Question

1) The defect rate for your product has historically been about 2.00%. For a sample size of 300, the upper and lower 3-sigma control chart limits are:UCL= _______LCL=_________

Answer 1

Answer:

UCL= 0.044

LCL=-0.004

Explanation:

Use following formula to calculate the UCL and LCL

UCL = p + z$\sqrt{\frac{p(1-p)}{n}}$

Where

P = defect rate = 2% = 0.02

z = sigma control chart limit = 3

n = samploe size = 300

PLacing values in the formula

UCL = 0.02+3$\sqrt{\frac{0.02(1-0.02)}{300}}$

UCL = 0.02 + 3 x 0.008082904

UCL = 0.02 + 0.024248711

UCL = 0.044248711

UCL = 0.044

Now calculate LCL using folllowing formula

LCL = p - z$\sqrt{\frac{p(1-p)}{n}}$

Where

P = defect rate = 2% = 0.02

z = sigma control chart limit = 3

n = samploe size = 300

PLacing values in the formula

LCL = 0.02 - 3$\sqrt{\frac{0.02(1-0.02)}{300}}$

LCL = 0.02 - 3 x 0.008082904

LCL = 0.02 - 0.024248711

LCL = -0.004248711

LCL = -0.004