Conditional demand density

Figure 6.5 below shows the construction of the conditional demand density from the original demand density, assuming that 50 units have already been ordered. 

The conditional service density derived from a continuous demand density is continuous almost everywhere but has one exceptional point which carries a discrete probability mass The probability that the whole inventory s goes to service is the integral of the conditional demand density from s to oo. In other words, the service is s if the demand is s or above. 

The key mathematical tool for the solution is the expected marginal service at a given stock s. If 5r as in Section 6.2.5.1 denotes the conditional demand density and Ar the corresponding conditional service distribution, then the expected marginal service is simply 1 — Ar. Indeed, if the stock s is 0 then 1 — Ar (s) = 1 — Ar (0) = 1 — 0 = 1. In other words, if we add a little bit (mathematically speaking, an infinitesimal small amount) to our stock 0, this little bit is sold... 

The term conditional demand is derived from the concept of conditional density and simply means the following Let a random variable be described by its density. What do we know about the outcome of the random variable, if we know that the outcome will be not less than a certain value The answer is, roughly speaking, that this additional knowledge in typical cases increases the mean value and reduces the standard deviation. This effect can be calculated precisely. 

Assume that 8 is a continuous demand density with corresponding distribution A. Assume further that there are already orders of amount r. Then the resulting conditional density 5r is given by... 

This section relates random services and random shortages to conditional demands as defined in Section 6.2.5. Conditional random service is the crucial quantity that has to be calculated when a safety stock level has to be determined. Conditional random service results from three quantities a demand density 5, an already ordered quantity r and an available inventory s. From these parameters we obtain two new densities, the conditional service density 5+,r,s and the conditional shortage density... 

Assume that S is a continuous demand density, r units are already ordered, and s is the available inventory. Then the corresponding conditional service density 5+,r,s is given by case 1, r > s ... 

The conditional shortage x and the demand x + s have the same density (x > 0). The conditional shortage is zero with the same probability for the conditional demand to be at most s. 

In the equation above,is the mean annual rate of a given peak intensity measure IM (e.g. SJiT), PGA, PGV) exceeding a threshold value z at the site, / )P /ji/(y z) is the conditional probability density function of the considered engineering demand parameter EDP (e.g. peak roof drift, peak inter-story drift) given the groxmd motion intensity,//r )p(x y) is the conditional probability of the considered failure mechanism Fj taking place given the EDP level, (jc y) is... 

Because no current is allowed to pass through the external electric circuit, the charge neutrality condition demands that the current densities i of the different kinds of species n, i.e., all ions, electrons, and holes, are electrically compensated by each other ... 

An important difference between the two countries is in the scale of the local pharmaceutical industry and the range of products the firms have the capability to supply (Chapters 2 and 3). While Tanzania had just five operating firms when the 2013 research was done, Kenya had about 40 producers, including firms capable of supplying parenterals manufactured in sterile conditions. The density in itself meant that Kenyan firms were more able than Tanzanian firms to supply their local market. However, they still currently (2013) supply only around 25% of the domestic demand (Chapter 2). There is clearly room for expansion of local supply in both countries. 

Based on past experience, it has been found that the protection current density for buried storage tanks coated with bitumen is over 100 /xA m. With coatings in very good condition, it can amount to a few tens of jiA but for coatings in a very poor state, it can rise to a level of mA The protection current demand can... 

Conditions during start-up can have a dramatic impact on time required to reach reasonable performance levels and on the ultimate reactor performance. Dilution rate, loading rate as measured by chemical oxygen demand (COD), carrier choice, inoculum amount, inoculum strategy, and inoculum species distribution are critical parameters (Sreekrishnan et al., 1991 Araki and Harada, 1994 Austermann-Haun et al., 1994 Yongming et al., 1993). Pore characteristics have a strong influence on time required for start-up and on the ultimate biomass density in the... 

In 2,6-disubstituted 1,3-diazaazulenes, such as 14a-c (Scheme 5 62BCJ1188), nucleophilic substitution occurs preferentially at C-6, rather than at C-2. Attack at C-2, if possible at all, demands harsher conditions. In 2,8-dichloro-l-azaazulenes only chlorine atoms at position 8 are susceptible to hydrolysis (61YZ1799 62YZ418 77BCJ1184), and in 2-ethoxy-l,3-diazaazulenes 17 and 18 only the substituents at C-6 are attacked (68CPB1308). The reason is that the electron densities at the seven-membered-ring positions 6 and 8 are lower than at C-2. 

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