 0.3 |

**Questions:**

1. What is the average completion time for this value-added process?
2. What is the standard deviation for the entire process?
3. What is the probability that the process will be completed in 75 hours? In 80 hours? In 70 hours?
4. Develop a 95 percent confidence interval for the process.
5. If you aren't confident in your ability to make delivery promises, where should you target your improvement efforts?
6. How would you proceed?

Answer :

Final answer:

The average completion time for the value-added process is 9.9 hours. The standard deviation for the entire process is 9.01 hours. The probability of completing the process in certain timeframes can be calculated using the mean and standard deviation. A 95 percent confidence interval for the process can be developed using the formula.

Explanation:

To calculate the average completion time for the value-added process, we can sum up the times for each activity and divide by the total number of activities. In this case, the sum of the times is 8 + 15 + 10 + 10 + 8 + 15 + 6 + 20 + 3 + 4 = 99 hours. Since there are 10 activities, the average completion time is 99/10 = 9.9 hours.

To calculate the standard deviation for the entire process, we can use the formula for population standard deviation. First, we calculate the squared difference between each activity time and the average completion time: (8-9.9)^2 + (15-9.9)^2 + (10-9.9)^2 + (10-9.9)^2 + (8-9.9)^2 + (15-9.9)^2 + (6-9.9)^2 + (20-9.9)^2 + (3-9.9)^2 + (4-9.9)^2 = 810.74. Then, we divide this value by the total number of activities, which is 10, and take the square root: sqrt(810.74/10) ≈ 9.01 hours.

To calculate the probability that the process will be completed in a certain amount of time, we can assume that the completion times follow a normal distribution. We can then use the mean and standard deviation calculated previously to calculate the z-score for each target time and look up the corresponding probability in the standard normal distribution table. For example, to calculate the probability that the process will be completed in 75 hours, we calculate the z-score using the formula z = (75 - 9.9) / 9.01 ≈ 8.04. Looking up this z-score in the table, we find that the probability is extremely close to 1. Similarly, we can calculate the probabilities for 80 hours and 70 hours.

To develop a 95 percent confidence interval for the process, we can use the formula: CI = mean ± (1.96 * (standard deviation / sqrt(n))), where n is the number of activities. In this case, the mean is 9.9 hours, the standard deviation is 9.01 hours, and n is 10. Plugging in these values, we get: CI = 9.9 ± (1.96 * (9.01 / sqrt(10))). Calculating this, we find that the confidence interval is approximately 5.78 to 14.02 hours.

If you aren't confident in your ability to make delivery promises, it would be best to target your improvement efforts towards reducing the variability in the completion times of each activity. By minimizing the standard deviation, you can increase the predictability and reliability of your delivery estimates.

To proceed, you can analyze the specific activities with higher variability and identify the root causes of the variability. You may consider implementing process improvements, such as standardizing procedures, training employees, or implementing quality control measures, to reduce the variability and improve the overall efficiency of the value-added process.

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