Statiscal Process Control

Homework Chap 3 & 13

1. Construct a [pic 1]-chart for this process using [pic 2]limits and describe the variation in the process.

P = total defectives/ total sample observation

= 307/20 (100)

=0.1535

UCL = 0.1535 + 2 [sqrt of (0.1535 (.85)]/100]

=0.22

LCL =  0.1535 – 2 [sqrt of (0.1535 (.85)]/100]

        = 0.081

[pic 3]

This diagram suggests that process is out of control. The proportion of defectives is increasing.  The root cause should be investigated.  

1. Construct a [pic 4]-chart using [pic 5]limits for this process and indicate if the process was out of control at any time.

C = 86/20 = 4.3

UCL= 4.3 +3 (sqrt4.3) = 12.9

LCL = 4.3-3(sqrt4.3) = - 1.92

[pic 6][pic 7][pic 8]

The sample observations are within control limits. It suggests that the quality measures are effective, thus it only needs continuous monitoring to ensure quality standards.

Problem 13-06.

1. Optimal production run quantity (Q)

2 (700)  (6000)

-------------------

9 ( 1 -  19.29/116)

= sqrt [ 42000000 / 7.47 ]

=749

1. Total annual inventory costs

CoD/Q + (Cc*Q)/2

=700 / 749 + (9*749)/2

= 3371

1. Optimal number of production runs per year

= D/Q

= 6000/749

= 8 runs per year

1. Optimal cycle time (time between run starts)

= 311 days / (D/Q)

= 39 days

e. Run length in working days.

= Q/p

= 749/116

= 6 days

Problem 13-20.

Southwood needs 715 containers each year. It costs $1200 to hold a container at its distribution center, and it costs $6000 to receive an order for the containers.

Determine the optimal order size, minimum total annual inventory cost, number of annual orders, and time between orders.

...