Question

The defect rate for data entry of insurance claims at Sadegh Kazemi Insurance Co. has historically been about 1.50%. This exercise contains only parts a,b,c,d, and e. a) If you wish to use a sample size of 100 , the 3 -sigma control limits are: UCLₚ = (enter your response as a number between 0 and 1, rounded to three decimal places).

Answer 1

The 3-sigma control limits for a sample size of 100 at Sadegh Kazemi Insurance Co. are UCLₚ = 0.015.

Step-by-step explanation:

In statistical process control, the control limits help identify whether a process is in control or not. For a defect rate of 1.50%, the standard deviation of a binomial distribution (assuming a large sample size) can be calculated using the formula σ = sqrt[p(1-p)/n], where p is the historical defect rate (1.50%) and n is the sample size (100). Substituting the values:

σ=sqrt[0.015(1−0.015)/100]≈0.0387

The 3-sigma control limits (UCLₚ and LCLₚ) are then calculated as:

`\[UCLₚ = p + 3σ = 0.015 + 3(0.0387) \approx 0.130\]`

`\[LCLₚ = p - 3σ = 0.015 - 3(0.0387) \approx -0.098\]`

However, control limits cannot be negative, so we discard the negative value and consider the lower control limit to be zero. Therefore, the 3-sigma control limits are UCLₚ = 0.130 and LCLₚ = 0.

These control limits help assess whether the current process is within statistical control. If observed values fall within these limits, the process is considered in control; if not, it suggests a special cause variation.

In this context, with a sample size of 100, the upper control limit (UCLₚ) of 0.130 indicates the threshold beyond which the defect rate is likely attributed to a special cause variation.